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89

A Very Simple Set of Process Control Rules

ZONĘ	SCORE
between target and 1-sigma	1
between 1-sigma and 2-sigma	2
between 2-sigma and 3-sigma	4
beyond 3-sigma	8

The zonę scores are cumulated as they occur until either an observation falls on the other side of the centerline or the cumulated score is ^ 8. If the score is > 8 an 'out of control' signal is recorded, otherwise the cumulation continues. Table 5 shows results for 100 simulations at each mean shift.

Up to a shift of 1.0 standard deviation in the mean, the zonę ARLs and SDs are smaller than those for either the WECO or the 'new' rules. This suggests larger alpha-errors for the zonę scheme for smali shifts in the mean.

Table 5. Simulated ARLs and SDs for 'Zonę' Control Rules²

Shift(p.)	ARL (zonę)	SD (zonę)
0.0	66.82	49.93
0.2	38.15	29.64
0.4	21.11	15.67
0.6	15.29	10.48
0.8	10.54	4.20
1.0	8.98	2.61
1.2	8.37	2.19
1.4	7.55	1.59
1.6	7.32	0.99
1.8	7.34	0.71
2.0	7.24	0.77
2.2	7.28	0.72
2.4	7.09	0.77
2.6	7.18	0.83
2.8	7.10	0.87
3.0	7.30	0.69

²Thanks to Ricki Ingalls, SEMATECH, for providing the simulation results.