Optimal maintenance policy for a multi-state deteriorating system with two types of failures under general repair

We present a general repair model for a multi-state deteriorating system subject to major and minor failures. The process is modeled as a semi-Markov decision process with the optimality criterion being the minimization of the long-run expected average cost per unit time. A modified policy-iteration algorithm using the embedded technique is developed as the computational approach used to find the optimal maintenance policy. The advantage of using the embedded technique is that it reduces the size of the linear system in the value-determination step of the algorithm resulting in reduced computational efforts for large state spaces. Numerical examples are given which illustrate the implementation of the computational approach.