Phased-Mission System Reliability Under Markov Environment

Abstract

We show how to determine the reliability of a multi-phase mission system whose configuration changes during consecutive time periods, assuming failure & 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. Our method provides exact solutions which can be easily implemented on a computer.