Mission Cost and Reliability of 1-out-of-$N$ Warm Standby Systems With Imperfect Switching Mechanisms

Abstract

In this paper, mission cost and reliability of 1-out-of-N: G nonrepairable warm standby systems with imperfect switching are modeled and analyzed using an iterative method. A general switching structure is considered, which consists of an overall fault detection mechanism (FDM) and a set of individual switches (one for each standby element). The failure of the FDM prevents the replacement of the failed online element by any standby element while the failure of an individual switch only makes the corresponding standby element unavailable. The entire mission fails either when the FDM fails before the failure of the online element during the mission, or when all the system elements have failed or become unavailable before the mission completion. Based on the proposed algorithm for the mission cost and reliability analysis, the optimal element sequencing problem is further formulated and solved for 1-out-of-N: G nonrepairable warm standby systems with nonidentical elements and imperfect switching mechanisms. The objective of the problem is to find the optimal initiation sequence of system elements that can minimize the expected mission cost while providing a certain level of system reliability. Examples are given to illustrate the considered problem and the proposed solution methodology.