Importance analysis based on logical differential calculus and Binary Decision Diagram. (June 2015)

• Record Type: Journal Article
• Authors: Zaitseva, Elena; Levashenko, Vitaly; Kostolny, Jozef
• Is Part Of: Reliability engineering & system safety. Volume 138(2015:Jun.)
• Page Start: 135
• Page End: 144
• Publication Date: 2015-06
• Subjects: Importance Measures -- Binary Decision Diagram -- Logical differential calculus; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2015.01.009
• Languages: English
• ISSNs: 0951-8320

Abstract

Abstract: System availability evaluation, sensitivity analysis, Importance Measures, and optimal design are important issues that have become research topics for reliability engineering. There are different mathematical approaches to the development of these topics. The structure function based approach is one of them. Structure function enables one to analyse a system of any complexity. But computational complexity of structure function based methods is time consuming for large-scale networks. We propose to use two mathematical approaches for decision to this problem for system importance analysis. The first of them is Direct Partial Boolean Derivative. New equations for calculating the Importance Measures are developed in terms of these derivatives. The second is Binary Decision Diagram (BDD), that supports efficient manipulation of Boolean algebra. Two algorithms for calculating Direct Partial Boolean Derivative based on BDD of structure function are proposed in this paper. The experimental results show the efficiency of new algorithms for calculating Direct Partial Boolean Derivative and Importance Measures. Highlights: New approach for calculation of Importance Measures is proposed. Direct Partial Boolean Derivatives are used for calculation of Importance Measures. New equations for Importance Measures are obtained. New algorithm to calculate Direct Partial Boolean Derivatives by BDD is developed.