Optimal truncated lot reinspection based on Beta-Binomial Lognormal failure counts
针对寿命服从对数正态分布、失效概率服从Beta分布的器件，提出最优截断重复抽样方案，通过求解整数非线性规划最小化最大期望样本量，并控制消费者与生产者风险，以半导体激光器生产为例验证其优于传统方法。
This paper introduces optimal truncated repetitive sampling plans for lot acceptance, specifically designed for devices whose lifetimes follow a Lognormal distribution and whose failure probability is modelled by a Beta distribution. The goal is to minimise the maximum expected sample size while ensuring that both consumer and producer risks are effectively controlled. The sampling plans are derived by solving integer nonlinear programming problems, leading to a minimax truncated repetitive scheme based on failure count data from Lognormal models. In most cases, the effect of overdispersion on the minimax test plan remains manageable and reasonable. The proposed methodology is demonstrated with an application to the production of semiconductor lasers, providing both illustrative and comparative examples. Overall, the optimal truncated repetitive sampling plans outperform traditional single and repetitive sampling methods, especially in terms of reducing the maximum expected sample size. Additionally, the proposed approach fosters greater trust between manufacturers and consumers, offering a more reliable framework for inspecting high-cost devices. By optimising inspection efforts and minimising unnecessary sampling, this methodology provides significant benefits in terms of both cost efficiency and product quality assurance.