Inspection Procedures when Failure Symptoms Are Delayed

A system fails at time T but does not display any symptoms of failure until time T + S; both T and S are random variables. Detection of failure is possible either because the system displays symptoms of failure or by means of an inspection before the appearance of symptoms. A cost c is associated with each inspection and a cost-rate v is incurred after failure until detection. For a restricted class of failure densities, the inspection procedure that minimizes the total expected cost can be found by means of an iterative algorithm.