On the Boolean extension of the Birnbaum importance to non-coherent systems. (April 2017)

• Record Type: Journal Article
• Authors: Aliee, Hananeh; Borgonovo, Emanuele; Glaß, Michael; Teich, Jürgen
• Is Part Of: Reliability engineering & system safety. Volume 160(2017)
• Page Start: 191
• Page End: 200
• Publication Date: 2017-04
• Subjects: Reliability analysis -- Importance measures -- Birnbaum importance measure -- Coherent systems -- Non-Coherent systems; 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.2016.12.013
• Languages: English
• ISSNs: 0951-8320

Abstract

Abstract: The Birnbaum importance measure plays a central role in reliability analysis. It has initially been introduced for coherent systems, where several of its properties hold and where its computation is straightforward. This work introduces a Boolean expression for the notion of criticality that allows the seamless extension of the Birnbaum importance to non-coherent systems. As a key feature, the novel definition makes the computation and encoding straightforward with well-established techniques such as Binary Decision Diagrams (BDDs) or Fault Trees (FTs). Several examples and a case study illustrate the findings. Abstract : Highlights: We propose a Boolean expression for the notion of criticality in coherent and non-coherent systems. The notion is connected with the Birnbaum importance measure. The connection with Andrew's and Beeson extension is discussed. The Boolean expression allows straightforward encoding in Binary Decision Diagrams.