System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy

Abstract

AbstractReliability analysis plays an important role in the machine repair systems. The purpose of this study is to propose reliability analysis of retrial machine repair systems with M operating units, W warm standby units, and a single repair server with recovery policy. Failure times, repair times, and retrial times for all units are assumed to follow exponential distributions. The single repair server is subject to breakdown, and failure times and repair times for the single server are also assumed to follow exponential distributions. The recovery policy is considered in this study to efficiently utilize the single repair server. Based on the transition rate diagram, the probability differential equations are derived, and Laplace transforms are then taken on these equations to derive system reliability and the mean time to system failure (MTTF). Both sensitivity analyses and relative sensitivity analyses are also performed. Some numerical experiments are designed and executed. The important results are outlined below. The failure rate of an operating unit (λ) significantly influences system reliability. Threshold of the recovery policy (q), the service rate of the working server (μ1), and the breakdown rate of the server (α) affect system reliability moderately. The service rate of the broken down server (μ2), the retrial rate (θ), and the repair rate to repair the broken down server (β) affect system reliability slightly; the failure rate of a standby unit (η) rarely influences system reliability. Furthermore, λ affects MTTF significantly, influence MTTF moderately, slightly affect MTTF, and η rarely affects MTTF.