Optimizing availability of heterogeneous standby systems exposed to shocks

The paper considers heterogeneous 1-out-of-N warm standby systems when all components can experience internal failures whereas operating components are exposed to the external shocks as well. The components' resilience to shocks decreases with the number of experienced shocks describing the corresponding deterioration in time. Therefore, a preventive replacement policy when the operating component is replaced after it survives a certain number of shocks (that becomes a decision parameter) is considered. The replacement time is random and not negligible. The distributions of corrective and preventive replacement times are assumed to be known for each component. The expression for the instantaneous (point) availability is derived and the original numerical algorithm for its evaluation is suggested. Then an optimization problem for a replacement policy that maximizes the overall mission availability over a finite time horizon is formulated and solved. Illustrative examples are provided.