A Bayes Sequential Sampling Inspection Plan

Abstract

1. Introduction and summary. Given a lot of size N whose items are obtained from a statistically controlled process with an unknown probability p, 0 0 is the loss involved in sending out a defective item instead of replacing it with a good one. The cost of inspecting n items (defective items detected during inspection are replaced by good ones) is cn, c > 0. An inspection plan is to be devised that minimizes (in some suitable sense) the risk (expected loss plus inspection cost). Let Vb denote any sequential inspection plan, which determines sequentially the (random) number 9T of items to be inspected. If the lot is sent out after inspecting n items, the cost of inspection incurred is nc and the expected loss due to the defectives remaining in the lot is (N - n)pk. Then the risk is (N - n)pk + nc = Npk + nk(c/k -p), and hence the risk associated with the plan At is given by