A decision model for deteriorating repairable systems

Complex systems are generally repaired rather than replaced after failures. If deterioration in a repairable system is detected, i.e., the successive inter-failure times become stochastically smaller and smaller, then the decision of when to overhaul or discard the system is of fundamental importance. However, such a decision involves many uncertainties, such as the initial status of the system, the degree of deterioration, expected system lifetime, repair cost, accidental cost, etc, which are important factors and need to be evaluated carefully. In this paper, a Bayesian decision theoretic approach is developed. A nonhomogeneous Poisson process with a power law failure intensity function is used to describe the behavior of the deteriorating repairable system. Also, a proposed natural conjugate prior distribution is applied to make the Bayesian decision-making process more effective and efficient.