A Method of Rapid Markov Reliability Calculation

Our reliability calculation method for a Markov state-transition graph enables a rapid computation by finding and cutting (removing) non-effective edges (NEEs). An NEE is an edge in a Markov state transition graph, the cut of which has little effect on the reliability calculation. NEEs can be found only by checking in a small graph, given the assumption that component failure rate is far smaller than component repair rate. NEEs are found and cut until the Markov graph is separated into two subgraphs. One subgraph is usually very small compared with the original, and the reliability can be approximately calculated on this small subgraph of the Markov graph. Proof and numerical examples are presented.