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How Do I Create Control Charts for Nonnormal Data in Excel Using SigmaXL?

Individuals Charts for Nonnormal Data (Box-Cox Transformation)

An important assumption for Individuals Charts is that the data be normally distributed (unlike the X-Bar Chart which is robust to nonnormality due to the central limit theorem). If the data is nonnormal, the Box-Cox Transformation tool can be used to convert nonnormal data to normal by applying a power transformation. The Johnson transformation and other distributions may also be used with Automatic Best Fit (see Process Capability, Capability Combination Report Individuals Nonnormal).
  1. Open the file Nonnormal Cycle Time2.xls. This contains continuous nonnormal data of process cycle times. We performed a Process Capability study with this data earlier in the Measure Phase, Part H.
  2. Initially, we will ignore the nonnormality in the data and construct an Individuals Chart. Click SigmaXL > Control Charts > Individuals. Ensure that entire data table is selected. If not, check Use Entire Data Table. Click Next.
  3. Select Cycle Time (Minutes), click Numeric Data Variable (Y) >>. Select Calculate Limits. Check Tests for Special Causes.

    Individuals Chart

  4. The resulting Individuals Chart is shown:
  5. Individuals Chart

    This chart clearly shows that the process is “out-of-control”. But is it really? Nonnormality can cause serious errors in the calculation of Individuals Chart control limits, triggering false alarms (Type I errors) or misses (Type II errors).

  6. We will now construct Individuals Control Charts for nonnormal data. Select Sheet 1 Tab (or press F4). Click SigmaXL > Control Charts > Nonnormal > Individuals Nonnormal. Ensure that the entire data table is selected. If not, check Use Entire Data Table. Click Next.
  7. Select Cycle Time (Minutes), click Numeric Data Variable (Y) >>. We will use the default selection for Transformation/Distribution Options: Box-Cox Transformation with Rounded Lambda. Check Tests for Special Causes as shown:

    Individuals Chart
  8. Click OK. The resulting control charts are shown below:

    SigmaXL Control Charts

    Note that there are no out-of-control signals on the control charts, so the signals observed earlier when normality was assumed were false alarms.

    The Individuals – Original Data chart displays the untransformed data with control limits calculated as:

      UCL = 99.865 percentile
      CL = 50th percentile
      LCL = 0.135 percentile

    The benefit of displaying this chart is that one can observe the original untransformed data. Since the control limits are based on percentiles, this represents the overall, long term variation rather than the typical short term variation. The limits will likely be nonsymmetrical.

    The Individuals/Moving Range – Normalized Data chart displays the transformed z-values with control limits calculated using the standard Shewhart formulas for Individuals and Moving Range charts. The benefit of using this chart is that tests for special causes can be applied and the control limits are based on short term variation. The disadvantage is that one is observing transformed data on the chart rather than the original data.

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