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A Rule-Based Approach to Multiple Statistical Test Analysis

Decision Rules

The goal of the research was to develop a sensitive, accurate procedurę for analyzing poisson time-between-events (TBE) data. With any single test, tradeoffs must be madę between sensitivity (speed) and accuracy (correct decisions). This research used a sensitive procedurę for fast detection paired with backup analysis to maintain accuracy.

The CUSUM, by itself, can provide for wide rangę of performance signatures. Using Iow values provide for extra sensitivity and quick detection, yet also allow for numerous Type I errors to occur. High values give extremely Iow Type I error rates, but show very long run lengths needed to detect a process change. Table 1 displays a section of a TBE CUSUM average run length table from Lucas (1985). The section displayed is for the values of k = 0.7, which corresponds to desired detectable process changes of 2 times the acceptable level. (i.e., 100 PPM detectable level for an acceptable level of 50 PPM).

From Table 1, a h^ = 2.1 will detect a two-times process change on an average of 9.56 runs. Unfortunately, the same value will return a detection on average of 49.9 runs when the process is still in control. Conversely, a hj = 5 .6 takes an average of 1870 runs to come to a false alarm decision. This value takes a rather long 26.9 runs to reach a detection when the process has changed though.

Table 1. Average Run Length comparison for the TBE CUSUM. Adapted from Lucas (1985)

Multiple of Acceptable Ratę

h	^kb	ht/kb	1.0	1.5	2.0
2.1	.7	3	50	16.0	9.56
2.8	.7	4	110	23.9	12.9
3.5	.7	5	230	33.1	16.4
4.2	.7	6	468	43.4	19.9
4.9	.7	7	948	54.8	23.4
5.6	.7	8	1870	66.9	26.9