Optimum Test Procedure Under Stress

A means of scheduling a test procedure is presented when one component, for example, out of n has failed. Each component has a given probability of failure. The time to examine each component is a random variable with known probability distribution. However, there is only a limited amount of time available for search. What test procedure should be utilized to maximize the probability of locating the failed component within the given time? The problem is solved using some renewal theory results and the functional equation approach of dynamic programming.