Optimal inspection order when process' failure rate is constant

Suppose that a lot has been produced by a process with a constant failure rate. So either the entire lot is good, or all units up to some point are good and from that point on are all defective. We wish to determine the order in which units in such lot should be inspected so as to minimize the expected number of inspections needed to identify all defectives. Unlike previous work in this area, we do not a priori assume that the last unit in the lot is defective, and that key difference turns out to dramatically influence the nature of the optimal inspection policy and the expected number of units inspected. After analyzing the optimal policy, we suggest a very simple and intuitive heuristic, which turns out to perform extremely well. Numerical results are provided.