Reliability of multi-phased mission systems

Abstract

Generally mission systems of multi-components perform phased sub-missions whose relevant structures are re-configured during phases. This thesis is concerned with the reliability of multi-phased mission systems. The purpose is to propose methods to obtain the exact mission reliability depending on various cases of phased mission systems. The first problem is concerned with mission systems of repairable components and deterministic phase durations. When component failure and repair times are exponentially distributed. Markov model related to transitions among system states is formulated. A reduced compact set model is formulated with system-up states only among all system states. Eigenvalues and eigenvectors of transition rate matrices are used to solve the differential equations about state probabilities. Considering the relations of state numbers between adjacent phases, the mission reliability is obtained sequentially. The second one is concerned with repairable components systems and probabilistic phase durations. When there is a requirement for mission time completion, or when there are requirements for mission phase change times, recursive equations to get the exact reliability are derived using the result of deterministic durations case. When there are requirements for each phase time of no requirements for mission time, the mission reliability is obtained as similar manner to deterministic durations case. The third one is to obtain the exact reliability for non-repairable components systems where durations are deterministic. Two methods to obtain the reliability are proposed, not assuming Markov environment. 1) Minimal cut enumeration, cut cancellation, then additive rule: In the inclusion-exclusion technique of additive rule, by means the property of the sample path of a component state, an efficient method is presented without past work``s transformation to an equivalent single phase. 2) Pivotal decomposition, then clustered source-to-si...