Reliability analysis of k-out-of-n systems with partially repairable multi-state components

In some environments the components might not fail fully, but can lead to degradation and the efficiency of the system may decreases. However, the degraded components can be restored back through a proper repair mechanism. In this paper, we present a model to perform reliability analysis of k-out-of-n systems assuming that components are subjected to three states such as good, degraded, and catastrophic failure. We also present expressions for reliability and mean time to failure (MTTF) of k-out-of-n systems. Simple reliability and MTTF expressions for the triple-modular redundant (TMR) system, and numerical examples are also presented in this study.