Note: See Nonnormal Process Data 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.[55] 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 might 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.[56] 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 partial listing of Calls
is shown in FigureĀ 18.216.
Figure 18.216: Answering Times from the Data Set Calls
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 |