An Algorithm for a Truncated Solution of a Fault Tree
B J Dugan · 1988
In [1], Martensen and Butler present a method for bounding the reliability of a system by analyzing only a subset of the entire set of state vectors. From the description of the algorithm given in the Appendix A of [1], it appears that the authors assume that there is no case in which a state representing $i+1$ failed components is more probable than some state with only $i$ failed components. We present a modification to the Martensen-Butler technique which holds in the more general case. The general approach taken in this paper is to bound the maximum probability associated with the state vectors that have not been analyzed. The state vectors are partitioned into subsets, and an error term equal to the maximum contribution of each subset to the system failure probability is calculated. A collection of subsets is formed such that the sum of the error terms associated with the subsets is smaller than the largest acceptable error in the overall system failure probability. The chosen subsets of state vectors need not be analyzed for their contribution to the system failure probability in order to be assured that the desired accuracy is reached.