Quantifying Reliability in a Complex Safety-Critical System: A Copula and Distorted Distribution Approach

Complex safety-critical systems (CSCS) play an important role in numerous industries, from aviation and auto-motive to healthcare and nuclear power. In the literature, several approaches have been used to assess the reliability of CSCS when the component lifetimes are independent and identically distributed. However, in real life, systems are composed of multiple types of interdependent components. To address this scenario, in this article, we propose a copula-based approach to examine the reliability of a CSCS that consists of multiple types of components. Our investigation is based on the assumption that components within the same type are interdependent but independent of components of other types. To quantify the dependency among components of the same type, we utilize the Farlie-Gumble-Morgenstern copula, and through minimal cut sets, we derive a distorted distribution that facilitates the assessment of the reliability of CSCS. Finally, we also perform a comparative analysis of the CSCS reliability by considering various values of Kendall's tau and Spearman's rho, which are measures of association between the dependent components. Our results reveal that as the positive (negative) correlation between the components strengthens, the reliability of CSCS tends to decrease (increase).