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

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