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.