Reliability Analysis of a k-out-of-n Single Server System Extending Service to External Customers Under N-Policy and Server Vacations
摘要
This study investigates the reliability of a k-out-of-n repairable system with a single server repairing failed system components. The server makes use of idle time by providing service to external customers. An N-policy is used to ensure the system’s reliability, even when it provides service to external components. The service for internal failed components begins only after N internal failed components have been accumulated. Furthermore, the external service is preempted when the server is busy with external failed components and the number of failed internal components reaches N. Once the internal component service is started, all failed internal components are repaired one by one. When both internal and external failed components get cleared from the system, the server goes on multiple vacations. The failure times of the system’s components follow an exponential distribution, while external customer’s arrival follows the Poisson process. The service times of internal and external customers follow a phase type distribution. Vacation time has an exponential distribution. Matrix Analytic Method is used to discuss system stability and steady-state distributions. The N-policy level is numerically optimised using an appropriate cost function.