Analysis of the Optimal Inspection and Maintenance Policy for the Deteriorating System with Phase-Type Approximation

The optimal model of inspection and maintenance for the deteriorating system is presented with the semi- Markov decision process. Since the sojourn time of deteriorating state, inspection interval and maintenance time are the stochastic variables which follow the general distribution, the phase-type approach is proposed to preserve the analytical tractability of the transition probability matrix. To solve the problem that the PH distribution changes the state space of system, the value iteration algorithm for the semi-Markov decision process is improved to get the optimal inspection and maintenance policy. In the process of iteration, the decision of policy within the subset is restrict to be the same. With this policy the long-run average cost rate of system is minimized. Finally, the numerical example is put forward to illustrate the implementation of the model and iteration algorithm.