00208 Ü1906ab0bcf2542dac76203983810dc

210

Messina, Montgomery, Keats & Runger

Table 4. Average Run Lengths for the Rules in Table 3

Trend	Prediction Error EWMA Signal Number Lambda = 0.4 with Tracking Signal (2 in a row)	CUSUM Signal Number for H = 5ct and K = la	CUSUM Signal Number for H = 5a and K = 2a
0.05	67.481	4.485	18.5
	(1.24764)	(0.40987)	(2.5668)
	*70 Did not Signal	* 1557 Did not Signal	* 1946 Did not Signal
0.10	55.825	2.920	8.766
	(1.01210)	(0.25339)	(1.93315)
	*6 Did not Signal	*1614 Did not Signal	* 1970 Did not Signal
0.25	26.477	1.5340	1.875
	(0.3855)	(0.09799) *1633 Did not Signal	(0.54307) * 1992 Did not Signal
0.5	13.845	1.1735	1.2727
	(0.1608)	(0.05381) * 1660 Did not Signal	(0.26004) * 1989 Did not Signal
1.0	7.433	1.0120	1.125
	(0.06613)	(0.00953) * 1669 Did not Signal	(0.12103) * 1984 Did not Signal

the control actions or both? To answer this Ä…uestion, we will compare the statistical properties of ARLs and false alarm rates before an assignable cause has been introduced into the process for the various SPC schemes associated with each. The assignable causes of sustained shifts and trends are analyzed separately. SubseÄ…uently, an overall strategy will be proposed for the control engineer to employ.

To evaluate the sustained shift in the process, we first compare the ARLs from Table 2 of Montgomery, Keats, Runger, and Messina (1994) for the deviation from target with the ARLs of Table 2 presented here. The Shewhart chart for individuals gives the best results for the deviation from target. Comparison with the combined prediction error EWMA and tracking signal shows that the control action procedurÄ™ performs better than the Shewhart. The reverse is true for large sustained shifts. A compromise can be reached by using a combined scheme EWMA prediction error and tracking signal scheme on the control actions to detect smali shifts Ä…uickly. To detect large shifts, the control engineer should apply a Shewhart chart for individuals on the deviation from target.