Abstract
This paper presents a comparative study of classical and Bayesian risks in the design of optimal failure-censored sampling plans for lognormal lifetime models. The analysis focuses on how variations in prior distributions, specifically the beta distribution for defect rates, influence the producer's and consumer's risks, along with the optimal sample size. We explore the sensitivity of the sampling plan's risks to changes in the prior mean and variance, offering insight into the impacts of uncertainty in prior knowledge on sampling efficiency. Classical and Bayesian approaches are evaluated, highlighting the trade-offs between minimizing sample size and controlling risks for both the producer and the consumer. The results demonstrate that Bayesian methods generally provide more robust designs under uncertain prior information, while classical methods exhibit greater sensitivity to parameter changes. A computational procedure for determining the optimal sampling plans is provided, and the outcomes are validated through simulations, showcasing the practical implications for quality control in reliability testing and industrial applications.