Reliability and Availability Analysis of k -out-of- M+S Retrial Machine Repair System with Two-Way Communication

This paper studies the reliability and availability of a k -out-of-( M+S ) retrial machine repair system with two-way communication, consisting of M primary components and S warm standby components. The system incorporates the retrial behavior of failed components. When the repairman becomes idle, he initiates outgoing calls after a random period either to failed components in the orbit for repair or to components outside the orbit for preventive maintenance. The main contribution of this study is the incorporation of proactive repairman behavior, which more realistically captures operational practices in certain engineering systems. By employing the matrix analytic method together with a recursive approach, the steady-state probabilities of the system are obtained, and several important performance measures are derived. Furthermore, the Runge–Kutta method is used to evaluate the system reliability and the mean time to failure. A sensitivity analysis is conducted to investigate the effects of key system parameters, supported by numerical experiments and graphical illustrations. Finally, a cost–benefit model is formulated, and a genetic algorithm is implemented to determine the optimal values of the decision variables that minimize the cost–benefit ratio.