On the Boolean extension of the Birnbaum importance to non-coherent systems

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. •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.