无替换试验下的截尾序贯最优检验研究  

Reserch on Optimal Truncated Sequential Test without Substitution

作　　者：陈慧娟 胡思贵 李秋德 方茂达 龙荣进 叶茂越 CHEN Huijuan;HU Sigui;LI Qiude;FANG Maoda;LONG Rongjin;YE Maoyue(School of Biology and Engineering,Guizhou Medical University,Guiyang,550025,China;School of Mathematics and Statistics,Guizhou University,Guiyang,550025,China)

机构地区：[1]贵州医科大学生物与工程学院,贵阳561113 [2]贵州大学数学与统计学院,贵阳550025

出　　处：《应用概率统计》2025年第1期65-82,共18页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(批准号:11561011,62166009);贵州省自然科学基金(批准号:ZK[2022]350);贵州医科大学博士启动基金(批准号:2020-015)资助.

摘　　要：为降低具有“高可靠、长寿命”试验特点产品的抽样检验成本,本文对无替换试验下的指数分布计量型截尾序贯最优检验进行了研究.建立了无替换试验下截尾序贯最优检验的相关理论,给出了检验方案的操作特征曲线与平均自然日历试验时间等关键统计特征量的计算表达式,并构建了样本空间排序法对截尾序贯最优检验方案进行了求解.通过与当前国际标准IEC61124中有替换试验下的截尾序贯检验方案相比,所获得的新检验方案在检验水平得到严格控制的条件下,能降低综合平均自然日历时间的比例达到近80%.与有替换试验下的截尾序贯最优检验方案相比,新检验方案亦能降低综合平均自然日历时间的比例在70%左右.本文所建立的检验方案大幅度降低了产品抽样检验的综合平均自然日历时间,因而能极大地节省“高可靠、长寿命”试验特点产品抽样检验的试验成本.In order to reduce the testing costs for products with high reliability and long-life testing characteristics,this paper studies the optimal truncated sequential tests for the exponential distribution without substitution.The theory of optimal truncated sequential test without substitution has been established.The calculation formulas for essential statistical features,such as the operating characteristic curve and expected natural calendar testing time of the test plans,are derived.A sample space sorting method has been established to address the optimal truncated sequential tests.Through comparison with the test plans provided by the international standard IEC61124,the results show that,with strict control over type I and type II error probabilities,the new test plans proposed here can save nearly 80%of synthesis expected natural calendar testing time.Moreover,in comparison with the optimal truncated sequential tests with substitution,the results show that,the new test plans can reduce nearly 70%of the synthesis expected natural calendar testing time.The new test plans proposed in this paper significantly decrease the synthesis expected natural calendar testing time,thereby substantially reducing the testing costs for products with high reliability and long-life testing characteristics.

关 键 词：指数分布 序贯分析 样本空间排序法 IEC61124 

分 类 号：O212.3[理学—概率论与数理统计]