Determining the optimal maintenance action for a deteriorating repairable system

This paper develops a decision model for risk management of the deterioration of a repairable system. When a failure occurs in a deteriorating system, an optimal maintenance decision that includes the possibility of system replacement, as compared to mere deterioration reduction, should be made. There are many uncertainties associated with deterioration, however, so the decision may require a probabilistic analysis. Here, a well-known nonhomogeneous Poisson process with a power law intensity function is used to model the uncertain behavior of the deteriorating system. A Bayesian statistical approach is adopted to allow for the uncertainty of the parameters of the power law intensity function, which imposes a conjugate prior distribution of the parameters. A power law maintenance cost function and the failure cost are analyzed to determine the magnitude of failure risk reduction by minimizing the expected cost incurred from the maintenance action and future failures. A numerical example is given.