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 $\bar{X}$ 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

Creating a Preliminary Individual Measurements Chart

Calculating Probability Limits

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