Optimal activation of components exposed to individual and common shock processes in asynchronous multi-phase missions

Many real-world systems operate in random shock environments, where system components may be exposed to different individual shock processes and some shocks may affect and deteriorate multiple components simultaneously. The existing studies typically considered either individual or common shock processes, but not both. This paper makes contribution by modeling and optimizing a multi-attempt multi-phase mission system subject to both individual and common shocks. System components are functionally equivalent, but heterogeneous in performance, cost, and shock resistance. Thus, their activation schedule may impact the mission success probability (MSP) and expected mission losses (EML). An optimization problem is formulated and solved, which finds the optimal component activation schedule (CAS) to minimize the EML. The solution method encompasses a new numerical recursive algorithm of evaluating the MSP and EML and an implementation of the genetic algorithm based on a proposed CAS solution representation. The proposed model is demonstrated using a case study of a cargo delivery mission performed by multiple aerial vehicles flying along different routes undergoing different shock processes during different phases. Effects of the mission failure penalty, allowed mission time, and common shock rate on mission performance and on the optimal CAS solutions are also examined using the case study.