Inspection policies and processes for deteriorating systems subject to catastrophic failure

Deteriorating reliability systems that are subject to catastrophic failure are analyzed in order to propose and evaluate some deterministic and stochastic inspection models. The underlying deterioration process is assumed to be an increasing Markov renewal process where the true state of the system can not be determined by simple observations. Instead, some tests can be done in order to detect if the system has positive deterioration or not. The results of the tests, however, are not perfect so that the probability of true and false detections depend on the unobserved state of the system. The system is inspected either deterministically at prespecified points in time, or stochastically at random points in time. Both types of models are considered to present explicit computational expressions for various performance measures like the expected number of inspections with different results and the probability of detection. Some practical applications of the results are also included.