Reliability and sensitivity analysis of a repairable k-out-of-n:G system with two failure modes and retrial feature

Abstract

This paper investigates the reliability and sensitivity analysis for a repairable k-out-of-n:G system with retrial of failed components. Such a model has important practical applications in fully automatic systems, and the most typical one is fully automatic manufacturing system. Markov models for availability and reliability of the system whose components are all subject to two failure modes are presented. There is no waiting space for failed components in the system. If a failed component finds the repairman busy and it can not be repaired at once, it will enter into the retrial orbit and try again for repair after some random period of time. Some reliability indexes, including steady-state availability, reliability function and mean time to system first failure, are derived by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided as well. Finally, some numerical experiments are conducted to show the effects of system parameters on the system reliability indexes.