00201 „4588c1cb831ecdbfa0f0e40ba1f7ac

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Strategies for Statistical Monitoring of Integral Control

distributed.

Table 1 presents the results for the sustained shifts. For each bÅ‚ock in the table, the results reported are the average value of the performance measure from eÄ…uation (7), the average sÄ…uared deyiation from target, and the associated standard error (in parentheses) based on 2000 simulations. The first column gives the performance measure prior to introduction of the shift; that is, for periods 1-250. The next column gives the performance for observation 251 through 500 for EPC only. The finaÅ‚ three columns give the weighted performance measure for the combined EWMA for the prediction errors and tracking signal with an added two-in-a-row rule, CUSUM with K = la and K = 2a respectively.

In each bÅ‚ock of these three columns appears a starred value. This value signifies the number of times in 2000 simulations that the specified scheme did not signal. Inspection of Table 1 indicates that both CUSUM

Table 1. Performance Measures for EPC/SPC Rules for Assignable Causes of a Shift in Process Mean at Obseryation 251 Based on 2000 Simulations for Control Actions

Shift	PM Prior To Shift	MacGregor PM	Prediction Error EWMA PM with Tracking Signal	CUSUM PM for H = 5ct and K = lo	CUSUM PM for H = 5a and K = 2 «
1	2.5496	2.55316	2.54569	2.54893	2.54837
	(0.00506)	(0.00514)	(0.00431) *130 Did not Signal	(0.00393) *1592 Did not Signal	(0.00363) *1830 Did not Signal
2	2.54714	2.59198	2.56251	2.56488	2.56887
	(0.00515)	(0.00518)	(0.00449) *114 Did not Signal	(0.003898) *1668 Did not Signal	(0.00368) * 1905 Did not Signal
5	2.54050	2.84738	2.62669	2.67944	2.69353
	(0.00517)	(0.00560)	(0.00490) *80 Did not Signal	(0.00415) *1708 Did not Signal	(0.00368) *1986 Did not Signal
7.5	2.54712	3.21829	2.69869	2.85086	2.88194
	(0.00507)	(0.00627)	(0.00516) *39 Did not Signal	(0.00452) *1792 Did not Signal	(0.00406) *1992 Did not Signal
10	2.54662	3.73557	2.77864	3.09068	3.14017
	(0.00511)	(0.00733)	(0.00536) *7 Did not Signal	(0.00542) *1741 Did not	(0.00453) *1995 Did not