Phased-mission system reliability under Markov environment

The authors show how to determine the reliability of a multi-phase mission system whose configuration changes during consecutive time periods, assuming failure and repair times of components are exponentially distributed and redundant components are repairable as long as the system is operational. The mission reliability is obtained for 3 cases, based on a Markov model. (1) Phase durations are deterministic; the computational compact set model is formulated and a programmable solution is developed using eigenvalues of reduced transition-rate matrices. (2) Phase durations are random variables of exponential distributions and the mission is required to be completed within a time limit; the solution is derived as a recursive formula, using the result of case 1 and mathematical treatment-a closed-form solution would be prohibitively complex and laborious to program. (3) Phase durations are random variables and there is no completion time requirement; the solution is derived similarly to case 1 using moment generating functions of phase durations. Generally, reliability problems of phased-mission systems are complex. The authors´ method provides exact solutions which can be easily implemented on a computer