The state-of-the-art methodologies for reliability analysis of imperfect repair

Abstract

The multi-unit system forms the foundation for various efficiency assessments in operational machining management, necessitating the evaluation of critical parameters. This research article analyzes a Markovian machine repair problem employing a controllable strategy and imperfect repair. Imperfect repair denotes that the repairer services failed machines, but the service may not be successful. The chosen controllable threshold-based strategy addresses the challenge of admitting failed units when the number in the reparable queue reaches the system's capacity to prevent significant expected waiting times. Repairers cease admitting new failed units until the queue size decreases to a predetermined level. Unadmitted failed units may undergo repair at an external facility, incurring additional costs. The number of failed units in the waiting line and the expected number of service-gained units are pivotal in a well-designed control policy. Utilizing the Laplace transform method, we derive the transient-state distribution of failed units in the system, establish various performance measures, and calculate the reliability function and mean time to the first failure of the system. Extensive numerical experiments and sensitivity analyses are also conducted to provide a comprehensive understanding of the studied system.