Reliability Modeling and Redundancy Allocation for Systems of Dependent Components Using Copula Functions

This study introduces a novel approach for redundancy allocation in series-parallel systems, incorporating component dependency via copula functions. By modeling these dependencies, we enhance the accuracy of system reliability assessment. Our methodology employs mixed-integer nonlinear optimization, balancing system reliability with constraints like cost and weight. In practical applications, the condition and reliability of components within the same system are influenced by similar external factors or by the condition of each other components, potentially leading to dependencies in their operational state and reliability assessments. When component reliability models are applied to complex systems composed of multiple dependent elements, the observed reliability behaviors tend to be more detailed and complicated. This complexity necessitates the adoption of novel perspectives to accurately evaluate and manage system reliability. We applied two distinct methodologies to solve the mixed-integer nonlinear optimization problem for our series-parallel model: interior-points nonlinear optimization and genetic algorithms. Interior-points method proved effects in efficiently approximating the complex relationship between decision variables and the objective function and provided an upper-bound on system reliability. The genetic algorithm excels at solving integer programming problems and delivers a robust and practical optimal redundancy strategy for these challenges.