Reliability analysis of (r,s)-out-of-n multi-state systems using copulas

Purpose This study evaluates the reliability of a multi-state system (MSS) with n components, each having two s-dependent components via copulas. Design/methodology/approach The study employs copula functions to model dependencies between components in an MSS. Specifically, it analyzes a (1,1)-out-of-n three-state system using Frank and Clayton copulas for reliability evaluation. A simulation-based case study of a micro-inverter solar panel system is also conducted using the Farlie–Gumbel–Morgenstern (FGM) copula. Findings The study finds that incorporating component dependencies significantly impacts the reliability of multi-state systems. Using Frank and Clayton copulas, the analysis shows how dependency structures alter system performance compared to independent models. The case study on a micro-inverter solar panel system, using the FGM copula, demonstrates that real-world systems with dependent components exhibit different performances. Also some effects of dependence parameters on the performance characteristics of the system such as mean residual lifetime and mean past lifetime are also examined. Originality/value This study is original in its use of copula functions to evaluate the performance of multi-state systems, particularly focusing on a (1,1)-out-of-n three-state system with dependent components. By applying Frank and Clayton copulas, the research advances reliability analysis by considering component dependencies, often overlooked in traditional models. Additionally, a case study on a micro-inverter solar panel system using the FGM copula highlights the practical application of these methods.