Redundancy Allocation for Series and Parallel Systems: A Copula-Based Approach

The allocation of redundant components to a system is a common method for enhancing the system's lifetime. This study explores the optimal allocation of redundancies in series and parallel systems with two components by assuming components and redundancies are dependent. That is, we perform the stochastic comparisons of the series (parallel) systems in the case of two redundancies at the component level. Specifically, we examine the stochastic comparisons across three scenarios: (i) components (and redundancies) have dependent lifetimes but are independent of each other, and components (redundancies) have identical marginal distributions in the two generated systems; (ii) components (and redundancies) have dependent lifetimes and are independent of each other, but the marginal distributions of components (redundancies) are different in the two generated system; and (iii) components and redundancies are interdependent and the marginals of the components (redundancies) in the two generated systems are same. In this study, we model the dependency using the concept of copula and perform the desired stochastic comparisons using generalized distorted distribution functions. Furthermore, we demonstrate our findings through various examples and counterexamples. Finally, we provide a simulation-based study and a real data analysis to illustrate our findings.