The Abraham-Locks-revised (ALR) sum-of-disjoint products (SDP) algorithm is an efficient method for obtaining a system reliability formula. The author describes a minor modification of the ALR algorithm called the Abraham-Locks-Wilson (ALW) method. The new feature is an alternative method of ordering paths and terms. ALW obtains a shorter disjoint system formula on a test example than any previous SDP method and allows small computational savings in processing large paths of complex networks. As there are different ways to obtain a reliability formula it is useful to use an approach which yields the smallest formula relative to computational effort expended. The extra effort in ordering the terms should be reasonably small and usually leads to improved efficiency in the later stages of the algorithm. ALW allows the analyst to operate in a more efficient way on many problems, particularly if the overlap ordering is used in the early stages of processing but is probably ignored for terms that contain a majority of the Boolean variables.
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