The SHEWHART Procedure

Displaying Trends in Process Data

Subsections:

Note: See X-Bar Chart for Data with Nonlinear Trend 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 $({\widehat{\bar{X}}}_ t)$ and the residual subgroup means $({\bar{X}}_ t - {\widehat{\bar{X}}}_ t)$ 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;
   drop i;
   datalines;
   1    10.0434   9.9427   9.9548   9.8056
        10.0780  10.0302  10.1173  10.0215
   2    10.1976   9.9654  10.0425  10.1183
        10.0963  10.1635  10.1382  10.1265
   3    10.0552  10.0695  10.2495  10.1753
        10.1268  10.1229  10.1351  10.2084
   4    10.1600  10.1378  10.2433  10.2634
        10.1808  10.1601  10.1035  10.0027
   5     9.9611  10.4322  10.1066  10.2653
        10.0310  10.1409  10.2709  10.0585
   6    10.2208  10.2298  10.2427  10.2315
        10.2048  10.2824  10.3347  10.1650
   7    10.2670  10.3793  10.2539  10.4037
        10.3281  10.1327  10.1986  10.1841
   8    10.2537  10.1981  10.2935  10.4308
        10.3195  10.3122  10.2033  10.3220
   9    10.2488  10.1866  10.3678  10.1755
        10.3225  10.2375  10.2466  10.3387
  10    10.3744  10.5221  10.2890  10.3123
        10.5134  10.3212  10.3139  10.1565
  11    10.3525  10.3237  10.4605  10.5139
        10.3650  10.1171  10.3863  10.2061
  12    10.3279  10.3338  10.1885  10.2810
        10.2400  10.3617  10.2938  10.2656
  13    10.1651  10.2404  10.1814  10.2330
        10.3094  10.3373  10.3266  10.3830
  14    10.3554  10.4577  10.5435  10.4805
        10.5358  10.4631  10.3689  10.1750
  15    10.2962  10.4221  10.3578  10.4694
        10.3465  10.4499  10.4645  10.3986
  16    10.6002  10.1924  10.3437  10.3228
        10.3438  10.3503  10.3761  10.3137
  17    10.4015  10.3592  10.3187  10.4108
        10.4834  10.4807  10.2178  10.3897
  18    10.4514  10.4492  10.3373  10.4497
        10.4197  10.3496  10.3949  10.1585
  19    10.3445  10.3310  10.4472  10.4684
        10.3975  10.2714  10.2952  10.6255
  20    10.2612  10.3824  10.4240  10.3120
        10.5744  10.4204  10.4073  10.3783
;