Reliability and cost-effectiveness optimization of G-systems with preventive maintenance strategy and unreliable repairman

This paper presents a comprehensive analysis of a repairable <k₁, k₂>-out-of-n: G system comprising two distinct component types and a single unreliable repairman. We develop both availability and reliability models to assess the system performance under realistic repair constraints. For the availability model, the matrix-analytical method is employed to derive the steady-state probability distribution. Key performance indicators, including system availability and other critical metrics, are systematically obtained to characterize long-term system behavior. For the transient reliability analysis, we investigate four numerical methods: the Runge-Kutta method, the Laplace transform method, the eigenvalue-based method, and the matrix exponential method. Through extensive numerical experiments, we compare their accuracy and reveal notable drawbacks in terms of stability and scalability. The comparative results show the numerical instability issue of the eigenvalue-based method, and thus, the Laplace transform method is selected to derive the mean time to failure. A sensitivity analysis is then conducted to explore the impact of key parameters and demonstrate that component failure rates impact the system reliability more than service rates. We further introduce a cost-effectiveness model, combining the steady-state availability with the associated cost. The particle swarm optimization algorithm is applied to determine the optimal recovery rates under different system configurations. Finally, the role of preventive maintenance in enhancing the cost-effectiveness ratio is inspected.