A study of the effect of imperfect inspection on the efficacy of maintenance for a non-repairable system with a defective state

We consider a non-repairable system with three possible states, good, defective and failed. The latter is detected as soon as it occurs provided that the system stops functioning. The defective state, which is only revealed by inspection, does not prevent the system from fulfilling the function for which it was designed. However given the high costs derived from a failure, it is worth replacing the system once it enters the defective state, see, Scarf and Cavalcante (2010). We present a model for inspection and maintenance consisting of periodic tests to check the state of the system. We investigate the quality of these procedures assuming that inspections may give an erroneous result. Such false positives and false negatives have been considered in previous works (Badia et al. 2002), (Berrade et al. 2010). In this paper, our aim is to provide additional insight about the effect of imperfect inspection. We assume that inspections constitute the only knowledge we have about the state of the system prior to failure. Therefore a false positive implies the replacement of the system by a new one.