Smaller sums of disjoint products by subproduct inversion

A new method is presented for calculating system reliability by sum of disjoint products. While the Abraham algorithm (1979) and its successors invert single variables, this new method applies inversion also to products of several variables. This results in shorter computation time and appreciably fewer disjoint products. Hence, the system reliability formula is considerably reduced in size. The Abraham algorithm, for instance, produces 71 disjoint products for network of 12 components and 24 minipaths, while this new method produces only 41 disjoint terms. This facilitates the numerical evaluation of the system reliability formula by reducing computation and rounding errors. Computer programs for both algorithms are included. They were written in Pascal and run on a microcomputer