## The Power of Special Cause Variation: Learning from Process Changes

Updated: July 28, 2023 by Marilyn Monda

I love to see special cause variation! That’s because I know I’m about to learn something important about my process. A special cause is a signal that the process outcome is changing — and not always for the better.

## Overview: What is special cause variation?

A control chart can show two different types of variation:   common cause variation (random variation from the various process components) and special cause variation.

Special cause variation is present when the control chart of a process measure shows either plotted point(s) outside the control limits or a non-random pattern of variation.

When a control chart shows special cause variation, a process measure is said to be out-of-control or unstable. Common types of special cause variation signals include:

•   A point outside of the upper control limit or lower control limit
•   A trend: 6 or 7 points increasing or decreasing
•   A cycle or repeating pattern
•   A run: 8 or more points on either side of the average

A special cause of variation is assignable to a defect, fault, mistake, delay, breakdown, accident, and/or shortage in the process. When special causes are present, process quality is unpredictable.

Special causes are a signal for you to act to make the process improvements necessary to bring the process measure back into control.

## RELATED: COMMON CAUSE VARIATION VS. SPECIAL CAUSE VARIATION

Drawbacks of special cause variation .

The source of a special cause can be difficult to find if you are not plotting the control chart in real time.  Unless you have annotated data or a good memory, control charts made from historical data won’t aid your investigation into the source of the special cause.

If a process measure has never been charted, it is almost certain that it will be out of control.  When you first start studying a process with a control chart, you will usually see a variety of special causes. To find the sources, begin a study of the status of critical process components.

When a special cause source cannot be found, it will become common to the process.  As time goes on, the special causes repeat and cease being special. They then increase the natural or common cause variation in the process.

## Why is special cause variation important to understand?

Let’s define quality as minimum variation around an appropriate target. The study of variation using a control chart is one way to tell if the process variation is increasing or if the center is moving away from the desired target over time.

A special cause is assignable to a process component that has changed or is changing. Investigation into the source of a special cause will:

• Let you know when to act to adjust or improve the process.
• Keep you from making the mistake of missing an opportunity to improve a process. If the ignored special cause repeats, you still don’t know how to fix it.
• Provide data to suggest or evaluate a process improvement.

If no special cause variation exists, that is, the process is in control, you should leave the process alone! Making process changes when there is no special cause present is called Tampering and can increase the variation of the process, lowering its quality.

## An industry example of special cause variation

In this example, a control chart was used to monitor the number of data entry errors on job applications. Each day a sample of applications was reviewed. The number of errors found were plotted on a control chart.

One day, a point was plotted outside the control limit. Upon investigation, the manager noticed it occurred when a new worker started. It was found the worker wasn’t trained.

The newly trained worker continued data entry. A downward trend of errors followed, indicating the training was a source for the special cause!

The manager issued guidelines for new worker training. Since then, there have been three new workers without the error count spiking.

## 3 best practices when thinking about special cause variation

Special causes are signals that you need to act to move your process measure back into control.

## Identify the source

When a special cause of variation exists, make a timely effort to identify its source.  A good starting point is to check if any process component changed near to the time the special cause was seen. Also, you could ask process experts to brainstorm why the special cause samples were out of control.

For example, a trend up in screw thickness could be caused by a gage going out of calibration.

## Make improvements at the source

Implement improvements to the source of special cause variation.  Once you make improvements to the source of the special cause (like re-calibrating that gage), watch what happens as the next thickness samples are plotted.  If the plot moves back toward stability, you know you found the issue!

## Document everything

As you identify recurring special causes and their sources, document them on a control plan so process operators know what to do if they see the special cause again.

For our gage, the control plan could direct a worker to recalibrate the next time the screw thickness trends up, sending the process back to stability.

• Are special causes always bad news?

No. A special cause can indicate either an increase or decrease in the quality of the process measure.

If the special cause shows increased process quality (for example, a decrease in cycle time), then you should make its source common to the process.

• If a process is in control (no special causes) is it also capable?

Not always. Control and capability are two different assessments.  Your process measure can be stable (in control) and still not meet the customer specification (capable).

Once a process measure is in control, you can then assess its capability against the customer target and specification limits. If the data is within customer limits and on target, the process is considered both in control and capable.

## Final thoughts on special causes

Every process measure will show variation, you will never attain zero variability. Still, it is important to understand the nature of variability so that you can use it to better improve and control your process outcomes.

The special cause variation signal is the key to finding those critical process components that are the sources of variation needing improvement. Use special cause variation to unlock the path to process control.

## Common Cause & Special Cause Variation Explained with Examples

Editorial Team

In any business operation, it is important to ensure consistency in products as well as repeatable results. Managers and workers alike have to be aware of the processes and methods on how to produce consistent outcomes at all costs. However, we cannot deny that producing exactly identical products or results is almost impossible as variance tends to exist. Variation is not necessarily a bad thing as long as it is within the standard of the critical to qualities (CTQs) specification limits.

Process variation is the occurrence when a system deviates from its fixed pattern and produces a result which differs from the usual ones. This is a major key as it concerns the consistencies of the transactional as well as the manufacturing of the business systems. Variation should be evaluated as it portrays the reliability of the business for the customers and stakeholders. Variation may also cost money hence it is crucial to keep variation at bay to prevent too much cost spent on variation. It is crucial to be able to distinguish the types of variance that occur in your business process since it will give the lead on what course of action to take. Mistakes in coming up with an effective reaction plan towards the variance may worsen the processes of the business.

There are two types of process variation which will be further elaborated in this article. The variations are known as common cause variation and special cause variation.

## Common Cause Variation Definition

Common cause variation refers to the natural and measurable anomalies that occur in the system or business processes. It naturally exists within the system. While it is true that variance may bring a negative impact to business operations, we cannot escape from this aspect. It is inherent and will always be. In most cases, the common cause variant is constant, regular, and could be predicted within the business operations. The other term used to describe this variation is Natural Problems, Noise, or Random Cause. Common cause variance could be presented and analysed using histogram.

## What is Common Cause Variation

There are several distinguishable characteristics of common cause variation. Firstly, the variation pattern is predictable. Common cause variation occurring is also an active event in the operations. it is controlled and is not significantly different from the usual phenomenon.

There are many factors and reasons for common cause variation and it is quite difficult to pinpoint and eliminate them. Some common cause variations are accepted within the business process and operations as long as they are within a tolerable level. Eradicating them is an arduous effort unless a drastic measure is implemented towards the operation.

## Common Cause Variation Examples

There is a wide range of examples for common cause variation. Let’s take driving as an example. Usually, a driver is well aware of their destinations and the conditions of the path to reach the destination. Since they have been regularly using the same road, any defects or problems such as bumps, conditions of the road, and usual traffic are normal. They may not be able to precisely arrive at the destination at the same duration every time due to these common causes. However, the duration to arrive at the destination may not be largely differing day to day.

In terms of project-related variations, some of the examples include technical issues, human errors, downtime, high trafficking, poor computer response times, mistakes in standard procedures, and many more. Some other examples of common causes include poor design of products, outdated systems, and poor maintenance. Inconducive working conditions may also result in to common cause variants which could comprise of ventilation, temperature, humidity, noise, lighting, dirt, and so forth. Errors such as quality control and measurement could also be counted as common cause variation.

## Special Cause Variation Definition

On the other hand, special cause variation refers to the unforeseen anomalies or variance that occurs within business operations. This variation, as the name suggests, is special in terms of being rare, having non-quantifiable patterns, and may not have been observed before. It is also known as Assignable Cause. Other opinions also mentioned that special cause variation is not only variance that happens for the first time, a previously overlooked or ignored problem could also be considered a special cause variation.

## What is Special Cause Variation

Special cause variation is irregular occurrences and usually happens due to changes that were brought about in the business operations. It is not your mundane defects and may be very unpredictable. Most of the time, special cause variation happens following the flaws within the business processes or mechanism. While it may sound serious and taxing, there are ways to fix this which is by modifying the affected procedures or materials.

One of the characteristics of special cause variation is that it is uncontrolled and hardly predictable. The outcome of special causes variation is significantly different from the usual phenomenon. Since the issues are not predictable, it is usually problematic and may not even be recorded in the historical experience base.

## Special Cause Variation Examples

As mentioned earlier, special cause variations are unexpected variants that occur due to factors that may affect the business system or operations. Let’s have an example of a special cause using the same scenario as previously elaborated for common cause variation example. The mentioned defects were common. Now, imagine if there is an unexpected accident that happens on the same road you usually take. Due to this accident, the time for the driver to arrive at the same destination may take longer than normal. Hence this accident is considered as a special cause variation. It is unexpected and results in a significantly different outcome, in this case, a longer time to arrive at the destination.

The example of special cause variation in the manufacturing sector includes environment, materials, manpower, technology, equipment, and many more. In terms of manpower, imagine a new employee is recruited into the team and still lacking in experience. The coaching and instructions should be adapted to consider that the person needs more training to be able to perform their tasks efficiently. Cases where a new supplier is needed in a short amount of time due to issues faced by the existing supplier are also unforeseen hence considered a special cause variation. Natural hazards that are beyond predictions may also be categorized into special cause variation. Some other examples include irregular traffic or fraud attack. An unexpected computer crash or malfunction in some of the components may also be considered as a special cause variation.

## Common Cause and Special Cause Variation Detection

Control chart

One of the ways to keep track of common cause and special cause variation is by implementing control charts. When using control charts, the important aspect to be considered is firstly, establishing the average point of measurement. Next, establish the control limits. Usually, there are three standard deviations which are marked above and below the average point earlier. The last step is by determining which points exceed the upper and lower control limits established earlier. The points beyond the limits are special cause variation.

Before we get into the control chart of common cause and special cause variation, let’s have a look at the eight control chart rules first. If a process is stable, the points displayed in the chart will be near the average point and will not exceed the control limits.

However, it should be noted that not all rules are applicable to all types of control charts. That aside, it is quite tough to identify the causes of the patterns since special cause variation may be related to the specific type of processes. The table presented is the general rule that could be applied in most cases but is also subject to changes or differences. Studying the chart should be accompanied by knowledge and experiences in order to pinpoint the reasons for the patterns or variations.

A process is considered stable if special cause variation is not present, even if a common cause exists. A stable operation is important before it could be assessed or being improved. We could look at the stability or instability of the processes as displayed in control charts or run charts .

The points displayed in the chart above are randomly distributed and do not defy any of the eight rules listed earlier. This indicates that the process is stable.

The chart presented above is an example of an unstable process. This is because some of the rules for control chart tests mentioned earlier are violated.

Simply, if the points are randomly distributed and are within the limit, they may be considered as the common cause variation. However, if there is a drastic irregularity or points exceeding the limit, you may want to analyse more into it to determine if it is a special cause variation.

Histogram is a type of bar graph that could be used to present the distribution of occurrences of data. It is easily understandable and analysed. A histogram provides information on the history of the processes done as well as forecasting the future performance of the operations. To ensure the reliability of the data presented in the histogram, it is essential for the process to be stable. As mentioned earlier, although affected by common cause variation, the processes are still considered stable, hence histogram may be used on this occasion, especially if the processes undergo regular measurement and assessment.

The data is considered to be normally distributed if it portrays a “bell” shape in the histogram. The data are grouped around the central value and this cluster is known as variation. There are several other examples of more complicated patterns, such as having several peaks in the histogram or a shortened histogram. Whenever these examples of complex structures appear in the histogram, it is fundamental to look into the data and operations more deeply.

The above bar graph is an example of the histogram with a “bell” shape.

However, it should be noted that just because the histogram displays a “bell” shaped distribution, that does not mean the process is only experiencing common cause variation. A deeper analysis should be done to investigate if there were other underlying factors or causes that lead towards the pattern of the distribution displayed in the histogram.

## Countering common cause and special cause variation

Once the causes of the variation have been pinpointed, here comes the attempt to combat and resolve it. Different measures are implemented to counter different types of variation, i.e. common cause variation and special cause variation. Common cause variation is quite tough to be completely eliminated. Drastic or long-term process modification could be used to counter common cause variation. A new method should be introduced and constantly conducted to achieve the long-term goal of eliminating the common cause variation. Some other effects may happen to the operations but as time passes, the cause may be gradually solved. As for special cause variation, it could be countered using contingency plans. Usually, additional processes are implemented into the usual operation in order to counter the special cause variation.

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## What is Special Cause Variation? How to Identify It?

March 8th, 2024

Variations are inherent in any process and the sources of these variations play a crucial role in determining process performance and stability. While common cause variations are predictable and result from the process design itself, special cause variation arise due to unexpected factors and lead to process instability.

Managing these special cause variations by identifying and eliminating their root causes is an integral part of quality management frameworks like Six Sigma and Lean. By doing so, processes can achieve stability and enhanced capability.

This enables improved competitiveness through cost reduction, lead time reduction, improved quality, and higher customer satisfaction.

Thus, organizations invest significant efforts in detecting and managing special causes of variation in their business processes.

## Understanding Special Cause Variation

Special cause variation refers to fluctuations in a process that happen because of unique or unusual factors that are not normally present.

These unnatural variations are unpredictable and assignable to a specific cause. They indicate that the process has become unstable and is producing defects or undesirable outcomes.

## Difference from Common Cause Variation

Common cause variation refers to natural or expected variability that exists in any process. This type of variation happens due to minor, ubiquitous causes that are inherent in the process design.

Common causes lead to random scattering of data points around the mean. On the other hand, special causes produce data points that stand out from the normal pattern of variation and signal that the process is out of control.

While common cause variation indicates a stable process, special cause variation implies instability requiring investigation and corrective action.

## Importance in Quality Management

Effective management of special cause variation is crucial for organizations looking to enhance their quality management programs.

By properly identifying and addressing special causes, companies can boost competitiveness, better meet customer expectations, and positively impact financials.

## Enhancing Competitiveness with Special Cause Variation

In today’s business landscape, quality has become a key competitive differentiator across industries. Companies that demonstrate consistent product/service quality and continuous improvement initiatives can gain an edge.

The ability to rapidly detect and mitigate special causes of variation enables organizations to enhance process stability .

This prevents the occurrence of unexpected defects and non-conformances which can erode quality perception. Maintaining robust quality standards is essential to stay ahead.

## Connecting with Quality-Focused Customers

Customers are increasingly assessing providers based on their quality management record and commitment to zero defects.

By tackling special cause variations through root cause analysis , corrective actions, and control mechanisms. etc. companies can limit unexpected issues that lead to customer dissatisfaction.

This accountability and proactive quality management culture aligns with customer requirements and values.

Communicating such initiatives and results also reassures customers regarding consistency. This helps strengthen loyalty and presents partnership opportunities with quality-focused customers.

## Identifying Special Cause Variation

Special cause variation is often difficult to detect without the right analysis tools. Identifying special causes requires going beyond typical process monitoring to specialized statistical techniques.

There are three main methods for recognizing when variation is due to special causes:

## Control Charts

Control charts are the most common way to identify special cause variation. Control charts plot data over time with statistically derived upper and lower control limits.

When data points fall outside these control limits , it indicates something unexpected has happened to the process.

This unexpected variance points to special causes rather than expected normal variation.

Common control charts used to monitor special causes include Xbar-R charts , Xbar-S charts , Individual charts, moving range charts, and P charts.

Statistical process control software makes it easy to generate control charts and receive alerts when special causes occur.

## Statistical Process Control

Statistical process control (SPC) is an analytical methodology that makes extensive use of control charts.

SPC carefully monitors processes to distinguish between expected and unexpected variations using statistical methods.

By visually separating normal and special cause variations on control charts, SPC provides objective evidence that can pinpoint the timing and magnitude of special causes.

SPC also calculates metrics like Cp and Cpk that quantify overall process variation and process capability.

Tracking these metrics provides further insight into process stability versus areas with heightened special cause variation.

## Root Cause Analysis

When control charts or SPC identify special cause variation, the next step is to determine the root cause. Root cause analysis gets to the underlying reason why the unexpected process change happened.

Various tools like the 5 Whys , fishbone diagrams , and failure mode analysis help uncover root causes. Tracing special cause variation back to the root cause is crucial for addressing problems permanently.

Otherwise, the same special cause could keep affecting the process unpredictably.

## Implications of Special Cause Variation

Special cause variation can have major implications if left unchecked.

Understanding and properly dealing with special causes is crucial for organizations that want to achieve process stability, improve customer satisfaction, and boost financial performance.

## Process Stability with Special Cause Variation

The presence of special cause variation indicates an unstable process. The output and performance metrics of an unstable process fluctuate unpredictably.

This makes the process unreliable and difficult to control. Identifying and eliminating special causes is the first step toward stabilizing a process.

Stable processes have consistent output and are predictable, easier to monitor, and simpler to improve.

## Customer Satisfaction

Customers expect consistent quality and on-time delivery of products and services. An unstable process leads to unpredictable product quality and delivery delays which frustrates customers. Fixing special causes improves process stability and capability.

This enables organizations to reliably meet customer expectations and increase satisfaction levels. Satisfied customers lead to repeat purchases and valuable word-of-mouth publicity.

## Financial Performance

Unstable processes lead to increased waste, rework, and returns. The additional effort and resources needed to fix these issues drive up costs and hurt profitability.

Special cause variation can also result in production and shipment delays that mean missed revenue opportunities and penalties.

Eliminating special causes reduces costs and improves process efficiency . This directly translates into increased profit margins, higher ROI, and stronger financial performance.

## Strategies for Management of Special Cause Variation

Effectively managing special cause variation is critical for organizations looking to improve quality, reduce costs, and boost customer satisfaction.

When a process experiences special cause variation, it indicates an unexpected change that needs to be addressed. Implementing targeted strategies can help get processes back into a state of statistical control.

## Corrective Actions

• Once a special cause is identified through statistical process control methods, structured problem-solving methodologies like PDCA (Plan-Do-Check-Act) or DMAIC (Define, Measure, Analyze, Improve, Control) can be utilized to develop corrective actions.
• Brainstorming sessions to determine potential causes and solutions can provide useful insights from team members. Fishbone diagrams are an effective tool to visually map out causes.
• Pilot testing proposed improvements on a small scale first to evaluate potential impact.
• Verify the effectiveness of corrective actions by monitoring the process over time using control charts. Special causes should be removed and variation should return to baseline common cause levels.

## Continual Improvement with Special Cause Variation

• Schedule periodic reviews of processes, even in the absence of special causes, to identify opportunities for incremental improvements.
• Utilize lean tools like 5S , poka-yoke , and process mapping to reduce waste and enhance process stability.
• Keep the workforce engaged by encouraging them to share improvement ideas and recognize implementation efforts.
• Consider automating certain process steps to reduce variability induced by human errors.
• Review process performance metrics regularly to ensure improvements are sustained over longer periods.
• Conduct refresher training for employees on methods like statistical process control, Six Sigma, and hypothesis testing.

By taking a structured approach combining short-term corrective actions and long-term continual improvement , organizations can effectively manage special cause variation events.

This drives greater consistency and stability in processes, directly enhancing product quality and customer satisfaction.

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## Know It When You See It: Identifying and Using Special Cause Variation for Quality Improvement

In this month’s Hospital Pediatrics , Liao et al 1 share their team’s journey to improve the accuracy of their institution’s electronic health record (EHR) problem list. They presented their results as statistical process control (SPC) charts, which are a mainstay for visualization and analysis for improvers to understand processes, test hypotheses, and quickly learn their interventions’ effectiveness. Although many readers might understand that 8 consecutive points above or below the mean signifies special cause variation resulting in a centerline “shift,” there are many more special cause variation rules revealed in these charts that likely provided valuable real-time information to the improvement team. These “signals” might not be apparent to casual readers when looking at the complete data set in article form.

Shewhart 2 first introduced SPC charts to the world with the publication of Economic Control of Quality of Manufactured Product in 1931. Although control charts were initially used more broadly in industrial settings, health care providers have also recently begun to understand that the use of SPC charts is vital in improvement work. 3 , 4 Deming, 5 often seen as the “grandfather” of quality improvement (QI), saw SPC charts as vital to understanding variation as part of his well-known Theory of Profound Knowledge, outlined in his book The New Economics for Industry Government, Education . Improvement science harnesses the scientific method in which improvers create and rapidly test hypotheses and learn from their data to determine if their hypotheses are correct. 6 This testing is central to the Model for Improvement’s plan-do-study-act cycle. 3 Liao et al 1 nicely laid out their hypotheses in a key driver diagram, and they tested these hypotheses with multiple interventions. In the following paragraphs, we will walk through some of their SPC charts to demonstrate how this improvement team was gaining valuable knowledge about their hypotheses through different types of special cause variation long before they had 8 points to reveal shifts. We recommend readers have the charts from the original article (OA) available for reference.

A fundamental concept in improvement science is understanding the difference between common cause and special cause variation. By understanding how to apply these concepts to your data, you will more quickly identify when a change has occurred and whether action should be taken. The authors’ SPC charts reveal examples of both common cause and special cause variation.

Common cause variations are those causes that are inherent in the system or process. 4 Evidence of common cause variation can be seen visually in the OA’s Fig 3, from January 2017 to October 2017, because the data points vary around the mean but remain between the upper and lower control limits (dotted lines). In contrast, special cause variations are causes of variations that are not inherent to the system. 4 Although there are different rules that signify special cause variation in SPC charts, some of the most common rules that we will focus on here include (1) a single data point outside of the control limits, (2) 8 consecutive points above or below the mean line, and (3) ≥6 consecutive points all moving in the same direction, termed a “trend.” 4 When any of these occur, it is paramount to identify when and why the special cause occurred, learn from the special cause, and then take appropriate action. By quickly detecting special cause variation, improvement teams can more readily assess the impact of interventions by validating whether their hypothesis for improvement is correct.

An example of special cause variation can be seen in the OA’s Fig 2, noted by the shift in the centerline in May 2018 from a baseline of 70% of problem lists revised during admission to a new centerline of 90% of problem lists reviewed during admission. Notice that this new, stable process represented by the new centerline starts after the team tested 3 separate interventions that were directly testing hypotheses related to their key drivers. Although the shift began in May 2018, the first special cause signal the improvement team would have seen is the first point outside of the upper control limit in January 2018, which comes immediately after their first 2 interventions. As more months go by, each month after continues to represent special cause variation because they are outside of the control limits. Finally, when the data point in May 2018 is plotted, it is apparent that an upward trend started in December 2017, with 6 consecutive data points increasing through May 2018. Therefore, the authors recognized special cause variation (a trend) by having 6 consecutive increasing points. Given their interventions were grounded in theory and the temporal relationship of the trend beginning in December 2017, with the preceding interventions in November and December 2017, there is a high degree of belief that the interventions are driving these results. In other words, their hypothesis that the EHR enhancements, the dissemination of a protocol, and the designation of a bonus would improve the percentage of times that the problem list is “reviewed” was confirmed as early as December 2017, long before the eventual centerline shift in May 2018.

Figure 3 in the OA is an SPC chart of one of the team’s process measures revealing the percentage of discharges with duplicate codes on the problem list. The authors demonstrate that the November 2017 EHR impacted the process, reducing the mean from 12% to 7%. The data contained in our Fig 1 are the same data as those shown in Fig 3 of the authors’ OA but without the first centerline shift, which reveals what the authors would have seen in real time during the course of their improvement efforts. With the November 2017 data point (labeled point 1 in Fig 1 ), the authors immediately have evidence of special cause variation, with a point outside of the lower control limit after their intervention. This continues with points 2 through 5, each below the lower control limit. Statistically speaking, any one of these is unlikely to happen by chance (which is why they are considered special cause), but the fact that the team is seeing this month after month reinforced their hypothesis. With the eighth consecutive point below the mean line occurring in June 2018 (circle), the team was able to finally shift the centerline. Looking at this from the perspective of the improvement team, the immediacy and consistency of feedback that they witnessed with points outside of the control limits from November 2017 through March 2018 were likely much more informative to their improvement efforts than the moment when they finally were able to shift the mean line. The authors highlight that the EHR enhancement was chosen for its higher reliability design concept, 7 making it easier for the providers to complete the intended behavior. The immediacy of special cause signal in November 2017 would indicate that their hypothesis was correct.

OA Fig 3 re-designed to represent data visualization prior to centerline shift.

Finally, viewing charts in combination provides further support of the team’s overall improvement theory. Notice that the special cause shift in Fig 3 of the OA (a process measure) occurs at the same time as the beginning of the special cause that is noted in Fig 2 of the OA, which is their outcome measure. In this case, a driving change in their process was temporally associated with recognizable change in their outcome. Similarly, the OA’ Fig 4, viewed in combination with its Figs 2 and 3, provide our final example of how revealing special cause variation across measures relates to the broader theory of the team’s improvement. Special cause variation is evident in Fig 4 of the OA, with points outside of the control limits associated with interventions in both November and December 2019. A similar pattern is seen in the authors’ other process measure chart, Fig 3 of the OA, during those same months associated with those interventions. Here, a couple of associations are addressed in the data. First, a high degree of belief that those two interventions affect those measures is provided in the data, as the authors hypothesized. Second, with such data, the authors also confirm the hypothesis that underlies the entire article: simply “reviewing” the problem list is also associated with active management of the problem list, and improvements to their process measures help drive their outcome. After >1.5 years of a fairly stable outcome measure (mainly common cause variation), the team’s use of these two interventions not only improved their process measures but also were associated with the December 2019 data point being outside of the control limits in the outcome measure in Fig 2 of the OA. In these situations, the team’s use of SPC charts provided the ability to understand relationships between process and outcome measures, in addition to rapidly testing hypotheses.

As revealed in the work by Liao et al, 1 we can improve the care we provide to patients every day with QI methodology. When researchers use SPC charts to report QI in scholarly venues such as this, readers often focus on centerline shifts. Although improvement teams take great joy in shifting a centerline, experienced teams much more commonly work to detect other types of special cause variation quickly to test their hypotheses and work through plan-do-study-act cycles. By understanding the rules of special cause variation and applying them to data in real time, teams will be provided with information that will inform hypotheses testing, bolster knowledge about a system, and ultimately accelerate improvement work.

## Acknowledgments

FUNDING: Supported by the Agency for Healthcare Research and Quality (grant T32HS026122). The content is solely the responsibility of the authors and does not necessarily represent the official views of the Agency for Healthcare Research and Quality.

FINANCIAL DISCLOSURE: The authors have indicated they have no financial relationships relevant to this article to disclose.

POTENTIAL CONFLICT OF INTEREST: The authors have indicated they have no potential conflicts of interest to disclose.

## Guest Column | February 15, 2021

7 rules for properly interpreting control charts.

By Mark Durivage , Quality Systems Compliance LLC

Control charts build upon periodic inspections by plotting the process outputs and monitoring the process for special cause variation or trends. Control charts are decision-making tools that provide information for timely decisions concerning recently produced products.

Control charts can be used to identify sources of variation, both common and special cause. Common cause variation is the variation inherent in the process. Common cause variation is also known as the noise of the process. A process with only common cause variation is highly predictable. A process that has a significant inherent common cause variation may not be capable of producing products that meet predetermined specifications. Common cause variation is said to account for 80% of the variation in any process and is considered management’s responsibility.

Special cause variation is variation that is not inherent to the process. A process with special cause variation is highly unpredictable. Special cause variation is said to account for 20% of the variation in any process and is considered the worker’s responsibility.

Control charts contain a centerline — usually the mathematical average of the samples plotted — and upper and lower statistical control limits that define the constraints of common cause variation and performance data plotted over time.

There are two general classifications of control charts: variables and attributes charts. Variables are things that can be measured. Attributes are things that can be counted. The type of data (variable or attribute) will dictate the appropriate type of control chart required to monitor a process. Table 1 can be used for control chart selection.

Table 1: Control Chart Selection Guide

Selection of the correct type of control chart is important to ensure the underlying statistical concepts are appropriate for the feature or attribute being measured.

A process is said to be in control when the control chart does not indicate any out-of-control condition and contains only common causes of variation. If the common cause variation is small, then a control chart can be used to monitor the process. If the common cause variation is too large, the process will need to be modified or improved to reduce the amount of inherent variation to an acceptable level.

When a control chart indicates an out-of-control condition (a point outside the control limits or matching one or more of the criteria in the rules below), the assignable causes of variation must be identified and eliminated.

The following rules can be used to properly interpret control charts:

Rule 1 – One point beyond the 3 σ control limit

Rule 2 – Eight or more points on one side of the centerline without crossing

Rule 3 – Four out of five points in zone B or beyond

Rule 4 – Six points or more in a row steadily increasing or decreasing

Rule 5 – Two out of three points in zone A

Rule 6 – 14 points in a row alternating up and down

Rule 7 – Any noticeable/predictable pattern, cycle, or trend

Analyzing a control chart for special cause variation can be facilitated by using the categories used with a cause-and-effect diagram. The flowing are the categories that I prefer to use:

• Equipment, Machines, and Tooling
• Environment

Rule 1, one point beyond the 3 σ control limits, seeks to identify points that are random or outliers, as shown here in red. When random or outlier points are identified, the following are potential special causes to consider:

• improper start-up
• improper setup
• sudden support system failure (cooling, heating, compressed air, vacuum, steam, etc.)
• tool failure/breakage
• equipment or machine failure
• improper equipment, machine, and tooling maintenance
• utility interruption
• temperature suddenly too low/high
• humidity suddenly too low/high
• equipment has not stabilized (warmed-up)
• missed process step
• new process
• inspection, measuring, and testing equipment not properly calibrated
• damaged inspection, measuring, and testing equipment
• change in raw materials
• change in components
• handling damage
• expired materials
• new operators
• operator interrupted or distracted
• operator overcompensating when making process adjustments

Rule 2, eight or more points on one side of the centerline without crossing, is considered a prominent shift (the shift can be on either side of the centerline). The points circled in red are considered a prominent shift. When a prominent shift is identified, the following are potential special causes to consider:

• damaged tooling
• temperature shifted too low/high
• humidity shifted too low/high
• new process parameters
• incorrect process parameters
• process has improved
• shift change

Rule 3, four out of five points in zone B or beyond, is considered a small shift (the shift can be on either side of the centerline). The points circled in red are considered small shifts. When a small shift is identified, the following are potential special causes to consider:

• intermittent support system failure (cooling, heating, compressed air, vacuum, steam, etc.)
• inspection, measuring, and testing equipment not adequate for the intended use
• mixed raw materials
• mixed components

Rule 4, six points or more in a row steadily increasing or decreasing, is considered a trend (the trend can be rising or falling). The points circled in red are considered a trend. When a trend is identified, the following are potential special causes to consider:

• gradual support system failure (cooling, heating, compressed air, vacuum, steam, etc.)
• temperature gradually drifting too low/high
• humidity gradually drifting too low/high
• variation in the raw materials
• variation in the components
• operator distracted

Rule 5, two out of three points in zone A, is considered a large shift. (the shift can be on either side of the centerline). The points circled in red are considered large shifts. When a large shift is identified, the following are potential special causes to consider:

• support system failure (cooling, heating, compressed air, vacuum, steam, etc.)

Rule 6, 14 points in a row alternating up and down, is generally considered to be overcontrol. The points enclosed in red are considered out of control. When this situation is identified, the following are potential special causes to consider:

• temperature intermittently too low/high
• humidity intermittently too low/high
• operator not waiting for the process to stabilize before making process adjustments

Please note, even though the operator may be over adjusting the process, there may be other special causes present.

Rule 7 is any noticeable/predictable pattern, cycle, or trend. The points circled in red are considered out of control. When these situations are identified, the following are potential special causes to consider:

• two or more processes
• multiple shifts

Stratification

When stratification is identified, it is generally due to one of two issues. The operators are purposefully truncating the measurements, or the process has improved significantly, which will require the recalculation of the statistical control limits.

It is time to consider augmenting your validated pharmaceutical, medical device, and tissue production processes, including processing, packaging, and labeling, with continuous process monitoring using control charts to ensure continued compliance with established specifications and requirements.

When implementing control charts as part of your continuous process monitoring activities, ensure the people responsible for completing the charts have been properly trained and understand the seven rules presented in this article.

I cannot emphasize enough the importance of establishing documented procedures to manage the tools and methods used. Best practice includes providing the rationale for your organization’s use of control charts for continuous process monitoring. The methods and tools presented in this article can and should be utilized based upon industry practice, guidance documents, and regulatory requirements.

References:

• Durivage, M.A., 2014, Practical Engineering, Process, and Reliability Statistics, Milwaukee, ASQ Quality Press
• Durivage, M.A., and Mehta, B., 2016, Practical Process Validation, Milwaukee, ASQ Quality Press
• Durivage, M.A., 2020, https://www.pharmaceuticalonline.com/doc/how-to-implement-continuous-process-monitoring-of-validated-processes-0001

## Know It When You See It: Identifying and Using Special Cause Variation for Quality Improvement

Affiliations.

• 1 Division of Pediatric Hospital Medicine, Department of Pediatrics, School of Medicine, Vanderbilt University and Monroe Carell Jr Children's Hospital at Vanderbilt, Nashville, Tennessee [email protected].
• 2 Division of Pediatric Hospital Medicine, Department of Pediatrics, School of Medicine, Vanderbilt University and Monroe Carell Jr Children's Hospital at Vanderbilt, Nashville, Tennessee.
• PMID: 33051243
• PMCID: PMC7891129
• DOI: 10.1542/hpeds.2020-002303

In this month’s Hospital Pediatrics , Liao et al share their team’s journey to improve the accuracy of their institution’s electronic health record (EHR) problem list. They presented their results as statistical process control (SPC) charts, which are a mainstay for visualization and analysis for improvers to understand processes, test hypotheses, and quickly learn their interventions’ effectiveness. Although many readers might understand that 8 consecutive points above or below the mean signifies special cause variation resulting in a centerline “shift,” there are many more special cause variation rules revealed in these charts that likely provided valuable real-time information to the improvement team. These “signals” might not be apparent to casual readers when looking at the complete data set in article form.

Shewhart first introduced SPC charts to the world with the publication of Economic Control of Quality of Manufactured Product in 1931. Although control charts were initially used more broadly in industrial settings, health care providers have also recently begun to understand that the use of SPC charts is vital in improvement work. , Deming, often seen as the “grandfather” of quality improvement (QI), saw SPC charts as vital to understanding variation as part of his well-known Theory of Profound Knowledge, outlined in his book The New Economics for Industry Government, Education . Improvement science harnesses the scientific method in which improvers create and rapidly test hypotheses and learn from their data to determine if their hypotheses are correct. This testing is central to the Model for Improvement’s plan-do-study-act cycle. Liao et al nicely laid out their hypotheses in a key driver diagram, and they tested these hypotheses with multiple interventions. In the following paragraphs, we will walk through some of their SPC charts to demonstrate how this improvement team was gaining valuable knowledge about their hypotheses through different types of special cause variation long before they had 8 points to reveal shifts. We recommend readers have the charts from the original article (OA) available for reference.

A fundamental concept in improvement science is understanding the difference between common cause and special cause variation. By understanding how to apply these concepts to your data, you will more quickly identify when a change has occurred and whether action should be taken. The authors’ SPC charts reveal examples of both common cause and special cause variation.

## Publication types

• Research Support, U.S. Gov't, P.H.S.
• Inpatients*
• Quality Improvement*

## Grants and funding

• T32 HS026122/HS/AHRQ HHS/United States
• Guide: Control Charts

## Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

• Last Updated: June 11, 2023
• Learn Lean Sigma

Control charts stand as a pivotal element in the realm of statistical process control (SPC), a key component in quality management and process optimization. These charts offer a visual representation of process performance over time, plotting measured data points to track variations, identify abnormalities, and discern trends.

Their primary function is to highlight uncontrolled variations which are deviations from the norm often attributed to external factors. This insightful identification is crucial in determining whether a process is stable and predictable, or in need of refinement. Developed in the 1920s by Walter A. Shewhart, control charts have revolutionized the ability to distinguish between common and special cause variations, enhancing the precision of process evaluation and improvement.

What are control charts.

Control charts are key statistical tools used in statistical process control (SPC), which is used for quality management and process optimization. Control charts are used as a way to display the performance of a process over time. This is done by plotting the measured output data points on a chart, allowing those viewing them to track how a process varies over time and identify any abnormalities, special-cause variation, or trends. The main reason control charts are used is to highlight any uncontrolled variations; these are variations that are outside the normal operation and can be the result of external or special factors. This identification helps in understanding if a process is stable and predictable or if it requires action for improvement.

Control charts were introduced by Walter A. Shewhart in the 1920s, bringing about a significant advancement in quality control. The main concept of control charts is being able to distinguish between common and special cause variations.

Common Cause Variation : This type of variation is inherent to the process. It’s the “noise” within the system, caused by factors that are usually consistent and predictable over time. This can be seen as the variation that appears inside the upper and lower control limits on the chart above.

Special Cause Variation : In contrast, this variation arises from external factors and is not part of the usual process. It indicates issues that need to be addressed to maintain the quality and consistency of the process. These can be seen with data points that appear outside of the upper and lower control limits.

By effectively identifying these variations, organizations can pinpoint areas requiring improvement and work towards enhancing their overall process stability and quality.

## Types of Control Charts

Control charts are categorized based on the nature of the data they manage – variable (quantitative) or attribute (qualitative).

Variable Data Control Charts : These charts are designed for data that can be measured on a continuous scale, such as time, weight, distance, or temperature. They’re ideal for tracking changes in the mean, or variability, of a process. The most common types are:

• X-bar and R Chart : Used to monitor the mean (average) and range (variability) of a process. Suitable for small sample sizes.
• X-bar and S Chart : Similar to the X-bar and R chart but more appropriate for larger sample sizes, as it monitors the mean and the standard deviation of a process.

Attribute Data Control Charts : These charts are used for data that are not measured but counted, typically focusing on items that are either conforming or non-conforming. They include:

P Chart (Proportion Chart) : Used to track the proportion of defective items in a sample. It’s useful when the sample size varies and the data is expressed as a proportion.

C Chart (Count Chart) : This chart is used to monitor the count of defects or nonconformities in an item or a unit. It’s useful when the number of opportunities for defects is constant.

## Components of a Control Chart

A control chart is more than just a line graph; it’s a sophisticated tool designed for process monitoring and improvement. Understanding its components is key to leveraging its full potential:

• Data Points : These are the core of the control chart, representing individual measurements or values collected from the process over time. Data points are plotted sequentially, usually along the vertical axis, against the time or sequence order on the horizontal axis. They provide a visual representation of how the process performs over time and are the basis for further analysis.
• Center Line : Typically, this is the process mean (average), or sometimes the median. It acts as a reference line around which data points are expected to fluctuate. The center line is crucial as it reflects the ‘normal’ performance level of the process where it should be operating if everything is stable and no special causes of variation are present.
• Control Limits : These limits define the boundary of expected process variation and are set at ±3 standard deviations from the center line. The choice of three standard deviations is statistically significant as it covers about 99.73% of the data points in a normal distribution, assuming the process is under control. The area within the control limits represents normal process variation (common cause variation), while points outside these limits indicate unusual variation (special cause variation) that may necessitate investigation.
• Out-of-Control Signals : These are indications that the process might be out of control. They are identified when data points fall outside the control limits or when they exhibit non-random patterns within the limits (like a series of points steadily increasing or decreasing). Such signals prompt further investigation to identify and correct the root causes of the variation.

## How to Create a Control Chart

Step 1: data collection.

To create a control chart, you first need data. You may already have this data, but consider that it needs to be gathered sequentially over a set period to reflect the process’s typical operation. It is also important that the data be as accurate and unbiased as possible.

When constructing a control chart, the amount of data collected is crucial and should be tailored to the specifics of the process. For most situations, gathering at least 20-25 subgroups, each with 4-5 individual measurements, is a good starting point. In total, aim for a minimum of 100 data points to establish a reliable baseline.

The data should be collected consistently over time, with the frequency and volume adjusted based on the process’s stability and output rate. It’s important to balance the need for precision and confidence in the results with the practicality of data collection. As you gain more insights into the process, be prepared to adapt your data collection strategy to ensure it adequately reflects the process’s variability and your analysis needs.

## Step 2: Calculate the Center Line

The next step is to establish a baseline for the process’s performance. The centerline is usually the mean (average) of the data set. The mean is calculated by adding all of the data points and dividing by the number of data points. This line will then be used as a reference point to compare individual data points and indicate the average performance of the process.

## Step 3: Determine the Control Limits

To calculate control limits for a control chart, first determine the process mean and standard deviation from your data. For example, if your process mean (average) is 50 and the standard deviation is 5, the Upper Control Limit (UCL) is calculated as the mean plus three times the standard deviation (3 x 5 = 15), therefore (50 + 3 5 = 65), and the Lower Control Limit (LCL) as the mean minus three times the standard deviation (50 – 3 5 = 35). These limits represent the boundary of normal variation for a process in control. Data points outside these limits suggest special-cause variations, indicating a process that may be out of control.

## Step 4: Plot the Data

Once you have your data and have calculated the mean, the standard deviation, and the control limits, the next step is to plot the chart. You can create a control chart in Microsoft Excel by setting your data out like in the example image and following these steps

• Select the Data
• Click Insert
• Click the line chart
• Select the first 2-D line chart

Alternatively, you can try our Control Chart analyzer tool, which will allow you to upload your data and get instant detailed analysis of observations and feedback of your data. Just like in the example below

## Step 5: Interpret the Chart

The final step involves analyzing the control chart. Interpreting a control chart involves closely examining it for data points that fall outside the established control limits or for specific patterns within these limits. Data points beyond the control limits are indicators of special cause variations, signifying an anomaly in the process that may require investigation. Additionally, even if points are within the control limits, certain patterns, such as consistent upward or downward trends, cycles, or too much clustering, can signal underlying issues. These patterns might point to potential areas for process improvement, highlighting the need for further analysis to understand and address the root causes.

## How to Analyze a Control Chart

Recognizing patterns.

• Shifts : Consist of eight or more consecutive points on one side of the center line. This could indicate a significant change in the process.
• Trends : Involve six or more consecutive points either increasing or decreasing. Trends can suggest a gradual change in the process.
• Cycles : These are repeating patterns of points. They might indicate seasonal effects or other recurring factors affecting the process.

## Acting on Analysis

• Investigate Causes : When any of these patterns are identified, it’s important to investigate the underlying causes. This could involve looking into changes in materials, machinery, methods, or the environment.
• Implement Changes : Once the cause is identified, appropriate changes can be made to correct or improve the process.
• Monitor Effects : After implementing changes, continue to use the control chart to monitor the process and ensure that improvements are sustained.

Control charts are indispensable in the toolkit of quality control, providing a systematic and visual approach to monitoring process stability and identifying areas for improvement. By plotting data points, establishing a center line, setting control limits, and interpreting the resulting chart, these tools enable the detection of special cause variations and the observation of patterns such as shifts, trends, and cycles.

Through careful analysis and subsequent actions based on these insights, control charts empower organizations to proactively address underlying issues, optimize processes, and maintain high-quality standards. The ultimate goal is not just to identify and rectify problems but to foster an environment of continuous process improvement and sustained operational excellence.

• Lowry, C.A. and Montgomery, D.C., 1995. A review of multivariate control charts.   IIE transactions ,  27 (6), pp.800-810.
• Woodall, W.H., Spitzner, D.J., Montgomery, D.C. and Gupta, S., 2004. Using control charts to monitor process and product quality profiles.   Journal of Quality Technology ,  36 (3), pp.309-320.

## Q: What is a control chart?

A: A control chart is a statistical tool used to monitor and analyze a process over time. It helps determine if a process is in control or if there are any special causes of variation present.

## Q: How does a control chart work?

A: A control chart consists of a graph with data points plotted over time. It typically includes a centerline representing the process average and control limits that define the acceptable range of variation. Data points falling within the control limits indicate that the process is stable, while points outside the limits may suggest the presence of special causes of variation.

## Q: What are the benefits of using control charts?

A: Control charts provide several benefits, including:

• Early detection of process changes or deviations.
• Identification of special causes of variation.
• Reduction in process variability.
• Improvement in process performance and quality.
• Objective data-based decision making.
• Effective communication of process performance to stakeholders.

## Q: What are the types of control charts?

A: There are various types of control charts, including:

• Individuals control chart: Used when individual data points are measured.
• X-bar and R chart: Utilized when data is collected in subgroups, and both the subgroup averages (X-bar) and ranges (R) are tracked.
• X-bar and S chart: Similar to the X-bar and R chart, but it uses the standard deviation (S) instead of the range (R) to measure variation.
• p-chart: Used for monitoring the proportion of nonconforming items or defects in a process.
• np-chart: Similar to the p-chart but used when the sample size is constant.
• c-chart: Used when the count of defects per unit is measured.

## Q: How do you interpret a control chart?

A: When interpreting a control chart, the following guidelines are generally followed:

• Data points within the control limits suggest a stable and predictable process.
• Points outside the control limits may indicate the presence of special causes of variation.
• Nonrandom patterns or trends, such as consecutive points on one side of the centerline, could suggest process shifts or other issues.
• It is important to investigate and address points beyond the control limits or any unusual patterns to identify and eliminate special causes.

## Q: What is meant by "common cause" and "special cause" variation?

A: “Common cause” refers to the natural variation that is inherent in a process and expected to occur randomly. It is also known as “normal” or “chance” cause variation. Control charts help identify and quantify this type of variation.

“Special cause” refers to unusual or non-random sources of variation that are not inherent to the process. These causes are typically assignable to specific factors or events and can lead to unexpected changes in the process output. Control charts help detect and investigate these special causes so that appropriate actions can be taken.

## Q: Can control charts be used in any industry or process?

A: Yes, control charts can be used in various industries and processes where data is collected over time. They are commonly applied in manufacturing, healthcare, finance, software development, and service industries to monitor and improve process performance.

## Q: What are the limitations of control charts?

A: Control charts have a few limitations, including:

• They rely on accurate and reliable data collection and measurement.
• Control charts assume that the process is in a state of statistical control at the beginning.
• Control charts may not identify small shifts or changes in a process if the sample size is small.
• Control charts do not identify the specific causes of variation; they only signal when variation is present.
• Control charts may not be effective in detecting certain types of non-random patterns or complex interactions among process variables.

## Q: Are there software tools available for creating and analyzing control charts?

A: Yes, there are many software tools available that can help create and analyze control charts. Some popular options include Minitab , JMP , Excel with add-ins like QI Macros , and various statistical software packages like R and Python that have control chart libraries and functions. These tools make it easier to plot control charts, calculate control limits, and perform statistical analyses.

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

## Free Lean Six Sigma Templates

Improve your Lean Six Sigma projects with our free templates. They're designed to make implementation and management easier, helping you achieve better results.

## Using tests for special causes in control charts

In this topic, which tests for special causes are included in minitab, which tests should i use to detect specific patterns of special-cause variation, which tests are available with my control chart, how do i specify tests and parameters for a control chart, how do i change the default tests and test parameters.

Apply certain tests based on your knowledge of the process. If it is likely that your data might contain particular patterns, you can look for them by choosing the appropriate test. Adding more tests makes the chart more sensitive, but may also increase the chance of getting a false signal. When you use several tests together, the chance of obtaining a signal for lack-of-control increases.

## Variables charts

• Test 1 (a point outside the control limits) detects a single out-of-control point.
• Test 2 (9 points in a row on one side of the center line) detects a possible shift in the process.
• Test 7 (too many points in a row within 1 standard deviation of the center line) detects control limits that are too wide. Wide control limits are often caused by stratified data, which occur when you have a systematic source of variation within each subgroup.

## Attributes charts

Rare event charts.

Experts recommend that you use both Test 1 and Test 2 when you create a G chart because the G chart may be slow to detect small to moderate decreases in the average number of days or number of opportunities between events.

To detect high rates of an event on a G chart, Minitab also includes the Benneyan test. The minimum data value for a G chart is 0. In most cases, the lower control limit for a G chart is also 0. Thus, in most cases, no points on a G chart can be below the lower control limit. The Benneyan test fails if there are too many consecutive points that equal 0.

Experts recommend that you use both Test 1 and Test 2 when you create a T chart because the T chart may be slow to detect small to moderate decreases in the average time between events.

Tests 1−8 are available for most variables control charts. Note that only tests 1−4 are available for R, S, and moving range charts.

Tests 1−4 are available for the attribute control charts.

On time-weighted control charts, Minitab only performs a test for points that go beyond the control limits. The other seven tests assume that the points are independent. Because the plotted points on time-weighted charts combine information from previous subgroups, the points are not independent.

When you create most control charts, you can select the tests to perform and change the parameters for each test. For example, suppose that you create an Xbar chart and you want to perform tests 1, 2, and 7. In addition, you want to draw control limits at 2.5σ instead of 3σ so that it is easier for points to fail test 1.

• Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar .
• Complete the dialog box as usual.
• Click Xbar Options , then click the Tests tab.
• 1 point > K standard deviations from center line
• K points in a row on same side of center line
• K points in a row within 1 standard deviation of center line (either side)
• Next to 1 point > K standard deviations from center line , enter 2.5 . The control limits will be drawn at 2.5σ instead of 3σ. Points will fail test 1 if they are more than 2.5 sigma from the center line.
• Click OK in each dialog box.

You can change the default tests and test parameters for future sessions of Minitab. For example, suppose you want to perform all test for special causes whenever you create a control chart. In addition, you want to draw the control limits for all control charts at 2.5σ instead of 3σ.

• Choose File > Options > Control Charts and Quality Tools > Tests .
• From the drop-down list, select Perform all tests for special causes . Minitab will now perform all applicable tests when you create a control chart.
• Next to 1 point > K standard deviations from center line , enter 2.5 . The control limits for control charts will be drawn at 2.5σ by default. Points will fail test 1 if they are more than 2.5σ from the center line.

This procedure will not undo any changes that you have made in the Tests tab for specific graphs in existing projects. For example, if you previously modified the parameters for an Xbar chart in the current project, Minitab will remember your settings for that chart. The new defaults will not be applied to Xbar charts in the current project.

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## Six Sigma Control Charts: An Ultimate Guide

• Written by Contributing Writer
• Updated on March 10, 2023

Welcome to the ultimate guide to Six Sigma control charts, where we explore the power of statistical process control and how it can help organizations improve quality, reduce defects, and increase profitability. Control charts are essential tools in the Six Sigma methodology, visually representing process performance over time and highlighting when a process is out of control.

In this comprehensive guide, we’ll delve into the different types of control charts, how to interpret them, how to use them to make data-driven decisions, and how to become a Lean Six Sigma expert .

Let’s get started on the journey to discover the transformative potential of Six Sigma control charts.

## What is a Control Chart?

A control chart is a statistical tool used in quality control to monitor and analyze process variation. No process is free from variation, and it is vital to understand and manage this variation to ensure consistent and high-quality output. The control chart is designed to help visualize this variation over time and identify when a process is out of control.

The chart typically includes a central line, which represents the average or mean of the process data, and upper and lower control limits, which are set at a certain number of standard deviations from the mean. The control limits are usually set at three standard deviations from the mean, encompassing about 99.7 percent of the process data. If the process data falls within these control limits, the process is considered in control, and variation is deemed to be coming from common causes. If the data points fall outside these control limits, this indicates that there is a special cause of variation, and the process needs to be investigated and improved.

Control charts are commonly used in manufacturing processes to ensure that products meet quality standards, but they can be used in any process where variation needs to be controlled. They can be used to track various types of process data, such as measurements of product dimensions, defect rates, or cycle times.

Also Read: What Is Process Capability and Why It’s More Interesting Than It Sounds

## Significance of Control Charts in Six Sigma

Control charts are an essential tool in the Six Sigma methodology to monitor and control process variation. Six Sigma is a data-driven approach to process improvement that aims to minimize defects and improve quality by identifying and eliminating the sources of variation in a process. The control chart helps to achieve this by providing a visual representation of the process data over time and highlighting any special causes of variation that may be present.

## The Objective of Six Sigma Control Charts

The primary objective of using a control chart in Six Sigma is to ensure that a process is in a state of statistical control. This means that the process is stable and predictable, and any variation is due to common causes inherent in the process. The control chart helps to achieve this by providing a graphical representation of the process data that shows the process mean and the upper and lower control limits. The process data points should fall within these limits if the process is in control.

## Detecting Special Cause Variation

One of the critical features of a Six Sigma control chart is its ability to detect special cause variation, also known as assignable cause variation. Special cause variation is due to factors not inherent in the process and can be eliminated by taking corrective action. The control chart helps detect special cause variation by highlighting data points outside control limits.

## Estimating Process Average and Variation

Another objective of a control chart is to estimate the process average and variation. The central line represents the process average on the chart, and the spread of the data points around the central line represents the variation. By monitoring the process over time and analyzing the control chart, process improvement teams can gain a deeper understanding of the process and identify areas for improvement.

## Measuring Process Capability with Cp and Cpk

Process capability indices, such as Cpk and Cp, help to measure how well a process can meet the customer’s requirements. Here are some details on how to check process capability using Cp and Cpk:

• Cp measures a process’s potential capability by comparing the data’s spread with the process specification limits.
• If Cp is greater than 1, it indicates that the process can meet the customer’s requirements.
• However, Cp doesn’t account for any process shift or centering, so it may not accurately reflect the process’s actual performance.
• Cpk measures the actual capability of a process by considering both the spread of the data and the process’s centering or shift.
• Cpk is a more accurate measure of a process’s performance than Cp because it accounts for both the spread and centering.
• A Cpk value of at least 1.33 is typically considered acceptable, indicating that the process can meet the customer’s requirements.

It’s important to note that while Cp and Cpk provide valuable information about a process’s capability, they don’t replace the need for Six Sigma charts and other statistical tools to monitor and improve process performance.

Also Read: What Are the 5s in Lean Six Sigma?

## Steps to Create a Six Sigma Control Chart

To create a Six Sigma chart, you can follow these general steps:

• Gather Data: Collect data related to the process or product you want to monitor and improve.
• Determine Data Type: Identify the type of data you have, whether it is continuous, discrete, attribute, or variable.
• Calculate Statistical Measures: Calculate basic statistical measures like mean, standard deviation, range, etc., depending on the data type.
• Set Control Limits: Determine the Upper Control Limit (UCL) and Lower Control Limit (LCL) using statistical formulas and tools.
• Plot Data : Plot the data points on the control chart, and draw the control limits.
• Analyze the Chart: Analyze the chart to identify any special or common causes of variation, and take corrective actions if necessary.
• Update the Chart: Continuously monitor the process and update the chart with new data points.

You can use software tools like Minitab, Excel, or other statistical software packages to create a control chart. These tools will automate most of the above steps and help you easily create a control chart.

## Know When to Use Control Charts

A Six Sigma control chart can be used to analyze the Voice of the Process (VoP) at the beginning of a project to determine whether the process is stable and predictable. This helps to identify any issues or potential problems that may arise during the project, allowing for corrective action to be taken early on. By analyzing the process data using a control chart, we can also identify the cause of any variation and address the root cause of the issue.

Here are some specific scenarios when you may want to use a control chart:

• At the start of a project: A control chart can help you establish a baseline for the process performance and identify potential areas for improvement.
• During process improvement: A control chart can be used to track the effectiveness of changes made to the process and identify any unintended consequences.
• To monitor process stability : A control chart can be used to verify whether the process is stable. If the process is unstable, you may need to investigate and make necessary improvements.
• To identify the source of variability : A control chart can help you identify the source of variation in the process, allowing you to take corrective actions.

## Four Process States in a Six Sigma Chart

Control charts can be used to identify four process states:

• The Ideal state: The process is in control, and all data points fall within the control limits.
• The Threshold state : Although data points are in control, there are some non-conformances over time.
• The Brink of Chaos state: The process is in control but is on the edge of committing errors.
• Out of Control state: The process is unstable, and unpredictable non-conformances happen. In this state, it is necessary to investigate and take corrective actions.

Also Read: How Do You Use a Six Sigma Calculator?

## What are the Different Types of Control Charts in Six Sigma?

Control charts are an essential tool in statistical process control, and the type of chart used depends on the data type. There are different types of control charts, and the type used depends on the data type.

The seven Six Sigma chart types include: I-MR Chart, X Bar R Chart, X Bar S Chart, P Chart, NP Chart, C Chart, and U Chart. Each chart has its specific use and is suitable for analyzing different data types.

The I-MR Chart, or Individual-Moving Range Chart, analyzes one process variable at a time. It is suitable for continuous data types and is used when the sample size is one. The chart consists of two charts: one for individual values (I Chart) and another for the moving range (MR Chart).

## X Bar R Chart

The X Bar R Chart is used to analyze process data when the sample size is more than one. It consists of two charts: one for the sample averages (X Bar Chart) and another for the sample ranges (R Chart). It is suitable for continuous data types.

## X Bar S Chart

The X Bar S Chart is similar to the X Bar R Chart but uses the sample standard deviation instead of the range. It is suitable for continuous data types. It is used when the process data is normally distributed, and the sample size is more than one.

The P Chart, or the Proportion Chart, is used to analyze the proportion of nonconforming units in a sample. It is used when the data is binary (conforming or nonconforming), and the sample size is large.

The NP Chart is similar to the P Chart but is used when the sample size is fixed. It monitors the number of nonconforming units in a sample.

The C Chart, also known as the Count Chart, is used to analyze the number of defects in a sample. It is used when the data is discrete (count data), and the sample size is large.

The U Chart, or the Unit Chart, is used to analyze the number of defects per unit in a sample. It is used when the sample size is variable, and the data is discrete.

## Factors to Consider while Selecting the Right Six Sigma Chart Type

Selecting the proper Six Sigma control chart requires careful consideration of the specific characteristics of the data and the intended use of the chart. One must consider the type of data being collected, the frequency of data collection, and the purpose of the chart.

Continuous data requires different charts than attribute data. An individual chart may be more appropriate than an X-Bar chart if the sample size is small. Similarly, if the data is measured in subgroups, an X-Bar chart may be more appropriate than an individual chart. Whether monitoring a process or evaluating a new process, the process can also affect the selection of the appropriate control chart.

## How and Why a Six Sigma Chart is Used as a Tool for Analysis

Control charts help to focus on detecting and monitoring the process variation over time. They help to keep an eye on the pattern over a period of time, identify when some special events interrupt normal operations, and reflect the improvement in the process while running the project. Six Sigma control charts are considered one of the best tools for analysis because they allow us to:

• Monitor progress and learn continuously
• Quantify the capability of the process
• Evaluate the special causes happening in the process
• Separate the difference between the common causes and special causes

## Benefits of Using Control Charts

• Early warning system: Control charts serve as an early warning system that helps detect potential issues before they become major problems.
• Reduces errors: By monitoring the process variation over time, control charts help identify and reduce errors, improving process performance and quality.
• Process improvement: Control charts allow for continuous monitoring of the process and identifying areas for improvement, resulting in better process performance and increased efficiency.
• Data-driven decisions: Control charts provide data-driven insights that help to make informed decisions about the process, leading to better outcomes.
• Saves time and resources: Six Sigma control charts can help to save time and resources by detecting issues early on, reducing the need for rework, and minimizing waste.

## Who Can Benefit from Using Six Sigma Charts

• Manufacturers: Control charts are widely used in manufacturing to monitor and control process performance, leading to improved quality, increased efficiency, and reduced waste.
• Service providers: Service providers can use control charts to monitor and improve service delivery processes, leading to better customer satisfaction and increased efficiency.
• Healthcare providers: Control charts can be used in healthcare to monitor and improve patient outcomes and reduce medical errors.
• Project managers : Project managers can use control charts to monitor and improve project performance, leading to better project outcomes and increased efficiency.

Also Read: What Are the Elements of a Six Sigma Project Charter?

## Some Six Sigma Control Chart Tips to Remember

Here are some tips to keep in mind when using Six Sigma charts:

• Never include specification lines on a control chart.
• Collect data in the order of production, not from inspection records.
• Prioritize data collection related to critical product or process parameters rather than ease of collection.
• Use at least 6 points in the range of a control chart to ensure adequate discrimination.
• Control limits are different from specification limits.
• Points outside the control limits indicate special causes, such as shifts and trends.
• Points inside the limits indicate trends, shifts, or instability.
• A control chart serves as an early warning system to prevent a process from going out of control if no preventive action is taken.
• Assume LCL as 0 if it is negative.
• Use two charts for continuous data and a single chart for discrete data.
• Don’t recalculate control limits if a special cause is removed and the process is not changing.
• Consistent performance doesn’t necessarily mean meeting customer expectations.

## What are Control Limits?

Control limits are an essential aspect of statistical process control (SPC) and are used to analyze the performance of a process. Control limits represent the typical range of variation in a process and are determined by analyzing data collected over time.

Control limits act as a guide for process improvement by showing what the process is currently doing and what it should be doing. They provide a standard of comparison to identify when the process is out of control and needs attention. Control limits also indicate that a process event or measurement is likely to fall within that limit, which helps to identify common causes of variation. By distinguishing between common causes and special causes of variation, control limits help organizations to take appropriate action to improve the process.

## Calculating Control Limits

The 3-sigma method is the most commonly used method to calculate control limits.

## Step 1: Determine the Standard Deviation

The standard deviation of the data is used to calculate the control limits. Calculate the standard deviation of the data set.

## Step 2: Calculate the Mean

Calculate the mean of the data set.

## Step 3: Find the Upper Control Limit

Add three standard deviations to the mean to find the Upper Control Limit. This is the upper limit beyond which a process is considered out of control.

## Step 4: Find the Lower Control Limit

To find the Lower Control Limit, subtract three standard deviations from the mean. This is the lower limit beyond which a process is considered out of control.

## Importance of Statistical Process Control Charts

Statistical process control charts play a significant role in the Six Sigma methodology as they enable measuring and tracking process performance, identifying potential issues, and determining corrective actions.

Six Sigma control charts allow organizations to monitor process stability and make informed decisions to improve product quality. Understanding how these charts work is crucial in using them effectively. Control charts are used to plot data against time, allowing organizations to detect variations in process performance. By analyzing these variations, businesses can identify the root causes of problems and implement corrective actions to improve the overall process and product quality.

## How to Interpret Control Charts?

Interpreting control charts involves analyzing the data points for patterns such as trends, spikes, outliers, and shifts.

These patterns can indicate potential problems with the process that require corrective actions. The expected behavior of a process on a Six Sigma chart is to have data points fluctuating around the mean, with an equal number of points above and below. This is known as a process shift and common cause variation. Additionally, if the data is in control, all data points should fall within the upper and lower control limits of the chart. By monitoring and analyzing the trends and outliers in the data, control charts can provide valuable insights into the performance of a process and identify areas for improvement.

## Elements of a Control Chart

Six Sigma control charts consist of three key elements.

• A centerline representing the average value of the process output is established.
• Upper and lower control limits (UCL and LCL) are set to indicate the acceptable range of variation for the process.
• Data points representing the actual output of the process over time are plotted on the chart.

By comparing the data points to the control limits and analyzing any trends or patterns, organizations can identify when a process is going out of control and take corrective actions to improve the process quality.

## What is Subgrouping in Control Charts?

Subgrouping is a method of using Six Sigma control charts to analyze data from a process. It involves organizing data into subgroups that have the greatest similarity within them and the greatest difference between them. Subgrouping aims to reduce the number of potential variables and determine where to expend improvement efforts.

## Within-Subgroup Variation

• The range represents the within-subgroup variation.
• The R chart displays changes in the within-subgroup dispersion of the process.
• The R chart determines if the variation within subgroups is consistent.
• If the range chart is out of control, the system is not stable, and the source of the instability must be identified.

## Between-Subgroup Variation

• The difference in subgroup averages represents between-subgroup variation.
• The X Bar chart shows any changes in the average value of the process.
• The X Bar chart determines if the variation between subgroup averages is greater than the variation within the subgroup.

## X Bar Chart Analysis

• If the X Bar chart is in control, the variation “between” is lower than the variation “within.”
• If the X Bar chart is not in control, the variation “between” is greater than the variation “within.”
• The X Bar chart analysis is similar to the graphical analysis of variance (ANOVA) and provides a helpful visual representation to assess stability.

## Benefits of Subgrouping in Six Sigma Charts

• Subgrouping helps identify the sources of variation in the process.
• It reduces the number of potential variables.
• It helps determine where to expend improvement efforts.
• Subgrouping ensures consistency in the within-subgroup variation.
• It provides a graphical representation of variation and stability in the process.

Also Read: Central Limit Theorem Explained

## Master the Knowledge of Control Charts For a Successful Career in Quality Management

Control charts are a powerful tool for process improvement in the Six Sigma methodology. By monitoring process performance over time, identifying patterns and trends, and taking corrective action when necessary, organizations can improve their processes and increase efficiency, productivity, and quality. Understanding the different types of control charts, their components, and their applications is essential for successful implementation.

A crystal-clear understanding of Six Sigma control charts is essential for aspiring Lean Six Sigma experts because it allows them to understand how to monitor process performance and identify areas of improvement. By understanding when and how to use control charts, Lean Six Sigma experts can effectively identify and track issues within a process and improve it for better performance.

Becoming Six Sigma-certified is an excellent way for an aspiring Lean Six Sigma Expert to gain the necessary skills and knowledge to excel in the field. Additionally, Six Sigma certification can provide you with the tools you need to stay on top of the latest developments in the field, which can help you stay ahead of the competition.

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How Do You Improve Logistics with Six Sigma?

Process Mapping in Six Sigma: Here’s All You Need to Know

What is Root Cause Analysis and What Does it Do?

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Research Article

## Using control charts to understand community variation in COVID-19

Contributed equally to this work with: Moira Inkelas, Cheríe Blair, Lloyd P. Provost

Roles Conceptualization, Formal analysis, Methodology, Writing – original draft

* E-mail: [email protected]

Affiliations Department of Health Policy and Management, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California, United States of America, Population Health Program, Clinical and Translational Science Institute, University of California Los Angeles, Los Angeles, California, United States of America

Roles Data curation, Writing – review & editing

Affiliation Division of Infectious Diseases, Department of Medicine, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America

Roles Data curation, Formal analysis, Writing – review & editing

¶ ‡ These authors also contributed equally to this work.

Roles Conceptualization, Writing – original draft

Affiliations Population Health Program, Clinical and Translational Science Institute, University of California Los Angeles, Los Angeles, California, United States of America, Department of Family Medicine, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America

Roles Conceptualization, Formal analysis

Affiliation Department of Medicine, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America

Roles Writing – review & editing

Affiliations Population Health Program, Clinical and Translational Science Institute, University of California Los Angeles, Los Angeles, California, United States of America, Division of Critical Care Pulmonology, Department of Medicine, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America

Roles Conceptualization

Affiliations Population Health Program, Clinical and Translational Science Institute, University of California Los Angeles, Los Angeles, California, United States of America, Department of Family Medicine, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America, Department of Epidemiology, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California, United States of America, Division of Chronic Disease and Injury Prevention, Los Angeles County Department of Public Health, Los Angeles, California, United States of America

Affiliation Division of Chronic Disease and Injury Prevention, Los Angeles County Department of Public Health, Los Angeles, California, United States of America

Roles Conceptualization, Data curation, Formal analysis, Methodology, Visualization, Writing – review & editing

Affiliation Associates for Process Improvement, Austin, Texas, United States of America

• Moira Inkelas,
• Cheríe Blair,
• Daisuke Furukawa,
• Jason H. Malenfant,
• Emily Martin,
• Iheanacho Emeruwa,
• Tony Kuo,
• Lisa Arangua,

• Published: April 30, 2021
• https://doi.org/10.1371/journal.pone.0248500
• Peer Review

Decision-makers need signals for action as the coronavirus disease 2019 (COVID-19) pandemic progresses. Our aim was to demonstrate a novel use of statistical process control to provide timely and interpretable displays of COVID-19 data that inform local mitigation and containment strategies. Healthcare and other industries use statistical process control to study variation and disaggregate data for purposes of understanding behavior of processes and systems and intervening on them. We developed control charts at the county and city/neighborhood level within one state (California) to illustrate their potential value for decision-makers. We found that COVID-19 rates vary by region and subregion, with periods of exponential and non-exponential growth and decline. Such disaggregation provides granularity that decision-makers can use to respond to the pandemic. The annotated time series presentation connects events and policies with observed data that may help mobilize and direct the actions of residents and other stakeholders. Policy-makers and communities require access to relevant, accurate data to respond to the evolving COVID-19 pandemic. Control charts could prove valuable given their potential ease of use and interpretability in real-time decision-making and for communication about the pandemic at a meaningful level for communities.

Citation: Inkelas M, Blair C, Furukawa D, Manuel VG, Malenfant JH, Martin E, et al. (2021) Using control charts to understand community variation in COVID-19. PLoS ONE 16(4): e0248500. https://doi.org/10.1371/journal.pone.0248500

Editor: Arthur Wakefield Baker, Duke University, UNITED STATES

Received: August 3, 2020; Accepted: February 26, 2021; Published: April 30, 2021

Copyright: © 2021 Inkelas et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are uploaded to GitHub ( https://github.com/datadesk/california-coronavirus-data#latimes-county-totalscsv ).

Funding: The research described was supported, in part, by the National Institutes of Health /National Center for Advancing Translational Sciences through UCLA CTSI Grant Number UL1TR000124 and the UCLA CTSI TL1 Grant Number TL1TR001883. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. API provided support in the form of salary for author LP but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles are articulated in the ‘author contributions’ section.

Competing interests: API provided support in the form of salaries for author LP. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

## Introduction

Coronavirus disease 2019 (COVID-19) mitigation and containment policies have significant economic, social, and health impact. Enacting sensible public policies in the COVID-19 pandemic requires real-time data that public leaders can easily interpret and act on. The constituencies for these data are expanding as regional and community stakeholders, including cities, businesses, and school districts, assume decision-making roles in the emergency response. Moreover, given that public health interventions require public cooperation and trust in guidance and decisions that are data-driven, there is also a need to engage the public at large to successfully implement mitigation and containment strategies. Offering data to inform policy and individual health behavior is a cornerstone of prevention and public health practice [ 1 ].

While providing relevant, accessible, and timely data is a core public health function, current displays of COVID-19 data lack features that policy-makers require for decision-making and that communities need to make the connection between their actions and the state of the pandemic. Such displays often use maps, day-to-day percentage changes, and cumulative counts that refresh daily. These formats obscure variation across places, populations, and time, which are essential to learning how actions and events affect COVID-19 cases and deaths. Over-aggregation impairs the ability of decision-makers to make real-time policy adjustments and to assess the impact of these adjustments. The public is unable to see local data that are most relevant and motivating to them regarding health behaviors [ 2 ].

Statistical process control method and theory focuses on ease of use and interpretation for end users [ 3 – 7 ] and learning under conditions of uncertainty [ 8 , 9 ]. Many commercial, healthcare, and education organizations use control charts to understand the behavior of processes or systems over time [ 8 – 11 ]. By distinguishing random (“common cause”) variation from non-random (“special cause”) variation, control charts reduce over-reaction to noise in data while enabling timely response when true signals show that conditions are improving or deteriorating [ 11 ]. They enable scientists, policy-makers, and community members alike to learn if a change to a policy or process has affected an outcome of interest [ 11 – 13 ]. Control charts can be used for multiple common types of data distributions including classification (binomial) P charts, continuous (Xbar charts) and individuals (I charts), and count (Poisson) C charts or U charts [ 12 ].

Despite their potential value, control charts are not part of standard public health practice [ 11 – 16 ]. This article illustrates how control charts can be used to achieve public health goals in the COVID-19 pandemic. We offer prototype control charts and displays to demonstrate their utility.

## Statistical process control

Control charts display data in an ordered format, most often ordered over time, to understand, manage, and improve the behavior of a specific process or system. The control chart includes a centerline (i.e., the mean of the data) and upper- and lower-control limits, which are three sigma above and below the centerline. When the measure is stable over time, the centerline and limits provide a rational prediction of future observations [ 12 ]. Values outside of the control limits indicate that the outcome is not being produced from one consistent homogeneous process [ 3 , 4 ]. When there is a signal of change, the centerline and control limits shift to reflect the new level of performance [ 12 ]. This study uses a hybrid control chart for count data and exponential growth or decline (I chart) developed by Perla et al. for use in a pandemic [ 17 – 19 ].

## Data sources on COVID-19 cases

This study analyzed data for selected regions of California. The county-level control charts use daily counts of COVID-19 from the Los Angeles Times COVID-19 repository, which provides a public datafile of cases reported by California counties [ 20 ]. The original data source is the Confidentiality Morbidity Report (CMR16) of laboratory-confirmed COVID-19 that counties report to the California Department of Health Care Services. The Los Angeles County Department of Public Health (LAC DPH) reports data for 272 distinct cities and neighborhoods.

## Control chart analysis

The control charts display daily reported COVID-19 cases. Charts for counties begin on March 2, 2020 and charts within LA County begin on March 16 for consistency. This study uses the hybrid control chart method developed by Perla et al. [ 17 ] to view epochs and phases in the pandemic. The four possible epochs are pre-exponential growth (C-chart), exponential growth (an individuals (I) chart fitted to log10 of the data series and transformed back to the original scale), post-exponential growth (a flat trajectory or exponential decline that is represented by an I chart), and stability after descent (C-chart) [ 17 , 21 , 22 ]. A region may experience one or multiple epochs. A phase is a time period that is represented by a distinct control chart; there can be multiple phases within an epoch.

To estimate the centerline and upper and lower control limits, the method requires at least eight observations to meet the minimum requirements for an effective C-chart [ 12 ] in the first and fourth epochs. The control charts automatically set the limits of the exponential growth period based on regression analysis of the first 20 observations [ 17 ]. The exponential growth phase is modeled by the log-linear regression I-chart [ 12 ]. We used model coding in R developed by Perla et al. [ 21 , 22 ] to transform the counts using the log10 function and calculated the intercept and slope through regression analysis for the log10 data; the regression line becomes the centerline (CL). Limits for the exponential phase in the charts are calculated from the median moving range of the residuals, with the upper limit (UL) and lower limit (LL) calculated as CL+3.14*MRbar and CL-3.14*MRbar, respectively. The CL, UL, and LL were then transformed to the original count scale. Charts that do not display an exponential growth phase are in C-chart format for the full period studied.

Formal use of control charts identifies special cause through established statistical rules combined with inspection by experts in the system being studied. Standard criteria for special cause are an observation outside of an upper or lower control limit or a shift of 8 successive observations above or below the centerline [ 11 , 12 ]. For the exponential Epochs 2 and 3, we used Shewhart criteria modified by Perla et al. [ 17 , 22 ], which require two points rather than one point above the control limits to signal the start of a new phase. The rationale is that COVID-19 data displays more than “usual” variation in the form of single large values that reflect “data dumps” from reporting entities; requiring a stronger signal prevents such a data artifact from triggering a new phase [ 22 ].

Notably, time series charts often reveal reporting artifacts. An example is peak values early in the week due to cases accumulating over a weekend. It is common practice in control charts to remove special cause variation due to such cyclic behavior by separating data lines within a chart or by subgrouping by a larger unit (i.e. week rather than day) to smooth variation. In this study, we preserved daily periodicity based on the statistical principles underlying control chart methodology, which is that data should not be summarized if it would mislead the user into taking actions that would not be taken had the original data been preserved [ 6 ]. Smoothing the data in these COVID-19 control charts would temper but not remove the apparent case reporting artifact, and seeing these patterns offers insights, namely that there is an impact from facility case reporting.

## Description of California counties and LA County subregions included in the analysis

California is home to more than 12 percent of the U.S. population and has a complex geopolitical landscape with 58 distinct counties. LA County is a vast region with over 10 million residents, 88 cities (including the City of Los Angeles), 272 designated neighborhoods, and three public health departments, of which the largest is the LAC DPH.

## Selection of counties and LA County subregions for inclusion in the analysis.

The study team selected an illustrative set of charts using criteria relevant to the COVID-19 pandemic. We included five counties from the second, third, and fourth quartiles for population and from northern, central, and southern regions of California. We selected one neighborhood and four cities within LA County. Within LA County, we sought variation in sociodemographic factors that we considered to be especially relevant to the COVID-19 pandemic: median income, overall health, median age, race/ethnicity, population density (people per square mile), median household size, and percentage of households that experience household crowding, which is a measure derived from the U.S. Census that is defined as the percentage of households with a ratio of total household members to rooms (excluding bathrooms) greater than one.

## Data sources.

Table 1 shows sociodemographics of selected areas. Measures of population, race/ethnicity, median income, household size, and population density come from the United States Census Bureau QuickFacts (2019) [ 23 ]. Median age comes from the 2018 American Community Survey (ACS) published by Towncharts [ 24 ]. Household crowding comes from the California Healthy Places Index (Public Health Alliance of Southern California) based on an ACS five year average for 2011–2015 [ 25 ]. Quartiles of health come from an overall ranking developed by County Health Rankings & Roadmaps (University of Wisconsin) that combines multiple health outcomes including premature death, poor or fair health, poor physical health days, poor mental health days, and low birthweight [ 26 ]. For the neighborhood within LA County, race/ethnicity comes from L.A. Mapping (Los Angeles Times) [ 27 ].

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https://doi.org/10.1371/journal.pone.0248500.t001

Table 1 also shows the proportion of COVID-19 cases from congregate living facilities in the first four months of the pandemic (March through June 2020); these data are available for some but not all counties through their public health department websites. For LA County overall and for cities and neighborhoods within the County, the congregate counts include cases from residential health and living facilities including skilled nursing facilities (SNFs), shelters, and correctional facilities. The congregate measure for Santa Clara County includes only residential long term care facilities [ 28 ]. The LA County DPH website provides COVID-19 test volume rates per 100,000 population by area, based on electronic lab reporting; the number per 100,000 in January 2021 showed modest variation for the areas in this study: 32,569 for Santa Monica, 19,279 for Lancaster, 26,980 for Bell, and 26,730 for Westlake.

Figs 1 and 2 show control charts for five counties. Four counties experienced exponential growth in COVID-19 cases in early March 2020, which was followed by a period of lower exponential growth in three and non-exponential growth in one. Each county experienced at least one period of exponential growth; one county (Santa Clara) experienced no exponential growth until a November surge that was observed in all counties. Imperial County showed a cyclic weekly pattern associated with the lack of case reporting on weekends; this analysis retained all days in the chart for comparability with other counties.

Shows daily case counts, midline, and upper and lower control limits. Source for county data is the New York Times. Source for Los Angeles cities/neighborhoods is the Department of Public Health COVID-19 dashboard (accessed 1/10/2020).

https://doi.org/10.1371/journal.pone.0248500.g001

https://doi.org/10.1371/journal.pone.0248500.g002

There was considerable variation in COVID-19 cases over time among the studied subregions in LA County. Two (Lancaster, Fig 1 and Lynwood, Fig 2 ) experienced initial exponential growth followed by a second phase of exponential growth with a lower midline before transitioning to a non-exponential epoch. Another (Westlake) experienced initial exponential growth and then entered a non-exponential epoch with multiple phases through the study period. This neighborhood had the highest residential density and household overcrowding relative to others as well as large household size (median of 3.0) ( Table 1 ). Other areas with relatively high crowding and household size experienced multiple phases but no exponential rise until late 2020. The city with the highest median income and lowest rate of overcrowding (Santa Monica) showed low case counts throughout the study period with a doubled rate in the last month of the study. For the first four months of the study period, nearly half (46%) of cases in this city came from congregate facilities, while the rate ranged from 15% to 28% for other areas.

Several subregions show one or two non-sequential daily rates that exceed the upper control limit; these may be due to reporting patterns from laboratories or the public health department.

Fig 2 shows charts for the City of Lynwood and LA County with annotated events such as public health authority COVID-19 orders, introduction of free testing centers, and holidays. The Lynwood chart is annotated with additional policies that are specific to this city, such as mandated use of facial coverings in public in the first week of April, about six weeks earlier than LA County. The charts show different time trends. The exponential epoch ended in Lynwood in June; a new phase of exponential rate in LA County began at the end of that month. Neither chart shows special cause several weeks after major holidays including Mother’s Day, the Fourth of July, and Labor Day.

During the COVID-19 pandemic, decision-makers need signals from data to intensify or relax safety requirements. Control charts are a tool for daily learning and action that public health could benefit from [ 29 – 31 ]. This study shows how a novel hybrid control chart could assist authorities to act early by signaling exponential and non-exponential growth or decline in public health measures. Control charts are commonly used in management and can be used in public health to distinguish random from meaningful variation. Use of this method could reduce overreaction to expected random variation and encourage immediate action when special cause variation signals a new phase or epoch of the pandemic.

Based on this study, a division within LAC DPH incorporated control charts into their approach for identifying COVID-19 outbreaks.

This study shows the value of disaggregating data as the large-scale closures that characterized the initial emergency response to COVID-19 evolved into metric-focused decision-making. California adopted six indicators for relaxing the initial safer-at-home order [ 32 ] and introduced a tiered system based on local data in October 2020 [ 33 ] as local authorities adopted additional policies. Disaggregation by region and time helps state, county, and within-county authorities act on the data. For example, local authorities could use the significant within-county variation to communicate to the public what is happening in specific neighborhoods and potentially to consider mitigation strategies that customize to subregions. Further, the study shows that a city could be mischaracterized as experiencing an outbreak of COVID-19 cases because case counts for the general public and congregate living populations are combined. This was especially relevant early in the pandemic when skilled nursing facilities accounted for a significant proportion of COVID-19 cases. Local jurisdictions may need this differentiation to target strategies–for example, if most cases are in congregate facilities. Disaggregated data could also enable a school district to consider if patterns in neighborhoods that feed into specific schools warrant augmented mitigation strategies.

Control charts such as those in this study can be easily interpreted once their format is understood. They can help localities check assumptions about time trends and assess the impact of planned changes (policies) and external influences (such as holidays). Their visual simplicity is designed for analysis, discussion, and decision-making. The disaggregated, time-ordered format can empower people in a specific city or neighborhood to identify potential causes of what they observe in the data. These COVID-19 charts may provide the same benefit to local communities during the pandemic as control charts offer to industries that use them for improving clinical care or other processes.

The interpretation of these charts is aided by annotation of key events. Especially when done in real time, annotation makes it possible to observe if specific policies or events are followed by signals of a new phase or epoch. This study shows that assumptions about increased COVID-19 cases following holidays such as Mother’s Day, the Fourth of July, and Labor Day were not borne out in the county or neighborhood data. Users of these control charts can employ the Bradford Hill causality criteria to aid interpretation [ 34 ]. Additionally, complementing control charts with a small number of meaningful measures, such as residential density and household size, helps decision-makers and the public interpret observed variation by area and over time. Local health agencies could work with cities to identify appropriate measures that aid interpretation, such as housing features and rates of mask-wearing. Other analytical methods such as modeling associations of demographics or other subregion features with case counts can complement control charts.

Lastly, the time-ordered format of a control chart contrasts with how public health data are often analyzed and displayed. Reporting patterns by public health departments (e.g., batch reporting by facilities, weekday versus weekend reporting, inclusion of congregate living residents and homeless individuals in cumulative case reporting, availability of illness dates versus reporting dates) could shape how stakeholders interpret the data. At minimum, control charts can make these limitations transparent and prompt decision-makers to ask for more interpretable displays. Engaging decision-makers in such discussions may help to justify public health investment in data reporting and analytics so that such questions can be answered from the outset in future outbreaks.

Notably, this study is limited in the interpretation of the displayed control charts. Statistical process control was intended for use in real time by people with intimate knowledge of the system, process, or community that the underlying data represent. Proper interpretation of data comes from engaged discussion. This study offers some possible interpretations of the observed special cause variation, but the purpose was to illustrate the approach rather than draw causal conclusions about policy events and COVID-19 cases. Rather than interpreting the data for action, the study intended to examine if areas exhibited variation and to illustrate the potential value of providing disaggregated data in control chart format to people who can make immediate use of them. Finally, COVID-19 case counts underestimate total COVID-19 cases, and there may be noise in the case counts that result from limited staffing for data entry, delayed reporting of cases out of jurisdiction, and the impact of time-varying testing constraints and laboratory turn-around-time, among others, which may vary by county and over time.

As with all significant changes to data reporting and analytics, adopting control chart methods will require time and resource investment. LAC DPH’s interest in using control charts to help inform outbreak management followed a series of virtual workshops on the method that a university partner offered to public health personnel. Health departments will need to create these displays and prepare their workforce to use them effectively, ideally as real-time learning tools. For optimal impact, public health personnel will need to assist community stakeholders to interpret and use the charts to meet their specific needs. Progress in this area for health authorities and their partnered community stakeholders has been made for topics such as infant mortality through learning collaboratives of state and local health departments [ 14 ] and in training programs for local health authorities [ 31 ].

## Conclusions

The COVID-19 pandemic has placed unprecedented data and analytic demands on public health. Clear, interpretable, disaggregated displays are essential tools for policy makers as they consider the health, economic, social, mental health, and educational burden of COVID-19 in their communities. Showing the data underlying public policy decisions could increase uptake of guidance regarding personal and collective behavior in communities. This may have been a missed opportunity as the COVID-19 pandemic progressed from an initial, centralized emergency response to a period of distributed decision-making on the part of employers, cities, school districts, and others. Healthcare organizations use control charts for learning and to encourage data-driven collective action [ 15 , 35 , 36 ]. Public health and population-oriented systems could also make use of this method. This statistical method provides an easy, effective, and inexpensive way for public health departments to meet some of the informational needs of governors, city councils, school boards, and the general public during an emergency response when timeliness of and insight from data are of utmost importance. Use of control charts in public health will require an appreciation of their value and investment of time and resources into their creation and use.

• 1. Public Health Accreditation Board. Standards and measures, version 1.5. December 2013. Alexandria, VA.
• View Article
• PubMed/NCBI
• 6. Moen R, Nolan T, Provost LP. Quality improvement through planned experimentation: Third edition. McGraw Hill. 2012.
• 7. Wheeler DJ. Understanding variation: The key to managing chaos: Second edition. SPC Press. 2000.
• 8. Deming WE. The New Economics for Industry, Government, and Education. Second edition. 2000.
• 12. Provost LP, Murray SK. The health care data guide: Learning from data for improvement. Jossey-Bass, San Francisco. 2011.
• 13. Bryk AS, Gomez LM, Grunow A, LeMahieu PG. Learning to improve: How America’s schools can get better at getting better. Harvard Education Press. 2015.
• 16. Perla R. Governors: Read this before reopening your state. U.S. News & World Report. April 14, 2020. https://www.usnews.com/news/healthiest-communities/articles/2020-04-14/the-coronavirus-data-model-governors-and-states-need-to-see .
• 18. Out of the crisis: Understanding variation in COVID-19 reported deaths in the US using Shewhart control charts. Institute for Healthcare Improvement (IHI). 2020. (Available on ihi.org).
• 19. COVID-19 Data Dashboard. COVID-19 Reported Deaths: Using Shewhart Control Charts to Understand Variation. Boston: Institute for Healthcare Improvement. 2020. (Available on ihi.org)
• 20. The Los Angeles Times. California Coronavirus Data. https://github.com/datadesk/california-coronavirus-data#latimes-county-totalscsv . Accessed January 11, 2021.
• 21. Perla RJ, Provost SM, Parry GJ, Little K, Provost LP. Shewhart charts for COVID-19 reported deaths. November 3, 2020. https://isqua.org/latest-blog/shewhart-charts-for-covid-19-reported-deaths.html . Accessed January 11, 2021.
• 22. Little K. Scripts to generate control chart limits used by IHI’s PowerBI application. November 10, 2020. https://github.com/klittle314/IHI_Covid_Public/blob/main/README.md . Accessed January 11, 2021.
• 23. United States Census Bureau. QuickFacts. https://www.census.gov/quickfacts/ . Accessed May 30, 2020.
• 24. Towncharts. https://www.towncharts.com/About-Towncharts-Data.html . Accessed May 30, 2020.
• 25. Public Health Alliance of Southern California. The California Healthy Places Index. https://map.healthyplacesindex.org/ . Accessed May 30, 2020.
• 26. University of Wisconsin Population Health Institute (UWPHI). County Health Rankings Report: California. Accessed May 30, 2020.
• 27. Mapping LA. Los Angeles Times. http://maps.latimes.com/neighborhoods/ Accessed May 30, 2020.
• 28. County of Santa Clara Emergency Operations. Coronavirus (COVID-19) data dashboard. Available at https://www.sccgov.org/sites/covid19/Pages/dashboard.aspx#LTCF . Accessed May 30, 2020.
• 29. Perla RJ, Provost L, Parry G. COVID-19 deaths in the U.S. have taken a turn for the worse. U.S. News & World Report. November 10, 2020. https://www.usnews.com/news/healthiest-communities/articles/2020-11-10/covid-deaths-in-the-us-are-poised-to-surge-model-shows
• 32. Governor Newsom outlines Six Critical Indicators the State will Consider Before Modifying the Stay-at-Home Order and Other COVID-19 Interventions. April 14, 2020.
• 33. California Department of Public Health. Blueprint for a safer economy. Covid19.ca.gov/safer-economy/ Accessed January 11, 2021.
• 800 -274-2874
• [email protected]

## Control Chart Rules and Interpretation

Control charts are a valuable tool for monitoring process performance.  However, you have to be able to interpret the control chart for it to be of any value to you.  Is communication important in your life?  Of course it is – both at work and at home.  Here is the key to effectively using control charts – the control chart is the way the process communicates with you.  Through the control chart, the process will let you know if everything is “under control” or if there is a problem present.  Potential problems include large or small shifts, upward or downward trends, points alternating up or down over time and the presence of mixtures.

This month’s publication examines 8 rules that you can use to help you interpret what your control chart is communicating to you.  These rules help you identify when the variation on your control chart is no longer random, but forms a pattern that is described by one or more of these eight rules.   These patterns give you insights into what may be causing the “special causes” – the problem in your process.

In this issue:

## Variation Review

Control chart review, the 8 control chart rules, possible causes by pattern.

• Video: Interpreting Control Charts

We have covered variation in 11 publications over the years.  Here is an excerpt from one:

Variation comes from two sources, common and special causes. Think about how long it takes you to get to work in the morning. Maybe it takes you 30 minutes on average. Some days it may take a little longer, some days a little shorter. But as long as you are within a certain range, you are not concerned. The range may be from 25 to 35 minutes. This variation represents common cause variation — it is the variation that is always present in the process. And this type of variation is consistent and predictable. You don’t know how long it will take to get to work tomorrow, but you know that it will be between 25 and 35 minutes as long as the process remains the same.

Now, suppose you have a flat tire when driving to work. How long will it take you to get to work? Definitely longer than the 25 to 35 minutes in your “normal” variation. Maybe it takes you an hour longer. This is a special cause of variation. Something is different. Something happened that was not supposed to happen. It is not part of the normal process. Special causes are not predictable and are sporadic in nature.

It has been estimated that 94% of the problems a company faces are due to common causes. Only 6% are due to special causes (that may or may not be people related). So, if you always blame problems on people, you will be wrong at least 85% of the time. It is the process most of the time that needs to be changed. Management must set up the system to allow the processes to be changed.”

The only effective way to separate common causes from special causes of variation is through the use of control charts.  A control chart monitors a process variable over time – e.g., the time to get to work.  The average is calculated after you have sufficient data.  The control limits are calculated – an upper control limit (UCL) and a lower control limit (LCL).  The UCL is the largest value you would expect from a process with just common causes of variation present. The LCL is the smallest value you would expect with just common cause of variation present.   As long as the all the points are within the limits and there are no patterns, only common causes of variation are present. The process is said to be “in control.”

Figure 1: Control Chart Example

There is one point beyond the UCL in Figure 1.  This is the first pattern that signifies an out of control point – a special cause of variation.  One possible cause is the flat tire.   There are many other possible causes as well – car break down, bad weather, etc.

Some of these patterns depend on “zones” in a control chart.    To see if these patterns exits, a control chart is divided into three equal zones above and below the average.  This is shown in Figure 2.

Figure 2: Control Chart Divided into Zones

Zone C is the zone closest to the average.  It represents the area from the average to one sigma above the average.  There is a corresponding zone C below the average.  Zone B is the zone from one sigma to two sigma above the average.  Again, there is a corresponding Zone B below the average. Zone A is the zone from two sigma to three sigma above the average – as well as below the average.

If a process is in statistical control, most of the points will be near the average, some will be closer to the control limits and no points will be beyond the control limits.  The 8 control chart rules listed in Table 1 give you indications that there are special causes of variation present.    Again, these represent patterns.

Table 1: Control Chart Rules

Our SPC for Excel software handles all these out of control tests.

It should be noted that the numbers can be different depending upon the source.  For example, some sources will use 8 consecutive points on one side of the average (Zone C test) instead of the 7 shown in the table above.  But they are all very similar.  Figures 3 through 5 illustrate the patterns.  Figure 3 shows the patterns for Rules 1 to 4.

Figure 3: Zone Tests (Rules 1 to 4)

Rules 1 (points beyond the control limits) and 2 (zone A test) represent sudden, large shifts from the average.  These are often fleeting – a one-time occurrence of a special cause – like the flat tire when driving to work.

Rules 3 (zone B) and 4 (Zone C) represent smaller shifts that are maintained over time.  A change in raw material could cause these smaller shifts.  The key is that the shifts are maintained over time – at least over a longer time frame than Rules 1 and 2.

Figure 4 shows Rules 5 and 6.  Rule 5 (trending up or trending down) represents a process that is trending in one direction.  For example, tool wearing could cause this type of trend.  Rule 6 (mixture) occurs when you have more than one process present and are sampling each process by itself.   Hence the mixture term.   For example, you might be taking data from four different shifts.  Shifts 1 and 2 operate at a different average than shifts 3 and 4.  The control chart could have shifts 1 and 2 in zone B or beyond above the average and shifts 3 and 4 in zone B below the average – with nothing in zone C.

Figure 4: Rules 5 and 6

Figure 5 shows rules 7 and 8.   Rule 7 (stratification) also occurs when you have multiple processes but you are including all the processes in a subgroup.  This can lead to the data “hugging” the average – all the points in zone C with no points beyond zone C.  Rule 8 (over-control) is often due to over adjustment.  This is often called “tampering” with the process.  Adjusting a process that is in statistical control actually increases the process variation.    For example, an operator is trying to hit a certain value.  If the result is above that value, the operator makes an adjustment to lower the value.  If the result is below that value, the operator makes an adjust to raise the value.  This results in a saw-tooth pattern.

Figure 5: Rules 7 and 8

Rules 6 and 7, in particular, often occur because of the way the data are subgrouped.  Rational subgrouping is an important part of setting up an effective control chart.   A previous publication demonstrates how mixture and stratification can occur based on the subgrouping selected.

These rules represent different situations – patterns = on a control chart.  It should be noted that not all rules apply to all types of control charts.  Table 2 summaries the rules by the type of pattern.

Table 2: Rules by Type of Pattern

It is difficult to list possible causes for each pattern because special causes (just like common causes) are very dependent on the type of process.  Manufacturing processes have different issues that service processes.  Different types of control chart look at different sources of variation.  Still, it is helpful to show some possible causes by pattern description.  Table 3 attempts to do this based on the type of pattern.

Table 3: Possible Causes by Pattern

Table 3 provides some guidance on what you should be thinking about as you try to find the reasons for special causes.  For example, if Rule 1 or Rule 2 is violated, you should be asking “what in this process could cause a large shift from the average?”.  Or if Rule 6 occurs, you should be asking “what in this process could cause there to be more than one process present?”  These type of questions can help guide brainstorming sessions to find the reasons for the special cause of variation.   The type of pattern can guide your analysis of the out of control point.

This publication took a look at the 8 control chart rules for identifying the presence of a special cause of variation.  The rules describe certain patterns of variation that will give you insights on where to look for the special cause of variation.  No one table can give you the reasons for out of control points in your process.  You have to use your own knowledge (and that of those closest to the process) to discover the reason.  Our SPC for Excel software handles all the out of control charts.

## Video: Interpeting Control Charts

• SPC for Excel Software
• SPC Training
• SPC Consulting
• Ordering Information

Thanks so much for reading our SPC Knowledge Base. We hope you find it informative and useful. Happy charting and may the data always support your position.

Dr. Bill McNeese BPI Consulting, LLC

## Connect with Us

• Control Chart Basics
• How Control Charts Work: Control Limits and Specifications
• Control Charts and Data Overload
• The Impact of Out of Control Points on Baseline Control Limits
• Which Out of Control Tests Should I Use?
• The Average Run Length and Detecting Process Shifts
• Control Charts and Adjusting a Process
• The Problem of In Control but Out of Specifications
• How to Mess Up Using Control Charts
• The Difficulty of Setting Baseline Data for Control Charts
• Control Charts, ANOVA, and Variation
• Three Sigma Limits and Control Charts
• Control Charts and the Central Limit Theorem
• Applying the Out of Control Tests
• How Much Data Do I Need to Calculate Control Limits?
• The Estimated Standard Deviation and Control Charts
• My Process is Out of Control! Now What Do I Do?
• When to Calculate, Lock, and Recalculate Control Limits
• The Purpose of Control Charts
• Control Limits – Where Do They Come From?
• Selecting the Right Control Chart
• The Impact of Statistical Control
• Use of Control Charts
• Control Strategies
• Interpreting Control Charts

Hi!  Your page has been significantly helpful.  Can you tell me how these rules would apply for an individuals-moving range chart?  Can these zones still be created?  Thanks in advance!

The zones test can be applied to the individuals chart; not the moving range chart.  I probably need to do an article of what rules apply to which charts.  But all apply the individuals chart.  On the moving range, points beyond the limits, a run below or above the average (twice as long as individuals chart since each data point is reused in the moving range, overcontrol, an seven trending up or down.

Hi Bill – useful stuff. However, I'm struggling to understand which Control Chart rules I should apply. For example, do I use Westgard, Nelson, WECO etc. – none of which seem to be the rules you've listed above. Are you able to shed any light on which rules to use on an individuals chart? Thanks.

Of course, points beyond the control limits always apply.  With the X chart for individuals, you apply all the rules listed in the article.  However, with the moving range chart, you only use points beyond the control limts, and long runs above or below the average range or trending up or down.   This is because you are reusing the data.  I will do the next publication on which tests apply to which charts.  Software, like SPC for Excel, will automatically select the appropraite tests for the control chart although you can change those options.

Sorry…I suppose what I was really trying to say is that there are slight variations to the available sets of rules. As I’m only just entering the world of SPC charts, my understanding is that WECO is the original set of rules (pretty much a cornerstone for all rule sets) and since then, newer iterations such as Nelson and Westgard have been developed. Therefore, I’m confused on which set of rules I should use. In Rule 5 above, you state the need to observe at least 7 consecutive points whereas Nelson rules (rule 3) state the requirement to observe at least 6. Is there a “correct” choice, or does it come down to how long you wish to observe a trend for before determining it to be out of control? Thanks.

Yes, there are slight variations in the rules.   Some have 7, others 6, others 8.   There is not a correct choice as such.  You are correct – it is how "sure" you want to be that there is signal.  Suppose we were tossing a coin and you paid me a dollar each time it was heads and I paid you a dollar each times it was tails.  If I got six heads in a row, you would start wondering about the coin.  7 times in a row you would wonder even more.  By 8 times, I am sure you think the coin is not a true coin. For example, consider a run above the average.  What is the probablity of getting 6 points in a row above the average?  It is 1.56% (simply .5^6).  For 7 points, it is 0.78%.  For 8 points it is 0.39%.  It is really your choice.  The probability of getting a point beyond the control limits for a true normal distribution (doesn't exist) is 0.27%.  So, picking something around there for the other tests is a good way to approach this – so 7 or 8 points looks good to me.

Hi Bill,Thanks for your page. It is indeed very useful. Tell me, when is it possible for  a control chart which is in control to be actually out of control?Regards, John

Thanks John.  Not sure I fully understand your question.  There is no way to assign a probability to a point being a special cause or not.  A point beyond the control limits could just be common cause of variation.  And just because a point is within the control limits does notmean there is a not a special cause of variation present.  The rules simply give a way of reacting to certain conditions that most likely are out of control points.

Your explanation in this article is really quite good, with one exception. Nowwhere in the article do you mention that the rules you are applying are intended only for use with averages ; usually of n=2 to 5 individual points. This is vitally important. Grouped means (histograms) are always normal distributions, whereas grouped individuals are totally unpredictable. They can result in a wide variety of distributions, usually not normally distributed. The makes control charting of individuals very risky, because the distribution is not normal, most of the time. The Shewart control chart was derived soley for averages, because they are always normal distributions, therebye predictable.

Hi! I work with pharmaceutical compressing process to create tablets, and I have some doubts about our chart crontol. From time to time we take some tablets samples and we analize some parameters like weight. The problem is: my samples have 30 tablets each, and I can't take the individual tablets in the exactly moment they leave the machine. So, how can I analize some events like shifts if I don't have the time precision of wich tablet? I'm from Brazil and we don't have here enought information about the topic. I really could use some help. =) Could you contact me?   Kind Regrats!

thanks for great explain, would u help to Calculate the probability that an in-control process will yield the “Simplified” Runs Rule violation of having 2 consecutive points at 1.5sigma or beyond

If you have Excel, you can use the NORMSDIST(z) function (or NORM.S.DIST for Excel 2001 and later) to determine this.  For example, the probability of getting a point below 1.5 sigma is NORMSDIST(-1.5) = 0.0668 or about 6.68%.  The probability of geting two beyond 1.5 sigma on the same side of the average is 0.0668^2 or .0045.

thanks for this article it’s really helpful. I wonder is there a standard to define when a process is back in control? How many points ‘under control’ would we need to observe after a special cause event to think it was back in control. I am trying to develop a simple “in control? Yes/No” indicator to sit along side our SPC charts. I don’t want to be continually alerting that there was a single blip 8 months ago for example. Any advice? Thanks

It is back in control, in my opinion, if the next point is back within the control limits – if it is a fleeting special cause of variation that comes and goes.  But suppose that out of control point stays around.  You have a point above the upper control limit.  The next point is back within the limits but it is above the upper control limit.  If it stays about the average for a run and you can't find out why, then you have re-calculate the control limits or adjust the process to bring it back into control.  This link has more details:

<span style="font-size: 13.008px;"> https://www.spcforexcel.com/knowledge/control-chart-basics/when-calculate-lock-and-recalculate-control-limits</span&gt ;

Dear Bill, thank you for the nice and clear explanation. I have one question, Shewhart control chart can still be created if the data are not normal, right? What about these interpretations, they can only be used if the data are normal? or can some of them be applied in case of non normality of the available whole data for the analysis? Thank you.

Thank you.  The data does not have to be normally distributed to use a control chart.  Most Xbar data is symmetrical assuming the subgroup size is large enough.  The zones tests require some symmetry about the average, but basically, you should not worry about normality.  You know  your process and will know if a control chart is signalling a special case most likely.

the method of calculation and underlying statistical basis for establishing the UCL & LCL is not clear in your article.  what are the calculations, and on what are they based?? thanks.

Hello, The calculations vary based on the type of control chart.  Please see this link for the various variable control charts: https://www.spcforexcel.com/spc-for-excel-publications-category#variable This link explains in genearl were they come from: https://www.spcforexcel.com/knowledge/control-chart-basics/control-limits

Hi Dr. Bill.Your info is really helpful. I just started to work on Control Chart that why have some basic question.We have a #4 trend for almost 2 years. I checked all the samples, Technician, collecting data process and machine are OK. I just keep an eye on it.  I have questions:1. If we have to make comment on this trend like  ” In control “ or “ Out of Control”.  Can we say “Our Control chart is IN CONTROL, we need to keep an eye on it and react whenever we got outliner“ ?2. If all condition is the same but the trend Is #4 for long time. Do we need to recalculate Control limit? What can I say to convince other ones to recalculate Control limit?Thx Dr. Mike Nguyen

If you have a long run above the average (or below), it means that something has changed to cause the average to move up or down.  It is "out of contorl".  If you can't find what happened – and it doesn't bascially change the product, then you can recalculate the control limits starting with the shift changed.  And use those for the future.

Texts over the years have allowed  e.g. 1 in 25 or 2 in ~50 points outside Control Limits w/o stating "out of control."  In your experience with data or reference material texts have you encountered any rule re:  % of points beyond limits.  At times I will deal with >50 or 100 Control Chart points.  Thanks…

A rough rule i have used over the years is that a process is pretty stable if less than 5% of thepoints are out of control.  That is close to what you reference.

Is there a hirearchy for these rules?  In other words, how would they be ranked in order of statictical significance?

You can theortically put a statistical probability to each rule assuming a normal distribution – they are all about the same probability.  In practical terms, start with the points beyond the control limits, then add the test for zone C later and then zone A and B after that.  This approach seems to work well.

Dr, McNeese: My background is in electromagnetic fields and measurements of such for safety purposes. The issue of how often instruments that are used for these measurements should be recalibrated is a common question. A presentation available on the web at http://aashtoresource.org/docs/default-source/newsletter/calibrationintervalspresentation.pdf suggests the use of control charts as one possible approach to assessing the need for recalibrating an instrument. Being totally unfamiliar with control charts, I am confused and hope you can shed some light on this matter. For instruments that are typicaly recalibrated once per year, how would control charts be used to suggest that either a longer, or shorter, recalibration interval might be acceptable? The primary objective is to determine an appropriate recalibration interval. If I follow the suggestion, it would seem that long term experience from repetititve calibrations would be required to accumulate sufficient data before one could deduce whether shorter or longer recal intervals were appropriate. Thank you for your insight.

Hello Richard, You are correct that it takes experience to judge how often to check the calibration of an instrument.  If it is critical to production, you should check it more frequently.  For example, when I ran a QC lab years ago, we checked each crtiical test at the start of each shift.  There are probably istruments that don't move too much or don't move in such a way to impact production – you might check those for calibration monthly or longer – it all depends on the situation.  Your knowledge of the process is a key in deciding.

if all the observations are within control limits, does that guarantee that the process variation contains only randomness?

No, it does not.  It is possible there are special causes of variation present even if the point is witin the control limits, just as it is possible that an out of control point could be due to common causes.  The control limits provide an economic way of being fairly sure there is a special cause of variation before you spend time and money looking for it.

Hi Bill, can you help me answer this question? Thank you so much.Control charts are used to monitor and control a process. They use control limits to define the range of natural variation in a process. If a sample is taken and the plot point falls outside of the control limits what does this​ signify? the process is in control. the process is out of control and should be checked for natural variation. the process should be monitored for future results. the process is out of control and should be checked for assignable variation.

Am I taking a test for you? The process is out of control and should be checked for assignable cause variation. Please read this article

Nicely presented

Hi Bill, I learned that we need to interpret control charts based on the 68-95-99 rule; and I would like to know, in your opinion, if there are no points outside the 3 Sigma limit (all points with 3Sigma each side), is a process still considered in control, if for example: only 1 of 3 consecutive points fall within 1 Sigma either side of the average.. meaning two of the three are either in the 2 or 3 sigma zones. If we have 100 points of data, we would expect 68 of them to be within 1Sigma from the average, if this is not true, but the process has no data point outside the 3Sigma, is the process considered "not in control"?Thank you.

I would not worry too much about probabilities – like 68 points out of 100 should be within one sigma of the average.  That is true for a perfect normal distribution but there are not no perfect normal distributions in real life processes.  If there are no points beyond the limits and none of teh zones tests have been violated, then the process is in statistical control.

Hi. Why aren't these rules applicable for the CUSUM and EWMA charts?

because the CUSUM and EWMA are only looking for a signal that goes beyond hte limits – the values are not symmetrical

HI SIR, , i HAVE GONE THROUGH THE EIGHT RULES OF CONTROL CHART . BUT IN THAT CONTEXT , WHAT IS THE IDEAL CONTOL CHART OR IS THERE ANY PICTURE OF THAT.

I am assuming you mean a control chart that is in control.   A control chart likes that will have most points near the  middle, a few near the control limits, no beyond the control limits and no patterns.

Hi there,Thank you for this really great article, I have returned to it so many times since I became aware of run charts. Given that Covid had such an impact on data all over the world would you consider this to be a "fleeting" change and control for it  with process shifts or "the new normal" and leave the data as is? I work in the world of crime data so shops closing nd people staying at home impacted Theft from shop and Burglary. TIA

Well, I wish the crystal ball to see into the future.  I think for now it is the new normal – at least until a vaccine is found and adminstered or better treatment is found and people get back to work like they were before the virus.  I think is good you are applying the control charts to crime data.

Thanks and here's hoping vaccines bring about normality again!

If I am plotting c chart for customer complaints, and 0 being my lower control limit. If i have 4 consecutive points touching LCL, then should I assume my process is in control?

If the LCL is below zero, then there really is not a lower control limit. I don't set it to 0.  Yes 4 points in a row at zero is in statistical control.  You need 7 to 9 below the average to be an out of control situation.

if the trending days are 5 in the same direction then the 6th day comes in the the opposite direction slightly less or the same value of the 5th day what should I do:- Exclude this point and continuou counting from the 7 th day as number 6 in the trend OR -Restart counting from day 7 ?Thanks in advance

Once a trend is broken, you start over with one point.

Also if the trending line is zigzag up then down then more up then down .How will I count the 7 trending points.?Thanks

Not sure I understand but if it zig-zags, it is not a trend, each point must be above the last one for an upward trend.

Hi Bill, thanks for the great posting! I got several questions: Is it possible that a single point triggers several rules all at the same time? If it is possible, how can I tell which rule was triggered first? In other word, is there any hierarchy or ranking among these eight rules?

Hello,  Thanks for the comment.  The only hierarchy I pay attention really is point beyond the control limits.  If that occurs, you work to find out what caused that.  A point beyond the limit can change the location of the average and sigma lines making the other tests not really valid.  After that, I would probably look at runs above the average if I have to pick another one (zone C).

U chart can be used in both when we have the same sample size or different sample sizes. Why do we still use c chart when we have the same sample size

It is easier to explain and you don't have to select an inspection unit.  But there is no need to use it since the u chart works also.

Hello Sirs and All…Can a high or increasing yield be a problem in SPC?Does it make sence to make a control chart for high yield?Example>>> LCL = 85% UCL = 95% CL=90% >>> Yield became higher than the UCL. Is this considered yield is out of control?

Yes you can have a control chart on high yield.  If the result is above the UCL, it is out of control – but on the good side.  IF you can find out what happened and make it part of the process, then you have improved it.

Are these rules meant to only be used for Xbar charts or can they be used for range and standard deviation control charts as well?

Hi Bill,Nice article, I got clarifications of some finer points. I have a question that is how do you arrive at 2 out of 3 or 4 out of 5 points for different zones to come to conclusion that they could be likely assignable causes. How do you assign propability of occurances of these 2 cases.

You can estimate the probabilities using a normal distribution.  The tests for zone A and zone B give about the same probability as a point beyond the control limits.  The probability of getting a point beyond the upper control limit is 0.00135.  The probability of getting one point in zone A or beyond is 0.0228. The probability of getting two points in a row in zone A or beyond is then (0.0228)(0.0228) = 0.00052. Note that this probability is smaller than the probability of getting one point beyond one of the control limits. Thus, if two points in a row fall in zone A or beyond, it is a stronger indication of an out of control situation than a point beyond the control limits. <br />Since this probability is so small, the requirement can be loosen somewhat by saying two out of three consecutive points in zone A or beyond. The probability of getting a point somewhere else on the chart besides zone A or beyond is 1 – 0.0228 = 0.9772. The probability of getting two out of three consecutive points in zone A or beyond is then (0.0228)(0.0228)(0.9972)(3) = 0.00156 (or one out of 640). You multiply by 3 because the point not in zone A could be the first, second or third point. The probability of obtaining this pattern for a process that is in control is then 0.00156, a small number. A similar approach can be used for zone B.

If I plot control chart which has only upper limit, is my process in control? How will I summarize on the trend reporting?

Many Thanks for the content!!!

Really useful.  Having difficulty as every chart I tend to create (usually to be used for assurance rather than improvement) the process limits are always hugely wide.  Its normally small numbers used and there is no baseline being applied.

Please send me an example.  bill @SPCforExcel .com

Hello, Sir. Your data center line will always depend on your data mean? What if moving data? Does the mean or center line will also change? Thanks.

Your average only "changes" if the control chart shows that has been a significant change in the process.  Then you recalculate the average and limits and interpret that process again.

Taking a course on SPC, and they didn’t explain why stratification is undesirable. Having read this page, now I understand why. Thanks!

## Avoid Two Common Mistakes with a Shewhart Chart

Why it matters.

Leaders are frequently faced with having to improve results in their organizations. Without a method, they can fall prey to two big mistakes: 1) acting like something is a unique event when it’s normal for the process, or 2) ignoring issues that are truly special, assuming they are normal. Making the right assessment can be difficult without the right tool: a Shewhart chart, also known as a control chart.

Shewhart charts, which display data over time with upper and lower control limits, are the only way to differentiate between common (predictable) and special cause variation. Common cause variation is inherent in the process, while special cause variation is due to an attributable cause. On the chart, common cause variation falls between the upper and lower control limit, and special cause variation is found above or below it or when one of several rules exist (example, a run of either eight or more points above or below the mean). A good example is your commute time. Some variation has to do with the process itself, such as hitting a red or a green light. If something out of the ordinary happens, like a car crash, that’s special cause variation.

Phil Monroe, a current hospital board member, explained why he uses Shewhart charts on the Deming Institute’s podcast : “I need to understand, ‘Is this process predictable?’ If it isn’t, I want it to be. If it is, then I can consider whether I’m happy with it and whether a process improvement project makes sense. The best way to answer this is to get the last 20 data points and plot it on a Shewhart statistical process control chart.”

People often question whether they need as many as 20 points, because they don’t have the data, or they track monthly or quarterly data. In most cases, you can start a Shewhart Chart with 12 data points and create trial limits. The reason for 20-30 data points is that’s when you have enough data to have confidence in the control limits used for determining special cause. If that means going back historically, do it. If that means increasing the frequency of measurement to daily or weekly, do that. If you have no data, start now with a run chart . You’d rarely want to measure less often than monthly.

Understanding whether you have common cause versus special cause variation helps guide your actions. If your process is unpredictable, you want to figure out what’s causing that special cause variation and remove it from the system — for example, you might address equipment or procedure issues that are leading some people to do the work differently than others. If your process is predictable but you don’t like the current performance, you must change the process producing it to get different results.

A key first role of a leader is to foster reliable, predictable processes, and then decide whether you like the performance and make a plan to improve it.

## Related Insights

Types of variance, common cause variation, common cause variation examples, special cause variation, special cause variation example, choose the right program, common cause variation vs. special cause variation.

Every piece of data which is measured will show some degree of variation: no matter how much we try, we could never attain identical results for two different situations - each result will be different, even if the difference is slight. Variation may be defined as “the numerical value used to indicate how widely individuals in a group vary.”

In other words, variance gives us an idea of how data is distributed about an expected value or the mean. If you attain a variance of zero, it indicates that your results are identical - an uncommon condition. A high variance shows that the data points are spread out from each other—and the mean, while a smaller variation indicates that the data points are closer to the mean. Variance is always nonnegative.

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Change is inevitable, even in statistics. You’ll need to know what kind of variation affects your process because the course of action you take will depend on the type of variance. There are two types of Variance: Common Cause Variation and Special Cause Variation. You’ll need to know about Common Causes Variation vs Special Causes Variation because they are two subjects that are tested on the PMP Certification  and CAPM Certification exams.

Common Cause Variation, also referred to as “Natural Problems, “Noise,” and “Random Cause” was a term coined by Harry Alpert in 1947. Common causes of variance are the usual quantifiable and historical variations in a system that are natural. Though variance is a problem, it is an inherent part of a process—variance will eventually creep in, and it is not much you can do about it. Specific actions cannot be taken to prevent this failure from occurring. It is ongoing, consistent, and predictable.

Characteristics of common causes variation are:

• Variation predictable probabilistically
• Phenomena that are active within the system
• Variation within a historical experience base which is not regular
• Lack of significance in individual high and low values

This variation usually lies within three standard deviations from the mean where 99.73% of values are expected to be found. On a control chart, they are indicated by a few random points that are within the control limit. These kinds of variations will require management action since there can be no immediate process to rectify it. You will have to make a fundamental change to reduce the number of common causes of variation. If there are only common causes of variation on your chart, your process is said to be “statistically stable.”

When this term is applied to your chart, the chart itself becomes fairly stable. Your project will have no major changes, and you will be able to continue process execution hassle-free.

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Consider an employee who takes a little longer than usual to complete a specific task. He is given two days to do a task, and instead, he takes two and a half days; this is considered a common cause variation. His completion time would not have deviated very much from the mean since you would have had to consider the fact that he could submit it a little late.

Here’s another example: you estimate 20 minutes to get ready and ten minutes to get to work. Instead, you take five minutes extra to get ready because you had to pack lunch and 15 additional minutes to get to work because of traffic.

Other examples that relate to projects are inappropriate procedures, which can include the lack of clearly defined standard procedures, poor working conditions, measurement errors, normal wear and tear, computer response times, etc. These are all common cause variation.

Special Cause Variation, on the other hand, refers to unexpected glitches that affect a process. The term Special Cause Variation was coined by W. Edwards Deming and is also known as an “Assignable Cause.” These are variations that were not observed previously and are unusual, non-quantifiable variations.

These causes are sporadic, and they are a result of a specific change that is brought about in a process resulting in a chaotic problem. It is not usually part of your normal process and occurs out of the blue. Causes are usually related to some defect in the system or method. However, this failure can be corrected by making changes to affected methods, components, or processes.

Characteristics of special cause variation are:

• New and unanticipated or previously neglected episode within the system
• This kind of variation is usually unpredictable and even problematic
• The variation has never happened before and is thus outside the historical experience base

On a control chart, the points lie beyond the preferred control limit or even as random points within the control limit. Once identified on a chart, this type of problem needs to be found and addressed immediately you can help prevent it from recurring.

Let’s say you are driving to work, and you estimate arrival in 10 minutes every day. One day, it took you 20 minutes to arrive at work because you were caught in the traffic from an accident zone and were held up.

Examples relating to project management are if machine malfunctions, computer crashes, there is a power cut, etc. These kinds of random things that can happen during a project are examples of special cause variation.

One way to evaluate a project’s health is to track the difference between the original project plan and what is happening. The use of control charts helps to differentiate between the common cause variation and the special cause variation, making the process of making changes and amends easier.

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#### IMAGES

1. Special Cause Variation

2. A guide to using SPC charts and icons, and reading demand charts

3. Common Cause & Special Cause Variation Explained with Examples

4. Control Charts

5. Common Cause & Special Cause Variation Explained with Examples

6. David M. Williams, Ph.D

#### VIDEO

1. Control Charts for Variables (Part 1)

2. QI Power Hour: Understanding Variation and its Importance to QI (Mar. 10/17)

3. Mahesh Hegde

4. X chart and Rchart||with example|| Statistical quality control|| Solved Numerical||SQC

5. Variable Control Chart (SPC)

6. 5 Special cause variation types

1. The Power of Special Cause Variation: Learning from Process Changes

A control chart can show two different types of variation: common cause variation (random variation from the various process components) and special cause variation. Special cause variation is present when the control chart of a process measure shows either plotted point(s) outside the control limits or a non-random pattern of variation. When a ...

2. Common Cause & Special Cause Variation Explained with Examples

Common Cause and Special Cause Variation Detection. Control chart. One of the ways to keep track of common cause and special cause variation is by implementing control charts. When using control charts, the important aspect to be considered is firstly, establishing the average point of measurement. Next, establish the control limits.

3. What is Special Cause Variation? How to Identify It?

Identifying Special Cause Variation. Special cause variation is often difficult to detect without the right analysis tools. Identifying special causes requires going beyond typical process monitoring to specialized statistical techniques. There are three main methods for recognizing when variation is due to special causes: Control Charts

4. Know It When You See It: Identifying and Using Special Cause Variation

The authors' SPC charts reveal examples of both common cause and special cause variation. Common cause variations are those causes that are inherent in the system or process. 4 Evidence of common cause variation can be seen visually in the OA's Fig 3, from January 2017 to October 2017, because the data points vary around the mean but remain ...

5. Using control charts to detect common-cause variation and special-cause

Common-cause variation is the natural or expected variation in a process. Special-cause variation is unexpected variation that results from unusual occurrences. It is important to identify and try to eliminate special-cause variation. Out-of-control points and nonrandom patterns on a control chart indicate the presence of special-cause variation.

6. 7 Rules For Properly Interpreting Control Charts

Control charts can be used to identify sources of variation, both common and special cause. Common cause variation is the variation inherent in the process. Common cause variation is also known as the noise of the process. A process with only common cause variation is highly predictable. A process that has a significant inherent common cause ...

7. Common cause and special cause (statistics)

Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common causes", also called natural patterns, are the usual, historical, quantifiable variation in a system, while "special causes" are unusual, not ...

8. Distinguishing between common cause variation and special cause

Special cause variation results from an assignable cause or external source to the process (Evans and Lindsay, 2013). People may intuitively believe that any variation or problems in a process is attributable to specific causes or particular events. ... Shewhart control charts represent the individual's experience and enable the individual to ...

9. Know It When You See It: Identifying and Using Special Cause Variation

Although many readers might understand that 8 consecutive points above or below the mean signifies special cause variation resulting in a centerline "shift," there are many more special cause variation rules revealed in these charts that likely provided valuable real-time information to the improvement team. These "signals" might not be ...

10. Guide: Control Charts

"Special cause" refers to unusual or non-random sources of variation that are not inherent to the process. These causes are typically assignable to specific factors or events and can lead to unexpected changes in the process output. Control charts help detect and investigate these special causes so that appropriate actions can be taken.

11. Run chart basics

The run chart shows graphically whether special causes are affecting your process. Run charts also provide tests for randomness that provide information about non-random variation due to trends, oscillation, mixtures, and clustering in your data. Such patterns indicate that the variation observed is due to special-cause variation.

12. Using tests for special causes in control charts

In addition, you want to draw the control limits for all control charts at 2.5σ instead of 3σ. Choose File > Options > Control Charts and Quality Tools > Tests. From the drop-down list, select Perform all tests for special causes. Minitab will now perform all applicable tests when you create a control chart.

13. Six Sigma Control Charts: An Ultimate Guide

The control chart helps detect special cause variation by highlighting data points outside control limits. Estimating Process Average and Variation. Another objective of a control chart is to estimate the process average and variation. The central line represents the process average on the chart, and the spread of the data points around the ...

14. Using control charts to understand community variation in COVID-19

It is common practice in control charts to remove special cause variation due to such cyclic behavior by separating data lines within a chart or by subgrouping by a larger unit (i.e. week rather than day) to smooth variation. ... This study offers some possible interpretations of the observed special cause variation, but the purpose was to ...

15. Control Chart Rules and Interpretation

All of the control chart rules are patterns that form on your control chart to indicate special causes of variation are present. Some of these patterns depend on "zones" in a control chart. To see if these patterns exits, a control chart is divided into three equal zones above and below the average. This is shown in Figure 2. ...

16. Avoid Two Common Mistakes with a Shewhart Chart

Making the right assessment can be difficult without the right tool: a Shewhart chart, also known as a control chart.Shewhart charts, which display data over time with upper and lower control limits, are the only way to differentiate between common (predictable) and special cause variation. Common cause variation is inherent in the process ...

17. Common Cause Variation Vs. Special Cause Variation

The use of control charts helps to differentiate between the common cause variation and the special cause variation, making the process of making changes and amends easier. Learn new trends, emerging practices, tailoring considerations, and core competencies required of a Project Management professional with the PMP Certification course.

18. PDF Control Chart Cheat Sheet

Special Cause: Variation that is due to something out of the ordinary. Example: A contruction zone, blizzard, or traffic accident. Special causes require immediate cause-effect analysis to eliminate the source of variation. Once special causes have been addressed and a process is stable, you can launch an effort to reduce common causes of ...