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 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. In this paper, we propose two metrics, i.e., the optimal repair time and the resilience reduction worth, to measure the criticality of the components of a network system from the perspective of their contribution to system resilience. Specifically, the two metrics quantify: 1) the priority with which a failed component should be repaired and re-installed into the network and 2) the potential loss in the optimal system resilience due to a time delay in the recovery of a failed component, respectively. Given the stochastic nature of disruptive events on infrastructure networks, a Monte Carlo-based method is proposed to generate probability distributions of the two metrics for all of the components of the network; then, a stochastic ranking approach based on the Copeland's pairwise aggregation is used to rank components importance. Numerical results are obtained for the IEEE 30-bus test network and a comparison is made with three classical centrality measures. Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grid structure that are based on its functionality. We show that the relative importance analysis based on centrality in graph theory can be generalized to power grid network with its electrical parameters taken into account. In the paper we experiment with the proposed electrical centrality measures on the NYISO-2935 system and the IEEE 300-bus system. We analyze the centrality distribution in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. We also present and discuss a number of interesting discoveries regarding the importance rank of power grid nodes and branches. The safety validation of automated driving of SAE level 3 and higher (AD) is still an unsolved issue. In the validation process, criticality metrics can be used for two different purposes. First, for the identification of test scenarios from recorded data that are later tested in simulation. Secondly, for an estimation of the safety of a specific AD system based on the likelihood of critical situations in test drives or in other words as a safety surrogate. In the past, different metrics for those purposes have been defined that work well in specific scenarios such as longitudinal traffic. However, a metric that describes criticality in all situations and is applicable to human and AD traffic is currently not available. In this paper, an approach to define a criticality metric is introduced. The metric is based on the definition of criticality as the level of driving requirements in the specific situation. The computation of the proposed metric uses elements of model predictive control using an objective function that contains four elements that describe the difficulty of the driving task. Based on those demands and a simplified driving dynamics model, the solution with the minimal criticality is computed. Finally, the metric is tested in four test scenarios that are typical for highway traffic. A short parameter variation study is conducted in order to study certain effects of the algorithm and to identify room for improvement.