Dependability modeling and maintenance optimization of a sequential 2-out-of-4 power generation system using a copula-based approach with human operator–repairman interaction

Purpose This article aims to analyze the dependability and maintenance performance of a sequential 2-out-of-4 system integrating dual human operator–repairman interactions under dependent failure conditions. The study explores how copula-based repair modeling enhances system resilience, mean time to failure (MTTF) and overall operational profitability compared to the traditional general repair framework. Design/methodology/approach A continuous-time Markov process is developed to describe the system’s stochastic behavior under partial and complete failures. Failure times follow exponential distributions, while repair times are modeled using both a general framework and a copula-based dependency structure to capture correlated repair behaviors. The supplementary variable technique and Laplace transform are used to derive analytical expressions for system availability, reliability, MTTF and expected profit. Numerical analyses and sensitivity studies are performed to illustrate the influence of repair dependencies and human interactions on system performance. Findings The results demonstrate that the copula-based repair mechanism significantly enhances system availability, MTTF and profit compared to the general repair approach. The inclusion of dual human operator–repairman teams improves restoration speed, minimizes downtime and contributes to higher resilience against cascading failures. Graphical and tabular results confirm that stronger dependency in repair actions yields improved system dependability metrics. Originality/value This study introduces a novel integration of copula-based dependency modeling into human-assisted maintenance optimization for sequential redundant systems. It bridges reliability theory and maintenance engineering practice, providing actionable insights for system designers and maintenance planners seeking to enhance resilience through intelligent repair strategies.