An optimized procedure to generate sums of disjoint products

This article describes an efficient procedure, the so-called Semi-Optimal Disjunction Approach (SODA), to generate a sum of the disjoint products (SDP) from a set of minimal products representing either the minimal s–t paths of reliability networks or the minimal cutsets of the coherent fault trees. The proposed procedure involves the concept of multiple-variables inversion or grouped-variables inversion. The process is improved by carrying out a reprocessing of the initial formula which reduces the number of terms of the result, and hence the overall computation time. A previous version of this article was submitted to RESS by the fall of 1993 and was accepted up to minor reversions a year later. Unfortunately, the final redaction has been delayed since then. The present version takes into account some other articles published in between and includes new ideas that improve the implementation of the proposed algorithm. At least on classical test examples, SODA produces shorter formulae than the other SDP methods known by the authors.