An extended optimal replacement model for a deteriorating system with inspections

Abstract This study considers a generalized replacement model for a deteriorating system in which failures can only be detected by inspection. The system is assumed to have two types of failures and is replaced at the occurrence of the Nth type I failure (minor failure), or the first type II failure (catastrophic failure), or at working age T, whichever occurs first. The probability of a type I or type II failure depends on the number of type I failures since the previous replacement. Such a system can be repaired after a type I failure, but is deteriorating stochastically. That is, the operating intervals are decreasing stochastically, whereas the durations of the repairs are increasing stochastically. Based on these assumptions, we determine the expected net cost rate and discuss various special cases of the model. Finally, we develop a computational algorithm for finding the optimal policy and present a numerical example to show the properties of the proposed model.