00087 �1f3e7dbe761c05b65b4291ad8270c7

86

Hurwitz & Mathur

Table 2. 'New' & WECO Rules: Average Run Length's Compared

Shift (p)	ARL (new)	ARL (WECO)	ARL1/ARL2
0.0	93.09	91.75	1.01
0.2	75.74	66.80	1.13
0.4	47.72	36.61	1.30
0.6	28.60	20.90	1.37
0.8	17.72	13.25	1.34
1.0	11.58	9.22	1.26
1.2	8.00	6.89	1.16
1.4	5.82	5.41	1.08
1.6	4.44	4.41	1.01
1.8	3.53	3.68	0.96
2.0	2.91	3.13	0.93
2.2	2.47	2.70	0.91
2.4	2.15	2.35	0.91
2.6	1.91	2.07	0.92
2.8	1.73	1.85	0.94
3.0	1.59	1.67	0.95

in the mean greater than about 1.6a, whereas the WECO rules are morę powerful for shifts below 1.6ct. The differences are surprisingly minor, however, when considering the gain in simplicity.

Comparing rules of run on the basis of ARL gives some indication of potential differences in the risk of control false alarms Calpha' error). The analysis, however, needs estimates of ARL standard deviations (SD). The Computer program of Champ and Woodall (1990) give estimates of ARL standard deviations, and these are shown in Table 3.

As can be seen, reading from the top down, SD1/SD2 column, WECO SD's begin at 4% smaller than 'new' SD, rise to 65% smaller at a shift in mean (p) of 1.0, then drop back to 4% at a mean shift of 2.2. Thereafter, the WECO ARL standard deviations are worse than the 'new* by about 3% to 14%.

In summary, the user will have to balance convenience of the 'new* rules against vaiying degrees of uncertainty in the ARLs. In practice, the authors have found that this tradeofif is well worth making.