Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

Classical Dodge-Romig sampling inspection plans with their operational modifications and practice-oriented extensions served a very useful purpose for a long time. Some theoretical and practical limitations surfaced later and their uses in Industry have been limited. Apart from practical difficulties, a few theoretical drawbacks are worth an examination. The requirement of ensuring a given (10%) customer's risk exactly poses problems, since the underlying variable (number of defectives in the sample) is discrete and there is hardly any mutually agreeable choice between a plan with a lower risk and a higher sample size and a plan with a bit higher risk and smaller sample size. Fuzzy mathematical programming offers a solution, with all its limitations. The fact that amount of inspection is minimized for the process average fraction defective-something really not known-should invite application of decision rules under uncertainty or risk. Considering the Type B O.C. curve, Mood's theorem is a rejoinder to the assumption of a fixed unknown fraction defective. Possibly, one can even doubt the applicability of the Binomial approximation to the hypergeometric in case of Type A O.C. function. It may be interesting to apply game theory approach to determining the plan parameters. The talk looks at some of these issues.