THE USE OF THE COMPONENT INFLUENCE GRAPH TO REDUCE THE SIZE OF MARKOVIAN AVAILABILITY PROBLEMS

In this paper we will develop a new method of solution of large Markov ian problems by means of auxiliary problems of smaller size. The influ ence graph of the physical components is built, each edge of the digra ph symbolizing the influence (if any) of the composant (node of the gr aph) on the rate of failure or repair of another component. The analys is of the digraph introduces a natural ordering and the buildup of app roximate differential systems which are solved recursively for the con ditional probabilities. Two examples are given to illustrate the metho d.