计数型最小样本量截尾值的序贯检验
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摘要
对具有"高成本、破坏性"计数型产品的可靠性验收试验,序贯检验方案的样本量截尾值对试验的成本预算起着决定性作用.为降低试验的成本预算,本文对最小样本量截尾值序贯检验(minimum truncated sample size sequential test, MTST)进行研究,给出MTST的定义、性质及求解方法.通过与目前广泛采用的国际标准IEC1123及序贯网图检验进行比较,结果表明MTST显著地减少了样本量截尾值.为进一步减少序贯检验的样本量截尾值,当已知产品质量的先验信息时,本文研究了Bayes最小样本量截尾值序贯检验方案(Bayesian minimum truncated sample size sequential test, BMTST),与MTST的比较表明, BMTST极大地减少了序贯检验的样本量截尾值及平均试验次数,能更好地缩减"高成本、破坏性"产品的试验成本预算及平均试验费用.
For the high-cost and destructive reliability acceptance test, the truncated sample size is a determining factor for its experimental cost budget. In this paper, the minimum truncated sample size sequential test(MTST)is studied. We present the definitions, the properties and the solution method of MTST. Through comparing with International Electrotechnical Commission(IEC) standard IEC1123 and sequential mesh test(SMT), the results show that MTSTs can reduce truncated sample size significantly. When a priori information about the product is known, in order to reduce the truncated sample size of the test further more, Bayesian minimum truncated sample size sequential test(BMTST) is studied. The cases studied show that, comparing with MTSTs, BMTSTs can largely reduce the truncated sample size and the average sample number simultaneously. Therefore, for the high-cost and destructive products, BMTSTs can greatly reduce the product experimental budget and the average test cost at the same time.
For the high-cost and destructive reliability acceptance test, the truncated sample size is a determining factor for its experimental cost budget. In this paper, the minimum truncated sample size sequential test(MTST)is studied. We present the definitions, the properties and the solution method of MTST. Through comparing with International Electrotechnical Commission(IEC) standard IEC1123 and sequential mesh test(SMT), the results show that MTSTs can reduce truncated sample size significantly. When a priori information about the product is known, in order to reduce the truncated sample size of the test further more, Bayesian minimum truncated sample size sequential test(BMTST) is studied. The cases studied show that, comparing with MTSTs, BMTSTs can largely reduce the truncated sample size and the average sample number simultaneously. Therefore, for the high-cost and destructive products, BMTSTs can greatly reduce the product experimental budget and the average test cost at the same time.
引文
1 United States Department of Defense.Handbook for Reliability Test Methods,Plans and Environments for Engineering,Development Qualification and Production.MIL-HDBK-781,1987
2 Siegmund D.Sequential Analysis.New York:Springer,1985
3闰章更,濮晓龙.现代军事抽样检验方法及应用.北京:国防工业出版社,2008
4 Lavigne L,Cazaurang F,Fadiga L,et al.New sequential probability ratio test:Validation on A380 flight data.Control Eng Pract,2014,22:1-9
5 Bolland M J,Grey A,Gamble G D,et al.The effect of vitamin D supplementation on skeletal,vascular,or cancer outcomes:A trial sequential meta-analysis.Lancet Diabetes Endocrinology,2014,2:307-320
6 Kulldorff M,Davis R L,Kolczak M,et al.A maximized sequential probability ratio test for drug and vaccine safety surveillance.Sequential Anal,2011,30:58-78
7 Shih M C,Lai T L,Heyse J F,et al.Sequential generalized likelihood ratio tests for vaccine safety evaluation.Stat Med,2010,29:2698-2708
8 Wald A.Sequential tests of statistical hypotheses.Ann Math Statist,1945,16:117-186
9 Wald A,Wolfowitz J.Optimum character of the sequential probability ratio test.Ann Math Statist,1947,19:326-339
10 Kiefer J,Weiss L.Some properties of generalized sequential probability ratio tests.Ann Math Statist,1957,28:217-217
11 Lorden G.2-SPRT’s and the modified Kiefer-Weiss problem of minimizing an expected sample size.Ann Statist,1976,4:281-291
12 Huffman M D.An efficient approximate solution to the Kiefer-Weiss problem.Ann Statist,1983,11:306-316
13 Lai T L.Optimal stopping and sequential tests which minimize the maximum expected sample size.Ann Statist,1973,1:659-673
14 Lai T L.Sequential analysis:Some classical problems and new challenges.Statist Sinica,2001,11:303-408
15濮晓龙,闰章更,茆诗松,等.计数型序贯网图检验.华东师范大学学报(自然科学版),2006,125:67-71
16 Li Y,Pu X L.Method of sequential mesh on Koopman-Darmois distributions.Sci China Math,2010,53:917-926
17李艳,濮晓龙.基于Koopman-Darmois分布族的序贯网图检验方法.中国科学:数学,2009,39:614-624
18 Li Y,Pu X L.A method for designing three-hypothesis test problems and sequential schemes.Comm Statist Simulation Comput,2010,39:1690-1708
19 Anderson T W.A modification of the sequential probability ratio test to reduce the sample size.Ann Math Statist,1960,31:165-197
20胡思贵.计数型截尾序贯检验的样本空间排序法.应用概率统计,2013,29:201-212
21 International Electrotechnical Commission.Reliability testing-Compliance test plans for success ratio.IEC1123,1991
22 Ganesan R,Rao A N V,Das T K.A multiscale Bayesian SPRT approach for online process monitoring.IEEE Trans Semicond Manuf,2008,21:399-412
23 Li J,Shen L,Zhao L.Success ratio sequential test plan using development test data.In:The Proceedings of 2009International Conference on Reliability,Maintainability and Safety.Piscataway:IEEE,2009,370-373
24胡思贵,周小静.计数型截尾序贯保证试验的研究.华东师范大学学报(自然科学版),2015,2015:47-56
2 Siegmund D.Sequential Analysis.New York:Springer,1985
3闰章更,濮晓龙.现代军事抽样检验方法及应用.北京:国防工业出版社,2008
4 Lavigne L,Cazaurang F,Fadiga L,et al.New sequential probability ratio test:Validation on A380 flight data.Control Eng Pract,2014,22:1-9
5 Bolland M J,Grey A,Gamble G D,et al.The effect of vitamin D supplementation on skeletal,vascular,or cancer outcomes:A trial sequential meta-analysis.Lancet Diabetes Endocrinology,2014,2:307-320
6 Kulldorff M,Davis R L,Kolczak M,et al.A maximized sequential probability ratio test for drug and vaccine safety surveillance.Sequential Anal,2011,30:58-78
7 Shih M C,Lai T L,Heyse J F,et al.Sequential generalized likelihood ratio tests for vaccine safety evaluation.Stat Med,2010,29:2698-2708
8 Wald A.Sequential tests of statistical hypotheses.Ann Math Statist,1945,16:117-186
9 Wald A,Wolfowitz J.Optimum character of the sequential probability ratio test.Ann Math Statist,1947,19:326-339
10 Kiefer J,Weiss L.Some properties of generalized sequential probability ratio tests.Ann Math Statist,1957,28:217-217
11 Lorden G.2-SPRT’s and the modified Kiefer-Weiss problem of minimizing an expected sample size.Ann Statist,1976,4:281-291
12 Huffman M D.An efficient approximate solution to the Kiefer-Weiss problem.Ann Statist,1983,11:306-316
13 Lai T L.Optimal stopping and sequential tests which minimize the maximum expected sample size.Ann Statist,1973,1:659-673
14 Lai T L.Sequential analysis:Some classical problems and new challenges.Statist Sinica,2001,11:303-408
15濮晓龙,闰章更,茆诗松,等.计数型序贯网图检验.华东师范大学学报(自然科学版),2006,125:67-71
16 Li Y,Pu X L.Method of sequential mesh on Koopman-Darmois distributions.Sci China Math,2010,53:917-926
17李艳,濮晓龙.基于Koopman-Darmois分布族的序贯网图检验方法.中国科学:数学,2009,39:614-624
18 Li Y,Pu X L.A method for designing three-hypothesis test problems and sequential schemes.Comm Statist Simulation Comput,2010,39:1690-1708
19 Anderson T W.A modification of the sequential probability ratio test to reduce the sample size.Ann Math Statist,1960,31:165-197
20胡思贵.计数型截尾序贯检验的样本空间排序法.应用概率统计,2013,29:201-212
21 International Electrotechnical Commission.Reliability testing-Compliance test plans for success ratio.IEC1123,1991
22 Ganesan R,Rao A N V,Das T K.A multiscale Bayesian SPRT approach for online process monitoring.IEEE Trans Semicond Manuf,2008,21:399-412
23 Li J,Shen L,Zhao L.Success ratio sequential test plan using development test data.In:The Proceedings of 2009International Conference on Reliability,Maintainability and Safety.Piscataway:IEEE,2009,370-373
24胡思贵,周小静.计数型截尾序贯保证试验的研究.华东师范大学学报(自然科学版),2015,2015:47-56