Control chart

Use control charts to indicate when a process is out of control and helps to identify the presence of special-cause variation.

In This Topic

C chart
I-MR chart
NP chart
P chart
U chart
Run chart
Xbar-R/S chart

C chart

Use a C chart, a statistical process control (SPC) tool, to plot the number of defects in each sample over time. Use C charts for processes in which the measurement system is only capable of counting the number of defects in a sampled unit. The C chart is an industry standard for monitoring and controlling process outputs over time. It assumes a constant sample size; for samples of different sizes, use the U chart.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did special causes exist during the timeframe of the plotted data?
Does evidence suggest something has changed or the process is performing differently than expected?
Does the defect rate of the process change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying the process steps that exhibit high defect rates, unstable variation, or other symptoms that indicate the need for improvement.
Start of project	Verify the process stability when performing a baseline capability analysis.
Mid-project	Investigate the effects of the input variables on the process output over time.
Mid-project	Verify the process stability when performing confirmation runs after implementing improvements.
End of project	Verify the process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control the inputs to the improved process after the project is complete.
Post-project	Monitor the output of the improved process after the project is complete.

Data

Your data must be discrete numeric Y (number of defects) values.

Guidelines

A defect is any nonconformance of a product or service. To count defects or defectives, you must have a clear definition as to what does and does not constitute a defect.
The defect rate is the average number of defects per sample.
You can use a categorical variable with the C chart to show the effects of different input conditions, which Minitab refers to as stages. For example, if you want to examine the defect rate of a forms processing operation (Y) to see the differences between three shifts, you can use the shift as the stage variable to see whether changes occurred in the defect rate, variation, or within-shift patterns between the three shifts.
When using a categorical variable to set up stages for the C chart, you should have at least 30 observations in each stage. The C chart requires enough data within each stage to reliably estimate the within-stage process defect rate.

How-to

Define what is and what is not a defect.
Verify you can accurately assess each unit (that is, verify the measurement system).
Establish a data collection strategy to define how you will sample units over time.
In Minitab, enter the number of observed defects from each sample in one column. Do not enter a sample size; the C chart assumes it is constant. Use the U chart for unequal sample sizes.
You can also use an historical record of process defects per unit as the basis for establishing control limits.
Optionally, Minitab can evaluate four rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits that help you make comparisons across stages. For example, you can examine changes in the process defect rate before, during, and after the implementation of a new procedure on one C chart.

For more information, go to Insert an analysis capture tool.

I-MR chart

An I-MR chart is a statistical process control (SPC) tool that consists of two charts:

The top chart (I) plots the individual measurements of a variable over time.
The bottom chart (MR) plots a moving range of the data. It is used for processes with continuous data.

An I-MR chart is an industry standard for monitoring and controlling process outputs over time. In manufacturing, an I-MR chart is generally used for low-volume production and destructive or expensive testing. Many situations exist in transactional or business processes in which an I-MR chart can be used (for example, sales and inventory data). Generally, if you can obtain rational subgroups, you should use the Xbar-R or Xbar-S chart; otherwise, use the I-MR chart.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did special causes exist during the timeframe of the plotted data?
Does evidence suggest something has changed or the process is performing differently than expected?
Does the mean of the process output change at different levels of a process input?
Does the variation of the process output change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying outputs that exhibit high common-cause variation, frequent special causes, unstable variation, or other symptoms that point to the need for improvement.
Start of project	Verify process stability when performing a baseline capability analysis.
Mid-project	Investigate effects of input variables on the process output over time.
Mid-project	Verify process stability when performing confirmation runs after implementing improvements.
End of project	Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control inputs to the improved process after the project is complete.
Post-project	Monitor output of the improved process after the project is complete.

Data

Your data must be values for continuous Y, but must not contain rational subgroups.

Guidelines

Look at the moving range chart (MR) first to determine whether the variation is reasonably in control. If so, the limits for the I chart are valid and the I chart can then be evaluated. If the variance is not in control, the process is unstable and the information on the mean of the process is not trustworthy.
The variation (and thus the limits on the I chart) is based on a moving range which implies that any two consecutive measurements are more similar (part of an assumed rational subgroup) than measurements further apart. If this is not the case, the interpretation of the I-MR chart is highly suspect.
You can use a categorical variable with the I-MR chart to show the effects of different input conditions, which Minitab refers to as stages. For example, if you want to examine hourly yield per FTE of a forms processing operation (Y) to see if differences exist between three operating groups, you can use operating groups as the stage variable and see whether any changes in the mean, variation, or within-shift patterns exist between the three groups.
If the sample size within each stage is not at least 30 observations, you may want to consider using a time series plot instead of the I-MR chart. The I-MR chart requires a sufficient number of observations in each stage to reliably estimate the mean and variation of the stage. The time series plot merely plots data values, so no requirement exists for sufficient sample sizes.
If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.

How-to

Verify the measurement system for the Y data is adequate.
Establish a data collection strategy to determine the best time interval for collecting data.
Enter the collected data into a single column in the Minitab worksheet. Minitab can also directly import data from databases, text files, Microsoft^® Excel, and so on.
Optionally, Minitab can evaluate eight rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits which help you make comparisons across stages. For example, you can examine changes in the process mean and variation before, during, and after the implementation of a new procedure on one I-MR chart.

For more information, go to Insert an analysis capture tool.

NP chart

Use an NP chart, a statistical process control (SPC) tool, to plot the proportion defective per sample or subgroup over time. You can use an NP chart for processes where the measurement system is only capable of determining whether a unit is defective or not defective. An NP chart is an industry standard for monitoring and controlling process outputs over time. An NP chart can be used for samples of different sizes; however, it is best suited for a constant sample size. For different sized samples, try the P chart instead.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did special causes exist during the timeframe of the plotted data?
Does evidence suggest something has changed or the process is performing differently than expected?
Does the rate of defectives for the process change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying process steps that exhibit high defect rates, unstable variation, or other symptoms that point to the need for improvement.
Start of project	Verify process stability when performing a baseline capability analysis.
Mid-project	Investigate effects of input variables on process output over time.
Mid-project	Verify process stability when performing confirmation runs after implementing improvements.
End of project	Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control inputs to the improved process after project is completed.
Post-project	Monitor output of the improved process after project is completed.

Data

Your data must be discrete numeric Y (number of defectives) values and the number of units sampled per lot.

Guidelines

If your sample sizes are different, your calculated control limits will also be different. However, if the largest or smallest sample sizes do not differ from the average sample size by more than 25%, use a constant sample size because it results in constant control limits and makes the chart more easily understood. If the sample sizes vary by more than 25%, consider using a P chart instead.
A defective is a process output (product or service) that has one or more defects.
You can use a categorical variable with the NP chart to show the effects of different input conditions. Minitab refers to this as stages. For example, if you want to examine the rate of defectives for a forms processing operation (Y) to see if differences exist between three different processing sites, you can use the site as the stage variable and see whether the mean, variation, or within-shift patterns change between the three sites.
When using a categorical variable to set up stages for the NP chart, you should have at least 30 observations in each stage. The NP chart requires enough data within each stage to reliably estimate the within-stage process defective rate.

How-to

Define what is and what is not a defective unit.
Verify you can accurately assess each unit (verify the measurement system).
Establish a data collection strategy to define how you will sample lots over time.
In Minitab, enter the count of defective products or services into one column and the sample or subgroup sizes in another column. If the samples are all the same size, you can specify a constant instead of using a separate column. Note: For unequal sample sizes, use a P chart instead of an NP chart.
You can also use a historical process defective rate as the basis for establishing control limits.
Optionally, Minitab can evaluate four rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits which help you make comparisons across stages. For example, you can examine changes in the process proportion defective before, during, and after the implementation of a new procedure on one NP chart.

For more information, go to Insert an analysis capture tool.

P chart

Use a P chart, a statistical process control (SPC) tool, to plot the proportion defective per sample or subgroup over time. Use a P chart for processes where the measurement system is only capable of determining whether a unit is defective or not defective. The P chart is an industry standard for monitoring and controlling process outputs over time and you can use it for samples of different sizes.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did any special causes exist during the timeframe of the plotted data?
Does any evidence suggest something has changed or the process is performing differently than expected?
Does the rate of defectives for the process change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying process steps that exhibit high defect rates, unstable variation, or other symptoms that point to the need for improvement.
Start of project	Verify process stability when performing a baseline capability analysis.
Mid-project	Investigate the effects of input variables on the process output over time.
Mid-project	Verify process stability when performing confirmation runs after implementing improvements.
End of project	Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control inputs to the improved process after the project is complete.
Post-project	Monitor output of the improved process after the project is complete.

Data

Your data must be discrete numeric Y (number of defectives) values and the number of units sampled per lot.

Guidelines

If your sample sizes are different, your calculated control limits will also be different. However, if the largest or smallest sample size do not differ from the average by more than 25%, you should use a constant sample size, which results in constant control limits and makes the chart more easily understood.
A defective is a process output (product or service) that has one or more defects.
You can use a categorical variable with the P chart to show the effects of different input conditions. Minitab refers to this as stages. For example, if you want to examine the rate of defectives for a forms processing operation (Y) to see if differences exist between three different processing sites, you can use the site as the stage variable to see whether the mean, variation, or within-shift patterns change between the three cites.
When using a categorical variable to set up stages for a P chart, you should have at least 30 observations in each stage. The P chart requires enough data within each stage to reliably estimate the within-stage process defective rate.

How-to

Define what is and what is not a defective unit.
Verify you can accurately assess each unit (verify the measurement system).
Establish a data collection strategy to define how you will sample lots over time.
In Minitab, enter the count of defective products or services into one column in and the sample or subgroup sizes in another column. If the samples are all the same size, you can specify a constant instead of using a separate column.
You can also use a historical process defective rate as the basis for establishing control limits.
Optionally, Minitab can evaluate four rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits that can help you make comparisons across stages. For example, you can examine changes in the process proportion defective before, during, and after the implementation of a new procedure on one P chart.

For more information, go to Insert an analysis capture tool.

U chart

Use a U chart, a statistical process control (SPC) tool, to plot the number of defects in each sampled unit over time. You can use a U chart for processes where the measurement system is only capable of counting the number of defects in a sampled unit. The U chart is an industry standard for monitoring/ controlling process outputs over time and can be used for samples that are different sizes, for example, different sized units or different sized lots of like-sized units.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did special causes exist during the timeframe of the plotted data?
Does evidence suggest something has changed or the process is performing differently than expected?
Does the defect rate of the process change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying the process steps that exhibit high defect rates, unstable variation, or other symptoms pointing to the need for improvement.
Start of project	Verify process stability when performing a baseline capability analysis.
Mid-project	Investigate effects of input variables on process output over time.
Mid-project	Verify process stability when performing confirmation runs after implementing improvements.
End of project	Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control inputs to the improved process after the project is complete.
Post-project	Monitor output of the improved process after the project is complete.

Data

Your data must be the discrete numeric Y (number of defects) values and the size of the inspected unit (for example, square inches of surface or words of text).

Guidelines

If your sample sizes are different, your calculated control limits will also be different. However, if the largest or smallest sample size differs from the average sample size by more than 25%, you should use a constant sample size because it will result in constant control limits and makes the chart more easily understood.
A defect is any nonconformance of a product or service. To count defects or defectives, you must have a clear definition as to what does and does not constitute a defect.
The defect rate is the average number of defects per unit. A process output (product or service) can have a defect rate less than or greater than one.
You can use a categorical variable with the U chart to show the effects of different input conditions. Minitab refers to this as stages. For example, if you want to examine the defect rate of a forms processing operation (Y) to see whether differences exist between three shifts, you can use the shift as the stage variable and see whether the mean, variation, or within-shift patterns change between the three shifts.
When using a categorical variable to set up stages for the U chart, you should have at least 30 observations in each stage. The U chart requires enough data within each stage to reliably estimate the within-stage process defect rate.

How-to

Define what is and what is not a defect.
Verify you can accurately assess each unit (verify the measurement system).
Establish a data collection strategy to define how you will sample units over time.
In Minitab, enter the number of observed defects from each sampled unit in one column and the size of each sampled unit in another column. If the units are all the same size, you can specify a constant instead of using a separate column.
You can also use a historical process defects-per-unit as the basis for establishing control limits.
Optionally, Minitab can evaluate four rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits that help you make comparisons across stages. For example, you can examine changes in the process defect rate before, during, and after the implementation of a new procedure on one U chart.

For more information, go to Insert an analysis capture tool.

Run chart

Use a run chart to provide a graphical means for looking at data dynamically (over time). Run charts often show patterns that do not appear in static displays of your data, such as histograms. A run chart is a useful tool for discovering evidence of influences on the process, all of which can be used to make process improvements

Answers the question:

Does the process exhibit any patterns (for example, trends, cycles, sawtooth, and mixtures) over time?

When to Use	Purpose
Start of project	While performing a baseline analysis, you typically use a control chart to verify that the process was stable. A run chart is an additional tool that tests for patterns that may not be detected in a control chart, yet may often reveal clues for making process improvements.
Mid-project	The first rule of data analysis is to graph the data before running statistical tests. Whenever you collect data over time, you should also graph the data over time to examine its dynamic behavior. A run chart provides tests for trends, cycles, and other patterns.

Data

Your data must be numeric (continuous or discrete) and collected over time.

Guidelines

The tests that appear in the run chart provide various insights into the process behavior over time.

If the mixtures test is significant (small p-value), then you are most likely collecting data from different sources, which could be different suppliers, different machines, and so on. However, basically, there is a consistent difference between subgroups causing the behavior you see.
If the cluster test is significant, then the process appears to be shifting at various points in time.
Oscillation may be a result of tool wear or other causes.
Trends are also caused by an outside influence.

How-to

You can use one of three ways to enter the data in Minitab:

With no subgroups, enter the data into a single column.
With subgroups, enter the Y data into a single column and the subgroup indicators in another column. If the subgroups are all the same size you can use a constant in lieu of the second column.
With subgroups, enter the data into multiple columns in the worksheet, where each row is a subgroup.

For more information, go to Insert an analysis capture tool.

Xbar-R/S chart

An Xbar-R/S chart is a statistical process control (SPC) tool that consists of two charts:

The top chart is an Xbar chart, which plots the subgroup means of a variable over time.
The bottom chart is either an R chart or an S chart, depending on whether you plot the subgroup ranges or their standard deviations.

You can use an Xbar-R or Xbar-S chart for processes with continuous data. This chart is an industry standard for monitoring and controlling process outputs over time. While you usually use Xbar-R and Xbar-S charts with subgroups that are the same size, you can also use them with different size subgroups to accommodate botched measurements or missing data.

Answers the questions:

How much common-cause variation does the process exhibit?
Is the process stable over time?
Did special causes exist during the timeframe of the plotted data?
Does evidence suggest something has changed or the process is performing differently than expected?
Does the mean of the process output change at different levels of a process input?
Does the variation of the process output change at different levels of a process input?
Do the dynamic patterns of the process output change at different levels of a process input?

When to Use	Purpose
Pre-project	Assist in project selection by identifying outputs that exhibit high common-cause variation, frequent special causes, unstable variation, or other symptoms pointing to the need for improvement.
Start of project	Verify process stability when performing a baseline capability analysis.
Mid-project	Investigate effects of input variables on the process output over time.
Mid-project	Verify process stability when performing confirmation runs after implementing improvements.
End of project	Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project	Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project	Control inputs to the improved process after project is complete.
Post-project	Monitor output of the improved process after project is complete.

Data

Your data must be continuous Y values collected in rational subgroups.

Guidelines

Look at the range chart (R) or standard deviation chart (S) first to determine whether the variation is reasonably in control. If so, the limits for the Xbar chart are valid and you can then evaluate the Xbar chart. If the variance is not in control, the process is unstable and the process mean information is not trustworthy.
The Xbar and R or S charts do not require normal data. Because you are plotting subgroup means, these charts eliminate the effect of nonnormal data for even small subgroups. This is based upon the central limit theorem, one of the foundations of statistical data analysis.
You can use a categorical variable with the I-MR chart to show the effects of different input conditions. Minitab refers to this as stages. For example, if you want to examine fill amounts for a bottling machine (Y) to see if differences exist between the filling heads, you can use the heads as the stage variable and see whether the mean, variation, or within-shift patterns change between the different heads.
When using a categorical variable to set up stages in the Xbar-R or Xbar-S chart, you should have at least 20 subgroups in each stage. The Xbar-R or Xbar-S chart must have enough data to reliably estimate the process mean and process variation within each stage.
If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.

How-to

Verify the measurement system for the Y data is adequate.
Establish a data collection strategy to define how you will sample subgroups over time. Ensure you are using rational subgroups whenever possible.
Collect data for the rational subgroups and enter the data into Minitab in one of the following ways:
- Enter all data in a single column and subgroup sizes in another column.
- Enter each subgroup in a row of the worksheet. All subgroups must be of equal size.
Minitab can directly import data from databases, text files, Microsoft^® Excel, and so on.
Optionally, Minitab can evaluate eight rules to determine if special causes are present.
Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits which help you make comparisons across stages. For example, you can examine changes in the process mean and variation before, during, and after the implementation of a new procedure on one Xbar-R or Xbar-S chart.

For more information, go to Insert an analysis capture tool.