Reliability evaluation of unrepairable k-out-of-n: G systems with phased-mission requirements based on record values

In this paper, the reliability evaluation problem for k-out-of-n: G phased-mission systems with imperfect fault coverage is studied. The system is composed of n identical components, and the mission consists of multiple, consecutive, and non-overlapping phases. Each phase of the mission has a specified requirement of the minimal number of working components, and therefore the system forms a certain k-out-of-n: G system at the phase. The failure distributions of the components are affected by working circumstance of the mission phases, and the degradation accumulates with the phases for each component. The formulas for computing the state probabilities of the system at different phases and the overall mission reliability are derived with the consideration of imperfect fault coverage for the components. The explicit expression of mission reliability is presented for the phased-mission systems with the same components requirements for all phases. In numerical examples, not only the mission reliability of the system is calculated, but also the optimal number of components is obtained to maximize the reliability for a given phased mission system.