Evaluation of inspection policies and processes for deteriorating systems subject to catastrophic failure

Abstract

The purpose pf this thesis is to study deteriorating systems subject to catastrophic failure in order to evaluate deterministic inspection policies and stochastic inspection processes. The underlying deterioration process is assumed to be an increasing Markov renewal process so that the system deteriorates over time. An important feature of the model is that the true state of the system cannot be known by simple observation; instead, some tests have to be carried out in order to detect if the system has positive deterioration or not. However the results of the tests are not perfect so that the probability of true and false detections depend on the unobserved state of the system. The system can be inspected in two ways. Inspections are done either deterministically at some prespecified" points Ln time which constitute deterministic inspection policies. On the other hand, inspections at random times are also possible and they constitute stochastic inspection processes. These inspection policies and processes are evaluated in various ways; explicit expressions to compute the expected number of tests are presented and some practical applications of our results are illustrated with some interesting examples.