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Applications of the EWMA

Closed-loop sigma (a_r) is calculated on the actual Y₂ data (control errors) while the controller-best sigma (o_A ) is calculated from the forecast errors (A_f). Again, for the case of L = 0, the control and forecast errors are the same. If it were necessaiy to use a non-zero value of L, then comparing these two columns would show the penalty for making less frequent adjustments. Finally, the common-cause sigma (<J_a) is estimated by passing the forecast errors to an IR chart with 3-sigma control limits based on the data, deleting data which violate out-of-control criteria on either the 1 or R chart, and calculating sigma on the rest. This provides a method for updating the common-cause sigma used by the controller.

The summary portion of Table 1 shows that process capability (as represented by common-cause sigma) is .281, compared with the closed-loop

Table 1. Process Capability Study for fj. Data from 11 July 1990 to 29 August 1990; g = .1

		Open-	Closed-Loop	Controller-Best	Common
		Loop	Sigma	Sigma	Cause
MachinÄ™	N	Sigma			Sigma
1	90	0.517	0.369	0.369	0.291
2	99	0.528	0.386	0.386	0.289
3	92	0.397	0.306	0.306	0.310
4	92	0.432	0.289	0.289	0.273
5	91	0.399	0.294	0.294	0.222
6	95	0.383	0.292	0.292	0.224
7	92	0.357	0.243	0.243	0.241
8	93	0.370	0.302	0.302	0.239
9	70	0.462	0.372	0.372	0.395
10	67	0.433	0.369	0.369	0.313
Summary Report
Variable		Label	Mean	Minimum	Maximum
CG_SIG		Open-loop sigma 0.531		0.357	0.949
BD SIG		Closed-loop sigma 0.369		0.243	0.694
GDSIG		Controller-best sigma 0.369		0.243	0.694
STDDEY	Common-cause sigma 0.281 0.170 0.422