Optimization of repairable systems with repairman's multiple vacations

Purpose - Technological advancements and growing complexity of many real-time systems, namely, communication, transportation, defense systems, etc., necessitate the importance to adopt a well-planned repair process such as phase type quasi-renewal process contributing to an improved system performance. Further, in an attempt to boost the role of maintenance as a financial benefactor, repairman's multiple vacation policy is incorporated. Also, the significance of the degree of repair is illustrated while indicating the suitability of the matrix-analytic approach via the phase type quasi-renewal operating/repair times in reliability. The paper aims to discuss these issues. Design/methodology/approach - The optimal replacement policy is obtained by employing the matrix-analytic method and minimum average cost rate. Findings - The considered models make a significant contribution towards establishing that the matrix-analytic method, using the phase type quasi-renewal process, aids in reducing the computations and also fills the gap in the literature in the study of deteriorating systems. Availability and rate of occurrence of failures are evaluated in transient and steady-state regime. Originality/value - This model differs from the existing models, in that, a repairman's multiple vacation, delayed repair time and representation of the failure occurrence by a mixed Poisson process have been incorporated into the analysis. Also, time-dependent case and N-policy have been adopted to explore the optimality issues using phase type quasi-renewal process analytically. The numerical illustrations warrant that the maintenance policy proposed in this paper produces a considerably lower cost.