Properties of Systems Which Lead to Efficient Computation of Reliability.
Michael O. Ball, J. Scott Provan · 1984
One of the most widely used approaches to computing systems reliability is to represent the system structure in terms of a Boolean sum of all minpaths. This expression is then transformed into a sum of disjoint terms. The probability of each term is then summed to obtain the reliability of the system. A key question with respect to the difficulty of this process relates to the ability to transform the initial sum into a sum of disjoint products. In this paper, the authors show that for the class of shellable systems, there always exists a disjoint product expression with a number of terms equal to the number of minpaths. The authors provide several examples of shellable systems for which an expression can be efficiently found.