Top-down Algorithm for Obtaining Prime Implicant Sets of Non-Coherent Fault Trees

Hiromitsu Kumamoto · Ernest J. Henley

31 citations0/0 files storedIEEE Transactions on Reliability

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Risk and Safety Analysis Reliability and Maintenance Optimization Engineering and Test Systems

Abstract

An algorithm for finding all the prime implicant sets is given for non-coherent fault trees involving gates other than simple AND and OR, e.g., EOR and NOT. The sets are a generalization of min cut sets and can be used in quantitative and/or qualitative system reliability analysis. The algorithm is a top-down analysis and avoids sum of product expressions of top event, which usually involve a large number of terms. Each step of the algorithm is clearly defined and it is proven that all prime implicant sets can be obtained. The algorithm is efficient, and rather complicated trees can be handled manually.

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References

1977Computer-aided Synthesis of Fault-trees 1977Computer aided synthesis of fault-trees 1972New methodology for obtaining cut sets for fault trees 1975On the Analysis of Fault Trees 1970PREP AND KITT: COMPUTER CODES FOR THE AUTOMATIC EVALUATION OF A FAULT TREE.1974Fault TreesߞA State of the Art Discussion

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1980Methods for Probabilistic Analysis of Noncoherent Fault Trees 1986An Algorithm for Exact Fault-Tree Probabilities without Cut Sets 1981Modularizing, Minimizing, and Interpreting the K&H Fault-Tree 2008Non-coherent Modelling in Compositional Fault Tree Analysis 1980Fault Trees, Prime Implicants, and Noncoherence 1981Prime Implicants of Noncoherent Fault Trees 1980Fault tree and reliability relationships for analyzing noncoherent two-state systems 2018A comparison of fault trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems part 2: Theoretical investigations

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