Minset Splitting for Improved Reliability Computation

Improved algorithms are presented for computing system reliability of coherent sets based on minsets (min paths or min cuts). Split these minsets into subsets so that the union of any k subsets include a minset and that any minset equals such a union. Then compute the probability that at least the components of k such subsets are functioning (failed). This method results in less complex computation for exact and approximate system reliability than the usual inclusion-exclusion method based on the minsets themselves. The method can be applied to coherent systems with minsets that have the property: they can be reunited from some subsets in a special way. Specific minset splitting leads to a formula without cancelling terms. Because systems with such splitting do not belong to the class of p-graphs, a new subset of coherent structures and a new algorithm is found so that system reliability computation avoids cancelling terms.