Importance measures provide a systematic approach to scrutinize critical system components, which are extremely beneficial in making important decisions, such as prioritizing reliability improvement activities, identifying weak-links and effective usage of given resources. The importance measures are then in turn used to obtain a criticality value for each system component and to rank the components in descending manner. Simulations tools are generally used to perform importance measure based analysis, but they require expensive computations and thus they are not suitable for large systems. A more scalable approach is to utilize the importance measures to obtain all the necessary conditions by proving a generic relationship describing the relative importance between any pair of components in a system. In this paper, we propose to use higher-order-logic (HOL) theorem proving to verify such relationships and thus making sure that all the essential conditions are accompanied by the proven property. In particular, we formalize the commonly used importance measures, such as Birnbaum and Fussell-Vesely, and conduct a formal importance measure analysis of a railway signaling system at a Moroccan level crossing as an application for illustration purpose.
Importance measure is a useful concept in reliability engineering and has been analyzed analytically @cite_2 as well as using simulation tools @cite_3 . The latter approach is practically adopted by industrial engineers due to their powerful features. These tools follow the typical approach of ranking the system components according to their criticality value. However, this approach requires high computations to obtain the criticality value for all system components and then perform the successive analysis, which may not be possible for large and complex systems. An alternate approach is to verify a relative measure relationship for any pair of components and obtain the necessary conditions, as described by Meng @cite_21 .
@cite_21 @cite_3 @cite_2
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This article provides us with some simple criteria to compare Birnbaum reliability importance measure of components in a general binary coherent system. Such criteria are particularly useful in the absence of information concerning component reliabilities. We also find several simple (necessary and sufficient) conditions concerning system structure, under which such comparison is possible. Examples are given to illustrate our results. This unique treatment systematically interprets a spectrum of importance measures to provide a comprehensive overview of their applications in the areas of reliability, network, risk, mathematical programming, and optimization. Investigating the precise relationships among various importance measures, it describes how they are modelled and combined with other design tools to allow users to solve readily many real-world, large-scale decision-making problems.Presenting the state-of-the-art in network analysis, multistate systems, and application in modern systems, this book offers a clear and complete introduction to the topic. Through describing the reliability importance and the fundamentals, it covers advanced topics such as signature of coherent systems, multi-linear functions, and new interpretation of the mathematical programming problems.Key highlights:Generalizes the concepts behind importance measures (such as sensitivity and perturbation analysis, uncertainty analysis, mathematical programming, network designs), enabling readers to address large-scale problems within various fields effectivelyCovers a large range of importance measures, including those in binary coherent systems, binary monotone systems, multistate systems, continuum systems, repairable systems, as well as importance measures of pairs and groups of componentsDemonstrates numerical and practical applications of importance measures and the related methodologies, including risk analysis in nuclear power plants, cloud computing, software reliability and moreProvides thorough comparisons, examples and case studies on relations of different importance measures, with conclusive results based on the authors own researchDescribes reliability design such as redundancy allocation, system upgrading and component assignment.This book will benefit researchers and practitioners interested in systems design, reliability, risk and optimization, statistics, maintenance, prognostics and operations. Readers can develop feasible approaches to solving various open-ended problems in their research and practical work. Software developers, IT analysts and reliability and safety engineers in nuclear, telecommunications, offshore and civil industries will also find the book useful.