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Optimization and Sensitiyity Analysis

Table 14. Cost Comparisons of the X and CUSUM Charts at Various Shift Lcvels

		Expected Cost
Chart Type	Shift	Mean	Median	StdDev
CUSUM	0.25	$342	$343	$71
Shewhart	0.25	$377	$373	$84
CUSUM	1.25	$211	$218	$44
Shewhart	1.25	$228	$228	$49
CUSUM	2.25	$187	$190	$41
Shewhart	2.25	$193	$201	$42

strictly economic approach, the CUSUM protects better against false alarm rates (meaning higher ARL1) and the X chart has morÄ™ power (meaning lower ARL2).    _

For the X control chart, as the size of the shift to be detected decreases, the sample size and sampling interval both increase. For the CUSUM chart, as the shift size decreases, the sample size increases slightly while the sampling interval decreases slightly. Comparing across chart procedures, it is elear that the X chart optimum cost configuration specifies larger samples be collected less freÄ…uently than the CUSUM chart.

Conclusions The purpose of this research is to make implementation of economic control chart models easier and to aid the designer in choosing an appropriate process monitoring techniÄ…ue. This study represents the first comprehensive comparison of the X and CUSUM statistical process control procedures on an economic basis. Our results indicate that the CUSUM remains the preferred altemative in detecting smali shifts in the process mean. In addition, we also show that for large shifts (over two process standard deviations) in the mean, the CUSUM continues to dominate the X procedurÄ™, although differences are less pronounced with the largest shift.

The implications of these results are that companies may use just one statistical control procedurÄ™, the CUSUM, for the entire rangÄ™ of shift conditions with the assurance that overall cost will be as Iow or lower than that associated with the use of theX chart alone or a combination of both