00089 8f7b0c57f2bf2f1d0044db398ef2f1

88

Hurwitz & Mathur

The ARL s for three sets of L & U values, including the recommended L = 1.5, U = 3.0, are given in Table 4.

Examining this table we can see that there is nothing to be gained by adjusting the TL' limit above a value of 1.5: ARLs increase monotonically at all levels of mean shift.

Zonę Control

One school of thought in SPC-based process control prefers so-called Zonę Control. We look briefly at the zonę control scheme proposed by Jaehn (1989) and develop ARL's for it. Jaehn's rules for zonę control are as follows:

Construct the usual WECO-style control chart; with the target plus six control lines, this gives six zones corresponding to the intervals between the target and the one-, two-, and three-sigma limits. Points falling in the various zones (or circles plotted in place of points) are each assigned a score as they are plotted. Scores are assigned as follows:

Table 4. New and AIternative Rules--ARLs

Shift (u)	L=1.5; U=3.0	L=1.625; U=3.0	L=1.75; U=3.0
0.0	93.09	131.60	179.05
0.2	75.74	105.43	142.28
0.4	47.72	64.41	85.33
0.6	28.60	37.37	48.38
0.8	17.72	22.42	28.29
1.0	11.58	14.21	17.45
1.2	8.00	9.53	11.38
1.4	5.82	6.74	7.84
1.6	4.44	5.01	5.69
1.8	3.53	3.89	4.31
2.0	2.91	3.14	3.41
2.2	2.47	2.62	2.79
2.4	2.15	2.25	2.36
2.6	1.91	1.98	2.05
2.8	1.73	1.77	1.81
3.0	1.59	1.61	1.63