On choosing optimal number of inspections with decreasing detection probability

Abstract

In this thesis, optimal number of inspections under various conditions are obtained for a single inspector by minimizing the expectation of a cost function that is linear in the number of inspections and in the number of undetected defectives. It is assumed that an inspector has a probability of detecting a defective in the lot that contains an unknown but Poisson distributed number of defectives, and that the detection probability decreases according to the number of inspections. Two modes of detection probability are considered : detection probability decreasing (1) linearly with the reciprocal of the number of inspections and (2) geometrically with the number of inspections. Finally, the case of two types of defectives is considered and optimal strategy for choosing the number of inspections is also obtained.