Replacement Rules for Partially Observable Equipment

摘要

Optimal inspection and replacement rules are considered for a simple piece of equipment. The equipment can be in one of only two states -- a good state or a bad state. The failure distribution of the equipment is Markovian. The true state of the equipment is unknown at all times except immediately after a replacement action. However, indirect indications of the state of the equipment can be obtained by taking observations of a quality characteristic. The distributions of the quality characteristic, conditional on the state of the equipment, are assumed to be continuous and known. It is shown that the sequence of observations and actions can be summarized into a statistic X(t) which represents the probability that the equipment is defective at time t. For a given cost structure, the objective is to minimize the expected total discounted future cost up to an infinite horizon. Two models are considered.