Note on disjoint products algorithms

The Abraham-Locks revised (ALR) algorithm, given by M.O. Locks (see ibid., vol.R-36, p.445-53, Oct. 1987), and the Abraham-Locks-Wilson algorithm, given by J.M. Wilson (see ibid., vol.39, p.42-6, Apr. 1990), are efficient systematic procedures for obtaining nearly minimal sum of disjoint products (SDP) system-reliability formulas for coherent source-to-terminal networks. These two procedures differ only in the manner in which the minimal paths of the system are ordered, but are the same in all other respects. The same error was made in both papers, based on a misinterpretation of how the rapid Boolean inversion technique operates. As a result, each paper is missing a single term-the ALR 60-term formula for the sample problem should be 61 terms and the ALW 58-term formula should be 59 terms. This note revises the explanation of inversion and presents corrected system formulas, as well as a minimizing Boolean algorithm for building up disjoint subformulas.<
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