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Optimization and Sensitivity Analysis

typical production situations.

The sensitivity analysis included six designed experiments using combinations of the two control chart types, two published examples and two process shift ranges. In smali process shift experiments, A again ranged from 0.25 standard deviations to 1.25 standard deviations. For the large shifts cases, A varied from 1.25 to 2.25 process standard deviations. Table 11 shows the scenarios which were studied. The two examples and two shift levels allowed us to test for consistency of results across vaiying input conditions.

The responses for each of the six experiments were expected cost per time unit and the control chart design parameters including the interval widths, sample size, and sampling interval. Cost was the response of primary interest while the other responses were analyzed to understand the impact that cost minimization has upon the design parameters. The analysis will be discussed by first comparing the results of the two procedures across examples for the smali process shift. Then the results from the LV example for the smali shift are compared with the results of the large shift .

Once again, the two examples of the previous section were used in the analysis. The first analysis consisted of a comparison of the X and CUSUM under a smali process shift condition (0.25-1.25). Table 12 shows the results for each of the five response variables. Only the parameters significant in at least one model are included in the table. The primary objective in model development was parsimony, or choosing the smallest number of parameters for adequate representation. The table displays the letter C for cases of parameter significance in the CUSUM case and an X for significance in the Shewhart case. The coefficients of determination (R²) are displayed to show the amount

Table 11. Sensitivity Run Combinations

Chart	3	l	CUSUM
Example Shift	Smali	Large	Smali	Large
Lorenzen and Vance			V	✓
Montgomery SQC	✓
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