Reliability Analysis of a Limited-Capacity Dual-Repair System with Hybrid Vacation Policies

This study investigates the reliability of a machine dual-repair system (MDRS) with limited capacity and multiple operational vacations (OV). Multiple operational vacation is a mechanism that involves the process of the two types of vacation, one as operational vacation (OV) and another one is non-operational vacation (NOV). In this machining system, there are M operating machines, to prevent redundant breakdowns of machines and S spare machines are used to ensure smooth functioning. The server can be in a busy state, an operational vacation state, or on Non-operational vacation state. State-transition equations are formulated based on the Chapman-Kolmogorov differential-difference equations, and with the help of these equations stationary probability distribution is obtained. The Runge-Kutta IV order numerical method is used to evaluate system performance measures. The cost has been optimized using Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) techniques by testing convergence as well as comparison of the outcomes of both PSO and GWO. The exploration of the essential performance measures and graphical representations has been conducted.