Structure of an optimal maintenance policy for a semi‐Markovian deteriorating system with major and minor failures

Abstract

AbstractWe consider a multistate system wherein deterioration is modeled as a semi‐Markov process with an absorbing state. The system can suffer major and minor failures. When the system reaches the absorbing state, major failure occurs and it is replaced. Meanwhile, minor failure can occur at each state. Upon occurrence of a minor failure, the system is minimally repaired. We propose an optimal state–age‐dependent maintenance policy for the system which minimizes an expected long‐run cost rate. We study structural properties of the optimal maintenance policy and show that a control‐limit policy holds under several assumptions. We also derive a special relation focused on minor failure related to the state–age‐dependent maintenance policy.