Optimal Experimental Plan For Multi-Level Stress Testing Under Progressively Hybrid Censoring

Reliability analysis is essential for understanding how products perform over time, particularly in environments where failure data is limited or costly to obtain. One effective approach is multi-level stress testing, where test units are subjected to varying levels of stress to accelerate failures and extract more information within constrained timeframes. This study presents a novel optimization-based framework for designing life-testing experiments under progressively Type-II hybrid censoring, assuming Weibull lifetime distributions. Leveraging a Variable Neighborhood Search (VNS) algorithm, we determine efficient allocations of test units and censoring parameters across multiple stress levels to enhance the precision of estimates of the model parameters. Optimal designs are obtained under both A-optimality and D-optimality criteria, with comprehensive numerical results illustrating the impact of stress configuration, sample size, and failure patterns on estimator performance and information gain. The proposed approach consistently identifies robust and computationally efficient designs, revealing that strategic allocation and selective censoring can substantially improve the determinant and trace of the Fisher information matrix. These results provide practical guidance for designing effective life-testing experiments, particularly in reliability studies involving limited sample sizes and multiple stress conditions.