A decomposition scheme for the analysis of fault trees and other combinatorial circuits

A new decomposition scheme for the analysis of fault trees and other more general combinatorial circuits is presented. The scheme is based on a tabular representation for the necessary information about a subsystem and generalizes the concept of modular decomposition. The basic algorithm is extended to obtain a very fast method for finding the sensitivity of the results to a large class of perturbations of the data. The scheme can be used to compute and analyze the sensitivity of many different types of measures on a circuit. The authors give a pair of axioms that capture sufficient conditions for the scheme to apply to computing a given measure and explicitly consider three different computational problems. A single algorithm is tailored to solve a new problem simply by supplying it with the necessary problem-specific subroutines. The efficiency of the algorithm depends on the choice of decomposition tree; the authors propose two simple heuristics for constructing a good decomposition tree. A theorem is obtained implying that if an efficient decomposition tree is found for the basic algorithm, the extended algorithm will also be efficient