Redundancy optimization for series-parallel phased mission systems exposed to random shocks

•Systems performing phased missions are considered.•The random environment is represented by stochastic shock process.•The shocks increase failure rates of all system elements.•A method for evaluating the mission success probability is presented.•A constrained redundancy allocation problem is formulated and solved.

Systems performing consecutive non-overlapping mission phases in a random environment are considered. Each phase is performed by a specific 1-out-of-n subsystem consisting of statistically identical parallel elements with the same functionality. The environment is modeled by the Poisson process of shocks commonly affecting all elements, by increasing their failure rate. A method for evaluating the mission success probability for arbitrary redundancy level in each subsystem is presented. The constrained redundancy allocation problem is formulated and solved. Illustrative examples are presented.