*By* **Rudy Kittlitz**

I found the article by Sullivan (2002) to be very interesting and want to make some brief comments. Detecting multiple change points is difficult. A probability plot of the data from his Table 1 as shown in Figure 1 reveals some interesting groupings. The plot suggests to me that there are at least three different sets of data. The individual groups tend to have a steeper slope than the data taken overall, implying that the groups have smaller standard deviations than the overall standard deviation of 1.2.

My CUSUM analysis of the data in Table 1 does
indicate some changes, versus no changes seen in Figure 2 of Sullivan
(2002). With 'wandering data,' a good estimate of the underlying standard
deviation is obtained by the MSSD (Mean Squared Successive Di.erence)
technique developed by von Neumann et al. (1941). The MSSD standard deviation
estimate is 0.92 for this data. For the CUSUM parameters, I used *h*
= 4.86, *k* = 0.5, FIR = 2.43, and 'Reset after a signal.' These
parameters give an ARL(0) of 370. The bene.ts of a Fast Initial Response
(FIR) were given by Lucas and Crosier (1982). The CUSUM plot shown in
Figure 2, from MINITAB, shows at least four distinct signals, which is
in agreement with Sullivan's analysis.

In this interesting and challenging field, I believe that all of the appropriate tools need to be brought together. Probability plots often reveal information that is hidden in other analyses and need to be used more. The CUSUM chart is a powerful tool, although many years of experience does help in setting the parameters appropriately.

Read Full Article (PDF, 116 KB)