Reliability and Profit Analysis of a Cold Standby System With Priority and Two Types of Repairmen

This paper investigates the reliability of a cold standby repairable system with heterogeneous maintenance resources and priority based scheduling. To deal with practical complexities, a reliability model is developed by considering two types of repairmen and a dual‐priority mechanism for the operation and maintenance sequences of critical components. Two different failure modes, namely hardware failures, and human errors, are taken into account in the analysis. Using the supplementary variable method, a set of integro‐partial differential equations is established to characterize stochastic state transitions, and the Laplace‐transform expressions for key performance indices including instantaneous availability and reliability are derived. The validity of the proposed model is verified by means of numerical inversion and Monte Carlo simulation. The analytical formulations are found to be in good agreement with simulation results. A case study of an ANSI centrifugal pump system from the chemical industry is provided to conduct sensitivity analysis for failure rates. Furthermore, an expected cumulative profit function is constructed to perform joint reliability and economic analysis, which balances operating revenue, downtime losses, and maintenance costs. Numerical results show that the proposed model can well describe the dynamic behavior of complex systems under coupled constraints, and it provides theoretical support for maintenance resource allocation and maintenance‐strategy optimization.