Repairable Compound Systems Reliability Analysis

Repairable systems reliability is an important branch of the reliability theory. For a repairable system, availability, reliability and mean time between failures are all important indexes. The article discusses the reliability of repairable series-parallel systems and repairable parallel-series systems with Markov method.For a system with the states transferring having Markov quality the transfer-probability matrix is the basis of analyzing system reliability after verifying the state space. State-transferring diagram and transfer-probability matrix are the cruxes of solving the repairable compound system reliability.In the article, the author summarizes the basic theories and methods analyzing the system reliability. Then, according to the fact that the series-parallel systems and parallel-series systems made up of many components have complicated state space and transfer-probability matrix, some new concepts are introduced. On the basis of these concepts, the author classifies the complicated state space well-organized, describes the structure of the state space and gets the quantity relation of each state. Thus, a ration description for compound system state-transferring diagram is obtained which greatly reduces the analyses and operation complexity.At the same time, to the discussed systems, the author studies the element classification and the structure relation of systems' transfer -probability matrix under the circumstance of a repairable equipment. Especially, the author brings forward a method-matrix growing to describe the change of transfer- probability matrix and gets the change law of transfer-probability matrix when some components of a system have changed.