Summary

A statistical process control (SPC) tool that consists of two charts:
  • The top chart is the 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 the 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 the 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

Continuous Y, data collected in rational subgroups.

How-To

  1. Verify the measurement system for the Y data is adequate.
  2. Establish a data collection strategy to define how you will sample subgroups over time. Ensure you are using rational subgroups whenever possible.
  3. 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.
  4. Minitab can directly import data from databases, text files, Excel, and so on.
  5. Optionally, Minitab can evaluate eight rules to determine if special causes are present.
  6. 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.

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.
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