Graphical Enhancements

Displaying Trends in Process Data

See SHWTREN in the SAS/QC Sample Library

Time trends due to tool wear, environmental changes, and other gradual process changes are sometimes observed in $\bar{X}$ charts. The presence of a systematic trend makes it difficult to interpret the chart because the control limits are designed to indicate expected variation strictly due to common causes.

You can use the REG procedure (or other modeling procedure) in conjunction with the SHEWHART procedure to determine whether a process with a time trend is in control. With the REG procedure, you can model the trend and save the fitted subgroup means $({\hat{\bar{X}}}_t)$ and the residual subgroup means $({\bar{X}}_t - {\hat{\bar{X}}}_t)$ in an output data set. Then, using this data as input to the SHEWHART procedure, you can create a trend chart, which displays a trend plot of the fitted subgroup means together with an $\bar{X}$ chart for the residual subgroup means, thus removing the time-dependent component of the data from its random component. Having accounted for the time trend, you can decide whether the process is in control by examining the $\bar{X}$ chart.

The following example illustrates the steps used to create a trend chart for a SAS data set named TOOLWEAR that contains diameter measurements for 20 subgroup samples each consisting of eight parts:

   data toolwear;
      input hour @;
      do i=1 to 8;
         input diameter @;
         output;
      end;
      label hour     = 'Hour'
            diameter = 'Mean Diameter in mm';
      datalines;
    1   10.04   9.94   9.95   9.81  10.08  10.03  10.12  10.02
    2   10.20   9.97  10.04  10.12  10.10  10.16  10.14  10.13
    3   10.06  10.07  10.25  10.18  10.13  10.12  10.14  10.21
    4   10.16  10.14  10.24  10.26  10.18  10.16  10.10  10.00
    5    9.96  10.43  10.11  10.27  10.03  10.14  10.27  10.06
    6   10.22  10.23  10.24  10.23  10.20  10.28  10.33  10.17
    7   10.27  10.38  10.25  10.40  10.33  10.13  10.20  10.18
    8   10.25  10.20  10.29  10.43  10.32  10.31  10.20  10.32
    9   10.25  10.19  10.37  10.18  10.32  10.24  10.25  10.34
   10   10.37  10.52  10.29  10.31  10.51  10.32  10.31  10.16
   11   10.35  10.32  10.46  10.51  10.37  10.12  10.39  10.21
   12   10.33  10.33  10.19  10.28  10.24  10.36  10.29  10.27
   13   10.17  10.24  10.18  10.23  10.31  10.34  10.33  10.38
   14   10.36  10.46  10.54  10.48  10.54  10.46  10.37  10.18
   15   10.30  10.42  10.36  10.47  10.35  10.45  10.46  10.40
   16   10.60  10.19  10.34  10.32  10.34  10.35  10.38  10.31
   17   10.40  10.36  10.32  10.41  10.48  10.48  10.22  10.39
   18   10.45  10.45  10.34  10.45  10.42  10.35  10.39  10.16
   19   10.34  10.33  10.45  10.47  10.40  10.27  10.30  10.63
   20   10.26  10.38  10.42  10.31  10.57  10.42  10.41  10.38
   ;

Displaying Trends in Process Data

Step 1: Preliminary Mean and Standard Deviation Charts

Step 2: Modeling the Trend

Step 3: Displaying the Trend Chart