Ideas and developments in importance measures and fault-tree techniques for reliability and risk analysis

This paper shows an efficient order for calculating importance measures and develops several new measures related to fault diagnostics, system failure intensity, system failure count, and configuration control. Definitions and relationships are extended to certain non-coherent systems and to models with mutually explicit events. Useful interpretations and applications are pointed out, and many roles of the Birnbaum importance are highlighted. Another important topic is the accuracy of various alternative methods used for quantification of accident sequence probabilities when negations or success branches of event trees are involved. Finally, the role of truncation errors is described, and criteria are developed for selecting truncation limits and cut-off errors so that importance measures can be estimated reliably and risk-informed decision making is robust, without unreasonable conservatism and without unwarranted optimism.