Computing Optimal Progressive Hybrid Censoring Schmes Using An Mcmc Type Probabilistic Approach

Progressive hybrid censoring schemes play a crucial role in optimizing life-testing experiments by balancing test duration and statistical efficiency. This study presents a Markov Chain Monte Carlo (MCMC)-based probabilistic approach for determining optimal progressive hybrid censoring schemes, incorporating a time-dependent component that enhances traditional progressive censoring methods.We implement our approach using three distinct probability distributions the multinomial, hypergeometric, and uniform distributions to simulate censoring schemes. The optimal censoring schemes are then identified based on three optimality criteria: A-optimality, D-optimality, and T-optimality, ensuring robust selection by minimizing estimator variance, maximizing Fisher information, and optimizing test duration, respectively..To evaluate the effectiveness of our method, we compare the results to existing solutions proposed in the literature . Our findings indicate that incorporating the time parameter enhances censoring scheme selection specifically for the T-optimality criterion, while its impact on D-optimality and A-optimality remains limited. This research provides a computationally efficient and statistically rigorous framework for optimizing censoring schemes in life-testing experiments, offering valuable insights for applications in engineering, manufacturing, and quality control, particularly in scenarios where test duration is a key consideration.