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 Specialized Control Charts

# Nonnormal Process Data

 See SHWNONN in the SAS/QC Sample Library

A number of authors have pointed out that Shewhart charts for subgroup means work well whether the measurements are normally distributed or not.* On the other hand, the interpretation of standard control charts for individual measurements (X charts) is affected by departures from normality.

In situations involving a large number of measurements, it may be possible to subgroup the data and construct an chart instead of an X chart. However, the measurements should not be subgrouped arbitrarily for this purpose.* If subgrouping is not possible, two alternatives are to transform the data to normality (preferably with a simple transformation such as the log transformation) or modify the usual limits based on a suitable model for the data distribution.

The second of these alternatives is illustrated here with data from a study conducted by a service center. The time taken by staff members to answer the phone was measured, and the delays were saved as values of a variable named TIME in a SAS data set named CALLS. A listing of CALLS is shown in Figure 49.24.

 recnum time 1 3.233 2 3.110 3 3.136 4 2.899 5 2.838 6 2.459 7 3.716 8 2.740 9 2.487 10 2.635 11 2.676 12 2.905 13 3.431 14 2.663 15 3.437 16 2.823 17 2.596 18 2.633 19 3.235 20 2.701 21 3.202 22 2.725 23 3.151 24 2.464 25 2.662 26 3.188 27 2.640 28 2.541 29 3.033 30 2.993 31 2.636 32 2.481 33 3.191 34 2.662 35 2.967 36 3.300 37 2.530 38 2.777 39 3.353 40 3.614 41 4.288 42 2.442 43 2.552 44 2.613 45 2.731 46 2.780 47 3.588 48 2.612 49 2.579 50 2.871
Figure 49.24: Answering Times from the Data Set CALLS

#### Calculating Probability Limits

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