Reliability Improvement of a Parallel-Series System via Duplication and Reduction Strategies Under the Akshaya Distribution

Parallel–series systems are fundamental in many industrial and engineering applications, yet their reliability assessment and improvement remain challenging, particularly when components exhibit non-constant failure rates. This study addresses this challenge by modeling a hybrid parallel–series system whose components follow the Akshaya lifetime distribution, a flexible model that can capture various hazard-rate shapes. For this system, we derive closed-form analytical expressions for key reliability indices, including the system reliability function, mean time to failure (MTTF), reliability equivalence factors (REFs), and δ-fractiles. To enhance system performance, four improvement strategies are formulated and analytically compared: failure-rate reduction, hot duplication, cold duplication with a perfect switch, and cold duplication with an imperfect switch. A comprehensive numerical case study validates the theoretical derivations and demonstrates the effectiveness of each strategy. The results show that cold duplication with a perfect switch yields the highest reliability gain, and the computed REFs provide a quantitative tool for balancing redundancy against component-level improvements. This work provides reliability engineers with a comprehensive analytical framework for the design and enhancement of complex parallel-series systems.