AI 中文总结
研究基于广义过程能力指数\(C_{py}\)，在II型混合截尾方案下提出阶段独立多重抽样计划（SIMSP），通过消除抽样阶段依赖提高检验效率，经约束优化确定最优设计，数值研究表明其经济高效且可行。
AI 中文摘要
本文提出了一种阶段独立多重抽样计划（SIMSP），通过减少每个抽样阶段所需样本数量来提高检验效率。与传统多重抽样计划不同，SIMSP消除了各抽样阶段对先前检验结果的依赖。该方法基于广义过程能力指数\(C_{py}\)，针对按比例保修政策下的不可修复产品开发。SIMSP在II型混合截尾方案（Type-II HCS）下设计，利用过程能力指数估计的渐近分布计算操作特性（OC）函数，并获得精确的Fisher信息矩阵用于进一步统计分析。通过制定约束优化问题，在制造商和消费者风险约束下最小化总成本来确定最优设计。数值研究考察了模型参数、保修政策特征和成本因素对最优解的影响。结果表明，该方法在满足可容忍风险要求的同时，为批量验收提供了经济高效且可行的方法。
英文摘要
This paper proposes a stage independent multiple sampling plan (SIMSP) to improve inspection efficiency by reducing the number of samples required at each sampling stage. Unlike conventional multiple sampling plans (MSP), the proposed SIMSP eliminates the dependence of each sampling stage on the outcome of the preceding inspection. The proposed approach is developed for non-repairable products sold under a pro-rata warranty policy based on the generalized process capability index $C_{py}$. The SIMSP is designed under a Type-II hybrid censoring scheme (Type-II HCS), which provides greater flexibility in controlling test time and failure information in life testing experiments. The asymptotic distribution of the process capability index estimate is used to compute the operating characteristic (OC) function, and the exact Fisher information matrix (FIM) is obtained for further statistical analysis. A constraint optimization problem is formulated to determine the optimal design by minimizing the total cost subject to the manufacturer's and consumer's risk. Numerical investigations are conducted to examine the effects of model parameters, warranty policy characteristics, and cost factors on the optimal solution. The results demonstrate that the proposed approach provides an economically efficient and feasible method for lot acceptance while satisfying the tolerable risks requirements.
