Directed Graph Techniques for the Analysis of Fault Trees

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Abstract
Since the introduction of the fault tree method for system safety and reliability analysis more than a decade ago, the method has gained considerable acceptance for qualitative analyses. It has also gained a degree of acceptance for quantitative analyses, despite difficulties encountered in performing the probabilistic evaluations using available methods. Some of the difficulties encountered with previous evaluation methods are avoided by the methods of this paper. The new methods involve the use of directed graphs (digraphs) and related matrix methods, and solutions for paths in a manner similar to that for conventional digraphs. Most of the attractiveness stems from the fundamental philosophy of speedily transforming the graphics into corresponding matrices. This puts the bulk of the solution effort into the mathematics where it belongs. The major benefit arises because the mathematical solutions are readily performed by standard matrix techniques, which can be implemented either manually or with the aid of a computer. The new methods have been used on various hypothetical logic combinations plus actual fault trees of typical sizes.

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