Reliability Versus Expected Mission Cost and Uncompleted Work in Heterogeneous Warm Standby Multiphase Systems

Abstract

This paper considers 1-out-of- ${N}$ : G warm standby (WS) systems subject to multiple-phased mission requirements, where performance, failure behavior, operation cost, replacement time, and cost of system elements can vary from phase to phase due to changing working conditions and stress levels. The system succeeds if its elements can accomplish a specified mission task within the maximum allowed time. A numerical algorithm is proposed for evaluating mission indices, including system reliability, expected mission cost, and expected uncompleted work of the heterogeneous, dynamic standby system considered. The influence of the maximum allowed mission time on mission indices is investigated. As demonstrated through examples, the proposed algorithm can also facilitate a determination of mission interruption based on reliability or cost-oriented criteria. Based on the proposed algorithm, an unconstrained optimal standby element sequencing problem is then formulated and solved for heterogeneous WS multiphase systems. The problem is to find the optimal activation sequence of system elements maximizing system reliability, or minimizing expected mission cost, or minimizing expected uncompleted work. The constrained optimization problems of minimizing expected mission cost subject to providing a desired level of mission reliability or uncompleted work are also solved. Illustrative examples of these optimization problems and their applications in estimating the role of each element in the mission success are presented.