Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks

Abstract

The paper considers homogeneous, 1-out-of-n warm-standby systems performing missions of the fixed duration when a failure of an operating element results in a mission failure. A system is operating in a random environment modeled by the Poisson process of shocks. Each shock can result in a failure of an operating element with probability increasing with the number of experienced shocks. Therefore, the preventive replacement is used to reduce the probability of an operation failure. The warm standby elements are also affected by the same shocks, however, being partially shielded, they experience milder adverse impacts. To increase the probability of a mission success, the preventively replaced operable elements can be used later as the warm standby elements. Thus, the performance history of each element can be complex consisting of alternating periods in both modes with different environmental impacts. An algorithm for evaluating the mission success probability for any preventive replacement policy with reusing of elements is suggested. The problem of obtaining the number of shocks triggering replacement of each operating element that maximizes the mission success probability is formulated and solved. A numerical example with detailed analysis is presented.