Analysis of a Repairable System with Two Failure States and Set-up Time

摘要

This paper introduces an unreliable repair facility with two failure states and set-up time into a classical one-unit repairable system. It is assumed that the lifetime of the unit and the set-up time and two replacement times of the facility have general continuous distributions. The failure distribution of the repair facility is exponential. By the supplementary variable method and the theory of differential equations, we obtain the Laplace transform solutions for the state equations and some reliability quantities of the system and the facility. Furthermore, with the generalized repair time of the unit defined, some new reliability quantities for the repair facility are presented and solved. Three special cases are derived. Finally, by comparison, the effects of the set-up time and the facility replacements caused by two failure states on the system performance are given.