This research investigates a k-out-of-n reliability system in which components are prone to failure, and a single unreliable server is responsible for their repair. During idle periods, the server utilises its time to serve external customer requests. Repair operations for internal components commence only after N such failures have occurred. To maintain the system’s reliability during the server’s engagement with external customers, an N-policy is enforced. If N internal failures take place while external service is ongoing, the server preempts the external service to address internal issues. The failure times of components and the arrival of failed external customers are assumed to follow Poisson distributions. The service times for both external requests and system repairs follow a phase-type distribution, while the server’s breakdown and repair duration are also modelled using exponential distributions. The Matrix Analytic Method is employed to analyse the system’s steady-state behaviour and stability. Additionally, a cost function is defined to facilitate the numerical optimisation of the N-policy threshold.