Analysis of a k-out-of-n Reliability System with Single Server, Internal and External Service, N-Policy, and Multiple Server Vacations

This study involves the evaluation of the reliability of a k-out-of-n repairable system with a single server responsible for repairing failed components. The server provides service to external customers in addition to servicing failed components in the system. To optimise revenue from external services without compromising system reliability, we introduce the N-policy. The repair of internal failed components starts only with the accumulation of N failed components. Once the service of internal components is started, all failed internal components are repaired one by one. As soon as the system is free of failed internal and external components, the server takes multiple vacations. Whenever the number of internal failed components reaches N, if the server is on vacation, it is interrupted, and the server immediately serves the internal component. Meanwhile, the server is in an external service, and then the service is preempted to serve the internal components. The failure times of the components of the system follow an exponential distribution, and external customers arrive according to the Poisson process. The service times of both internal and external customers follow an exponential distribution. The vacation time follows an exponential distribution. By using the Matrix Analytic Method, we discuss system stability and steady-state distribution. The N-policy level is optimised numerically using a suitable cost function.