The method for exactly solving bi-objective RAP with phase-type distribution under mixed redundancy strategy

High reliability is essential for complex industrial systems. Redundancy design enhances system reliability, making the redundancy allocation problem (RAP) pivotal in reliability optimization. However, existing bi-objective RAP models under a mixed redundancy strategy rely on approximate reliability calculations or restrictive assumptions of exponential time-to-failure (TTF) distributions for components. Furthermore, heuristic-based approaches currently adopted for solving bi-objective RAP neither guarantee Pareto optimal nor systematically identify all optimal solutions. This study proposes a novel bi-objective RAP model with exact reliability evaluation, where the TTF distribution of components is considered a generalized phase-type distribution. For the first time, an exact dynamic programming (DP) algorithm is developed to solve bi-objective RAP models under a mixed redundancy strategy, ensuring the identification of complete Pareto-optimal solutions. Numerical experiments demonstrate that our work, with an accurate reliability evaluation method and an exact DP algorithm, achieves a higher-quality Pareto frontier with superior reliability and lower costs than previous studies. Additionally, the algorithm is used to obtain the exact solution of single-objective RAP, further expanding our research's theoretical depth and application scope in reliability optimization. Finally, a case study about a supervisory control and data acquisition system confirms the method's operational effectiveness and applicability in reliability engineering.