Advances in the reliability analysis of coherent systems under limited data with Confidence boxes

Abstract

The paper proposes an uncertainty quantification framework enabling the analyst to compute statistically calibrated confidence bounds of the reliability of coherent systems, even in the case where data are limited in number. More specifically, we propose to use confidence boxes to do so. Such proposal is motivated by the fact that confidence boxes offer a guarantee on statistical performances regardless of the amount of available data through repeated use, which is especially useful when considering the fact that reliability or failure data for the reliability analysis are often limited in availability. The aim of the work is to provide tools allowing the analyst to obtain the true confidence intervals over the system failure and reliability at any desired level. The paper first review the basics of confidence boxes and reliability analysis, before providing general computation tools. From which, a mathematical formalism is presented which relates the component configurations with the corresponding Boolean logic expressions to perform the forward propagation of the confidence boxes under varying dependencies between the components. The feasibility of the proposed framework is then demonstrated through three case studies involving complex systems under varying engineering settings in the form of: 1) the pressurised tank system; 2) the TRIGA nuclear research reactor cooling system; and 3) the bridge structure system. Through the case studies, the validity of our studies is empirically shown and an evaluation on the strengths and limitations of the proposed framework is presented. Finally, the paper provides perspectives on the future research works that can be undertaken from here on. To provide a better understanding of the proposed framework, an open R source code to reproduce the results and perform other related studies is available via: https://github.com/Adolphus8/Computing-with-Confidence.git