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Optimization and Sensitmty Analysis

account for over 90% of the variability in the cost response, regardless of input scenario or control chart type.

For control chart design purposes, generał agreement occurred across examples and between control charts. A affects every design parameter response. For the decision interval, the cost per false alarm (Y) was significant for both charts. Although several parameters aflfect sampling interval, the universally significant parameters are the cost while producing out-of-control (Ci), and the variable sampling cost (b). In addition to X, the time to sample and chart one item (E) was significant in all four cases. Thus, if the designer is aware of restrictions on sample size or sampling interval, it is important to accurately estimate parameters such as X, Ci and E.

Because these monitoring techniąues are not used to detect only relatively smali shifts, it is important to determine if the list of significant parameters is affected by large process shifls. We used the LV example with the same input values except the process shift to be detected now ranged from 1.25 to 2.25 process standard deviations. The results in Table 13 show perfect agreement across shift size and control chart type for the cost response. The same four inputs: X, Co, Ci and A were significant in each of the four models. Each model accounted for over 90% of the variability under the large shift condition. Also, many of the parameters significant in the smali shift case for the decision variable responses were again significant in the large shift case.

Realizing that only four of the 12 input variables have significant impacts on the cost response is comforting news to those interested in designing cost efficient monitoring systems. Of equal importance are the bottom linę cost totals compared across control chart procedures. Assuming the environment is now favorable for implementing either the analytic CUSUM or the X control chart in a variables measurement situation, which chart should be used if cost is of ultimate importance? Output analysis of these designed experiments provides the answer to this ąuestion. Table 14 shows the results of applying the LV example to the two procedures across two levels of process shift. For the 0.25 and 2.25 shift cases, 32 design runs from the sensitivity analysis were averaged. The 1.25 shift case appeared in both the smali and large designs so 64 runs were available for computing those cost statistics.

Regardless of the shift size, the CUSUM is less expensive. The cost differences between the two procedures is minimal for the large shift scenarios. These results imply that a company may choose to implement a single procedurę for all shift conditions. Benefits associated with this decision are reduced training costs, easier modifications to software and over-all simplification of the monitoring process. The control chart designer is often concemed with the values of the various design parameters as well as the