Run chart basics

In this topic, what is a run chart, what do the points and center line on a run chart mean, run charts help detect special-cause variation, nonrandom patterns that a run chart can identify.

A run chart represents your process data over time. Use a run chart to look for evidence of special-cause variation in your process.

Example of a run chart

special cause variation on run chart

Except for one observation, the points vary randomly around the center line (median). The approximate p-values for clustering, mixtures, trends, and oscillation are all greater than the significance level of 0.05. Therefore, there is no indication of special-cause variation or non-randomness.

A run chart plots the individual observations in the order that they were collected. The gray points represent the individual values. The blue points represent either the subgroup means or subgroup medians.

If the subgroup size = 1, the center line is the median of all data, regardless of the option you select for the plotted points.

Even with skewed data, the median of the subgroup means is usually close to the median of the subgroup medians. The y-axis has a wide range because the raw data are also plotted, so the difference is usually not noticeable.

Variation occurs in all processes. Common-cause variation is a natural part of the process. Special-cause variation, comes from outside the system and causes recognizable patterns, shifts, or trends in the data. 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.

There are four basic patterns of nonrandomness that a run chart will detect.

Mixture patterns

special cause variation on run chart

If the p-value for mixtures is less than 0.05, you may have mixtures in your data. In this chart, the mixture may indicate that the data come from different processes.

Cluster patterns

special cause variation on run chart

If the p-value for clustering is less than 0.05, you may have clusters in your data. In this case, the circled data may represent clusters of data.

Oscillating patterns

special cause variation on run chart

If the p-value for oscillation is less than 0.05, you may have oscillation in your data. In this case, the circled data seem to vary up and down frequently.

Trend patterns

special cause variation on run chart

If the p-value for trends is less than 0.05, you may have a trend in your data. In this case, the upward trend is circled and easily visible.

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Ted Hessing

Run Chart: Creation, Analysis, & Rules

Posted by Ted Hessing

A run chart is a line chart of data plotted over time. In other words, a run chart graphically depicts the process performance or data values in time order. Viewing data over time gives a more accurate conclusion rather than just summary statistics.

Run Chart

A run chart is also known as a trend chart or a time series plot. Usually, run charts are used in the measure phase of the DMAIC project and it helps to identify trends or shifts in the process and allows testing for randomness in the process.

Difference between Run chart and control chart

Control charts are used to monitor the stability of the process. In other words, they measure any type of output variable over time. The goal is to see the results consistently fall within the control limits . On the control chart, both upper and control limits are defined. Typically, control limits are defined as three standard deviations from the mean. If the results fall within the control limits, then the process is stable; otherwise, it suggests that the process is not stable.

A run chart is similar to a control chart , but the key difference is it can reveal shifts and trends, not the process stability. Since the run chart does not have control limits, it cannot detect out-of-control conditions. However, it will graphically depict how the process is running. You can turn a run chart into a control chart by adding upper and lower control limits. A pattern or trend indicates the presence of special cause variation in the process.

Why use a run chart

A run chart is used to determine whether or not the central tendenc y of the process is changing. Following are a few reasons to use a run chart

When to use run charts

Key components of Run Chart

Run chart interpretation rules

The following paragraphs are the run chart decision rules used to avoid inaccurate analysis and initiate appropriate improvement actions:

Shift : – Seven or eight values in succession above or below the median line is a shift. Do not consider the points that fall on the median line as they are not toward or against the shift. A shift indicates a dramatic change in the process.

special cause variation on run chart

Runs  – Too many or too few runs in the data displayed on the chart. In other words, one or more consecutive points are all lying on the same side of the line. Ignore the points exactly on the line!

special cause variation on run chart

Clustering  – Too few runs or groups of points in one or more areas of the plot. It indicates measurement or sampling problems.

special cause variation on run chart

Trend  – Seven or more consecutive points are increasing or decreasing. A basic rule of thumb is when a run chart exhibits seven or eight points successively up or down, then a trend is clearly present in the data and needs process improvement. This rule does not care whether the consecutive points are above, below, or crossing the median.

special cause variation on run chart

Mixtures  – Too many runs in a chart with absences of points near the median line.

special cause variation on run chart

Astronomical Point  – Astronomical points occur when there is one value that is very different from the other data values on the chart. It would be a value that is highly unlikely to occur again and would appear as an outlier.

Run Chart

Counting Runs

A non-random pattern is signaled by too few or too many runs, or crossings of the median line. A run is a series of points in a row on one side of the median. In other words, one or more consecutive points are all lying on the same side of the line. If only chance is influencing the process being measured with a run chart, then there should be a regularity at which data points go above and below the median to satisfy this condition. Some points can fall exactly on the median line, which makes it hard to decide which run these points belong to. Hence, ignore if the value is exactly on the median line.

To apply the above-mentioned interpretation of the rules, we first need to identify the useful values/observations in the data set. This can be achieved by counting the number of runs and avoiding the values on the median line.

If you observe a greater or fewer number of runs than expected in the chart, that means there is a non-random pattern in the process. Swed and Eisenhart developed a chart in 1943 to determine the minimum and the maximum number of runs required for each data point to follow the random variation in the process. In other words, no special cause existed in the process.

special cause variation on run chart

How to create run chart

Run Chart Excel Template

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Draw and interpret the following weekly mobile charger rejection data using the run chart.

special cause variation on run chart

 Solution

Run Chart

Limitations

The formation of a run chart is based on the input values. It does not help identify unexpected or surprise events.

It cannot identify the stability of the process as it does not have control limits.

Every process will have some inherent variation. Often, normal process variation concludes that a trend or cycle exists in the process.

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Comments (12)

Is there perhaps some SAS code that would create the graph in step 5 above. I see that the SAS support document refers to Shewhart Charts.

Sorry, Jacques. I’m not familiar with SAS code.

How many data points a run chart should include before applying any of the decision rules ?

I like having 15 or more data points, Arthur.

If the 6 consecutive points come below or above mean line. Then it is trend or not?

I think you’re looking for the rule of 7 here, Hunny.

Hi Ted. When do you use MEAN/MEDIAN/MODE as your central tendency? If you can give examples, would be wonderful.

Good question, Cesar.

Here’s a great resource.

Great stuff, Ted! The article filled some gaps as to how a run chart should be interpreted.

Appreciate the warm comments!

Just to clarify the reason behind in this statement: “A run is defined as if the previous and next values are on opposite sides of median line and ignore if the value is on median line” Why we should ignore the values if it is on the median line?

Hello Enrique,

Updated the paragraph for better clarity.

A non-random pattern is signalled by too few or too many runs, or crossings of the median line. A run is a series of points in a row on one side of the median. If only chance is influencing the process being measured with a run chart, then there should be a regularity at which data points go above and below the median to satisfy this condition. Some points can fall exactly on the median line, which makes it hard to decide which run these points belong to. Hence ignore if the value is exactly on the median line.

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special cause variation on run chart

Special Cause Variation

Published: November 7, 2018 by Marilyn Monda

special cause variation on run chart

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 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:

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.  

Frequently Asked Questions (FAQ) about special cause variation

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.  

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.

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Marilyn Monda

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What is a run chart? How to create a run chart Using a run chart to test for special causes Examples of run charts Further reading Sources

What is a run chart?

A run chart is used to study collected data for trends or patterns over a specific period of time. A run chart will help you:

The run chart is a running record of a process over time:

A run is defined as one or more consecutive data points on the same side of the mean line.

See Also : PH&QI Toolbox: Control Chart

How to create a run chart

Using a run chart to test for special causes

Test #1: the presence of too much or too little variability.

Use when there are too few or too many runs.

Test #2: The presence of a shift in the process

A special cause exists if a run contains too many data points (i.e., with 20 or more data points, a run of 8 or more data points is considered "too long"; with less than 20 data points, a run of 7 might also be considered "too long").

Test #3: The presence of a trend

A trend is defined as an unusually long series of consecutive increases or decreases in the data, (usually at least 6 or 7).

Examples of run charts

Isanti county, wic no-show rate.

This run chart from Isanti County shows the percentage of WIC appointments missed over a 1.5-year period.

Click to view larger image.

Run Chart

More examples of run charts

The Use of Control Charts in Health-Care and Public-Health Surveillance (PDF) Journal of Quality Technology

Plotting Basic Control Charts: Tutorial Notes for Healthcare Practitioners (PDF) Quality and Safety in Health Care

Further reading

Basics of the Control Chart (PDF) MDH Office of Performance Improvement / UMN School of Public Health

Control Chart American Society for Quality

The Control Chart: An Epidemiological Tool for Public Health Monitoring Public Health

Finding the Right Tool for your Purpose (PDF) MDH Office of Performance Improvement

Public Health Memory Jogger Public Health Foundation, GOAL/QPC

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Quality Improvement

By now you’ve managed to run your PDSA cycle and gather some data both before and after the intervention. This section will discuss the best way to present your data for the outcome measure and how to interpret it. Don’t forget the process and balancing measures you have collected. They should be analysed alongside your outcome measures.

Basics of a Run Chart

The best way to visualise the effects your changes have been having is to plot a graph over time, thereby creating a run chart. This can be done both during and after the collection of data. It will help in two different ways. First, it provides feedback for the changes you have made. Second, it helps you understand the normal variation that is encountered as the outcome measure is collected.

Elements of a Run Chart

Run Chart Elements

Creating a Run Chart

The data you have collected should be entered into a spreadsheet. Create three columns: time series, data and median. The median can be created once you have 12 data points. Once you have 12 data points, use the graph function to plot your run chart with time series on the x-axis and your data on the y-axis. The median should appear as a straight line across the chart. Make sure you annotate the chart and provide qualitative information to reflect when changes were introduced.

Interpretation

You’ve collected your data and plotted it into a run chart. Now you must interpret your results! Before doing this, it is important to take a step back to understand what the chart represents.

Every process has inherent random (common cause) variation. Using run charts, we are able to look for non-random (special cause) variation within the data. Non-random variations provide evidence that the performance has actually changed and is not the result of random variation within the process. We are able to do this by counting runs and applying the four rules of run charts.

Counting Runs

A run consists of one or more consecutive data points on the same side of the median (ignore points that fall on the median). To count runs, either:

Four Rules of Run Charts

There are four rules that help tell if observed patterns are random (common cause variation) or non-random (special cause variation). If any one rule occurs, you can say there is evidence of non-random patterns (i.e. change has occurred). These rules can only be applied once you have 12 data points (and thus a median) within your run chart. The rules are as follows:

Four Rules of a Run Chart

Read more from NHS Improvement on run charts .

Maximising Use of the Four Rules

If the Shift or Trend rules apply, look into whether the change is associated with your intervention or whether there is another change that is driving it.

When the Too Many/Too Few Runs or Astronomical Data rules apply, this presents an opportunity to look for new ideas for tests of change. Try to understand what has been happening within your test cycle and look for the cause of these changes. For example, you could replicate the cause of an astronomical data point if it produced a beneficial change.

Calculating the Number of Runs

If your number of runs falls outside the upper and lower limit of expected runs, it is likely you are looking at a non-random (special cause) variation. You can approximate the limits using the following formulas:

Table of Run Values

Shewhart Chart (Statistical Process Control Chart)

Once 20 data points have been collected, the median can be transformed into a mean. This allows the addition of upper and lower control limits provided your data has a normal distribution. They are calculated as 3x the standard deviation from the mean. An additional rule can be applied using the control limits to help further identify whether changes are the result of random (common cause) variation or non-random (special cause) variation.

Additional Rule

Control limits help determine if the process is stable (only random variation) or not stable (contain non-random variation). This rule should be applied provided none of the four rules of run charts ( explained above ) are met.

Statisctical Process Chart

If you have no evidence of non-random (special cause) variation, this suggests your process is stable and predictable. Therefore, your Control Chart will only display random (common cause) variation. You should try to reduce the variability of your process in order to standardise outcomes and ensure patient care is consistent. Changing random variation will often require changes to the whole system and potentially to contributing factors outside of the system. You can further assess and quantify random (common cause) variation by examining the number of points that fall between both the control limits and within the middle third region of your chart. You should find this number approximates two-thirds the total number of points on your chart.

One final word on control charts. If your target falls outside of the control limits, it is unlikely that your system is set up to allow you to meet that target. If it is met, this would be an unusual occurrence and unlikely to be sustained.

Read more from NHS Improvement on control charts .

Also in Quality Improvement

Introduction

Aims and Measures

Generating Ideas For Change

Data Collection

PDSA Cycles

Other Charts

Expanding Tests

Helping Change Spread

Psychology of Change

Team Working

7 Rules For Properly Interpreting Control Charts

Guest Column | February 15, 2021

7 rules for properly interpreting control charts.

By Mark Durivage , Quality Systems Compliance LLC

432423

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

special cause variation on run chart

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:

special cause variation on run chart

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:

special cause variation on run chart

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:

special cause variation on run chart

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:

special cause variation on run chart

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:

special cause variation on run chart

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:

special cause variation on run chart

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:

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

special cause variation on run chart

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:

Stratification

special cause variation on run chart

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:

About The Author:

Mark

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IMAGES

  1. Special Cause Variation

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  2. David M. Williams, Ph.D

    special cause variation on run chart

  3. Common Cause & Special Cause Variation Explained with Examples

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  4. Common Cause Variation vs Special Cause Variation Archives

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  5. 5. spc control charts

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  6. variatie algemene specifieke oorzaken specific common cause variation

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VIDEO

  1. New Tundra Run Variation In Fall Guys Season 2

  2. Too Late to Run Chart (Pibby Sonic and Talis)

  3. 20: Line of Best Fit

  4. Building and Using Run Charts

  5. GGFDIUHDFG0 sing Run Chart

  6. Doughnut Chart/Donut Chart

COMMENTS

  1. Using Run Charts for Healthcare Improvement, An Introduction

    Run charts and control charts were developed as tools to distinguish one type of variation from another. Common cause variation is random variation which can

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

    Special-cause variation is unexpected variation that results from unusual occurrences. It is important to identify and try to eliminate special-cause variation.

  3. Run chart basics

    Variation occurs in all processes. Common-cause variation is a natural part of the process. Special-cause variation, comes from outside the system and causes

  4. Run Chart: Creation, Analysis, & Rules

    You can turn a run chart into a control chart by adding upper and lower control limits. A pattern or trend indicates the presence of special cause variation

  5. 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

  6. A guide to creating and interpreting run and control charts

    These non-random patterns indicate special cause variation on a run chart. Rule 1. • A shift in the process or too many data points in a run (6 or more

  7. Run Chart

    Using a run chart to test for special causes · Test #1: The presence of too much or too little variability · Test #2: The presence of a shift in

  8. Run Charts

    You can further assess and quantify random (common cause) variation by examining the number of points that fall between both the control limits and within the

  9. 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

  10. Run Chart Rules for Interpretation

    There are four rules that can be applied to a run chart to help determine whether or not the variation within the dataset is due to the random variation