Reliability Evaluation for a Circular Con/k/n:F System With a Novel Differential Repair Policy

In many industrial environments, some components fail and cannot be repaired immediately. We propose a novel repair policy for addressing component failure issues in a circular consecutive-$k$-out-of-$n$:F (abbreviated as Cir/Con/k/n:F) system. This repair policy assigns preemptive priority for repair to the component whose breakdown results in system failure (called emergency repair), while renders an ordinary repair to the failed components without causing failure of the system. The ordinary repairs are recorded by the repairman in the order of their failure, which is said that the broken components are stored in “orbit.” When the repairman becomes idle, he makes the orbital search for failed ones according to the first-failed-first-repair discipline, which can be interrupted by an emergency repair. We carry on an extensive investigation on reliability and queueing indices of the considered model. Specifically, we present a Cir/Con/2/6:F system as an example to give sensitivity analysis for the reliability performance. Numerical inversion of Laplace transform–Stehfest method is adopted to obtain approximate solutions for reliability function. Furthermore, the minimization problem of the CBR is addressed by adopting sequential quadratic programming algorithm. This study offers new insights into balancing the expected total repair cost and associated benefits in the Cir/Con/k/n:F system.