| In modern production processes,sampling inspection is an important method in quality management and quality control.For products with high-cost and destructive testing,low-cost and high-reliability testing or high-reliability and long-life testing,such as the hit-rate of missiles,reliability of large electronic systems,reliability of bullets and fuzes,the storage life of missiles and the service life of aircraft black boxes,etc,how to improve test efficiency and reduce test cost is a key problem in the designs of sampling test.Compared with conventional sampling tests with fixed sample sizes,sequential tests can reduce the average sample numbers or the expected testing time dramatically,hence they can reduce the test costs significantly.In the current international and national standards,such as IEC1123(1991),IEC61124(2012),ISO2859.1(1999),GB/T8051(2008),GJB899(2009),GB/T2828.1(2012),etc,truncated sequential probability ratio tests(TSPRTs)are generally adopted.However,T-SPRTs are not the optimal testing programs.In this study,optimal truncated sequential tests of binomial distribution and exponential distribution are studied,and application of the proposed optimal truncated sequential tests to the quality testing of springs for railway vehicles is investigated.The research significance of this study lies in that,on the one hand,it can reduce the test cost or cost budget in products sampling test;on the other hand,it can make up for the deficiencies of truncated sequential tests specified in current national and international standards,and provide theoretical and methodological support to revise these standards.The main work of the thesis is as follows.1)For products with testing characters of high-cost and destructive,the truncated sample size of a sequential test is a decisive factor of the testing cost budget.In order to reduce the cost budget,the minimum truncated sample size sequential test(MTST)of binomial proportion is studied.Definitions,properties and the solving methods of MTST are proposed.Through comparing with the test programs specified in international standard IEC1123(1991)and the sequential mesh tests(SMTs)proposed by Pu et al(2006),the results show that proposed MTSTs can reduce the truncated sample sizes and the average sample numbers(ASNs)significantly.When the priori information of products is known,a Bayesian minimum truncated sample size sequential test(BMTST)is proposed to reduce more truncated sample size.The relative definitions of BMTST are difined and the procedures to solve BMTST are established.Through comparing with MTSTs,the results show that BMTSTs can reduce up to 60% of the truncated sample size and ASN simultaneously for the products with relative high qualities.BMTSTs can save the test cost budget and test cost greatly.2)In order to save the test cost for products with testing characters of low-cost and high-reliability,optimal truncated group sequential tests of binomial proportion is studied.Through analysis of the testing cost structure,average test cost(ATC)is introduced as a new optimal criterion.Based on the new criterion,the optimal truncated sequential tests with design parameters including the testing boundaries,success discriminant value,stage sample vector,stage size and truncated sample size are defined.Since the computation time to find the optimal design through exhaustive search is intolerably long,a sample space sorting method is established to find a near-optimal one.Through comparing with the test programs specified in the international standard ISO2859-1(1999),the results show that the truncated group sequential tests proposed in this thesis can generally reduce about 20% of ATCs.3)In order to save the test cost or test time for products with testing characters of high-reliability and long-life,optimal truncated sequential tests of exponential distribution are studied.Definitions and concepts of optimal truncated sequential tests are discussed.With the introduction of new symbolic representations,the operating characteristic(OC)function and expected test time(ETT)function of a truncated sequential test are derived.A sample space sorting method(SSSM)is established to find a near-optimal solution.Through comparing with the test programs specified in the international standard IEC 61124(2012)and the Russian national standard GOST R27.402(1995),the results show that the near optimal tests proposed in this thesis can keep the type I and type II error probabilities almost equal to the nominal levels.Moreover,both synthetical ETT and maximum ETT can be further reduced.In fact,comparing with the test programs given in GOST R 27.402(1995),the proposed optimal tests can save up to 14.62% of ETT,which means they can reduce test costs significantly.4)When products have passed qualification tests and environmental stress screening tests,and the condition of production is stable,an acceptance test with extremely short test time,which is called assurance test,is proposed in the American military standard MIL-STD-781(1980).In order to save more test costs in acceptance tests,assurance test and its equivalent truncated sequential test are studied.Considering a typical case,the OC function and ETT function of the assurance test are derived in a concise manner.Equivalent tests and equivalent truncated sequential tests of the assurance test are defined.Procedures to obtain a near-equivalent truncated sequential test of the assurance test are established.Through comparing the proposed near-equivalent truncated sequential test with the corresponding assurance test,the results show that the test proposed can achieve OC curves almost the same as those of the assurance test.Moreover,the ETT can be reduced significantly.In fact,comparing with the assurance test,the test proposed can generally save around 50% of ETT,hence saving the test cost greatly.5)The proposed optimal truncated group sequential test is applied to quality test of hot-coiled compression springs for railway vehicles.Since truncated group sequential tests specified in the national standard GB/T2828.1(2012)are widely used in current sampling tests.Some issues of the truncated group sequential tests given in GB/T2828.1(2012)are discussed,including too large truncated sample sizes and average sample sizes,and too large deviations between the type I and type II error probabilities made in the tests and in the one stage sampling tests.Based on the characteristic analysis of the truncated group sequential tests given in GB/T2828.1(2012),an optimized truncated group sequential test is proposed.Procedures to obtain the optimized truncated group sequential test are established.Through comparing with the tests specified in GB/T2828.1(2012),the advantages of the proposed optimized test are validated.Finally,the optimized truncated group sequential test is applied to quality testing of a compression spring for railway vehicles.Through comparing with the test programs specified in GB/T2828.1(2012),the results show that the optimized test proposed in this thesis can save 13.99% of the average test cost. |
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