Selecting Bayesian Acceptance Plans for Quality Control by Pattern Search

This paper reports the results of an experimental evaluation of the effectiveness of pattern search as a solution algorithm for determining optimal Bayesian single sampling acceptance plans for quality control over a broad range of such problems. Since the effectiveness of pattern search is presumably dependent on the choice of the pattern search parameters, the following factors were systematically manipulated as independent variables: (1) starting vector, (2) pattern multiplier, (3) step size, and (4) sophistication of exploratory move (one versus two dimensional). The effectiveness measures (dependent variables) were: (1) % expected total cost obtained by pattern search above the optimal expected total cost, (2) central processing unit (CPU) time, and (3) number of search iterations. While the results showed that solution quality and computational efficiency were affected by some of the search parameters both in terms of main and interaction effects, pattern search as a solution routine in quality control acceptance sampling was shown to be seriously deficient when used in a single application. However, 20 multiple applications of pattern search using single dimensional exploration and varying search parameters overcame this deficiency by efficiently converging on an optimal solution. Such a solution procedure compares favorably to other existing solution methods.