Research On Optimal Test Of Exponential Distribution Based On Dynamic Programming Metho

In the fields of aviation,aerospace,military industry and medical and health,the sequential sampling test is usually adopted for the reliability sampling test of products.Compared with conventional sampling tests with fixed sample sizes,sequential sampling tests can reduce the average sample numbers or the expected test time dramatically,hence they can reduce the test costs significantly.For the products with lifetime that subject to exponential distribution,truncated sequential probability ratio test(T-SPRT)is the frequently used test plan in the international and national standards IEC 61124,GOST R 27.402,GJB899 A,MIL-HDBK-781 A and so on.However,a large number of studies have shown that T-SPRT is not the optimal truncated sequential test.Therefore,this paper studies the optimal truncated sequential test of exponential distribution.The research significance of this study lies in that,on the one hand,it can reduce the expected test time dramatically in products sampling test and save the test costs;on the other hand,it can provide a standard for evaluating the other sequential tests.The main work and content of the paper are as follows.1)The optimal truncated sequential test of exponential distribution is studied.The definition and related concepts of the optimal truncated sequential test(OTST)for exponential distribution are given.The calculated expressions of statistical indicators such as the expected test time(ETT),the probability of making errors and are derived,and the OTST is solved by the dynamic programming method.By comparing with the T-SPRTs given by standards IEC 61124 and GOST R 27.402,the results show that the OTSTs proposed in this paper can strictly control the probability of making errors and minimize the expected test time.Furthermore,the OTSTs is also compared with the approximately optimal truncated sequential tests solved by sample space sorting method.The results show that the optimal test plans solved by the two methods are almost the same,but the dynamic programming method established in this paper has higher computational efficiency.Especially for the sampling test with large truncated sample size,the dynamic programming method can greatly reduce the computational time of the optimal plans.Additionally,in order to further reduce the test cost in products sampling test,the truncated sequential test on maximum sample size(OTSTMSS)is studied.By comparing the OTSTMSS with the OTST,the results show that the OTSTMSS can reduce the proportion of expected test time about more than 5%.2)The optimal truncated sequential test of exponential distribution with prior information is studied.When the product has passed the qualification test,the test data is regarded as prior information about the quality of product and introduced to the design of production acceptance test,and then the Bayesian truncated sequential test of exponential distribution is studied.The definition of the Bayesian truncated sequential test(BTST)for exponential distribution are given.The calculated expressions of the posterior risk of the producer and consumer are derived,and the method for solving the BTSTs based on dynamic programming is established.By comparing with the acceptance test plans given by the Chinese military standard GJB899 A,the superiority of the BTSTs is verified.The results show that BTST has the less expected test time and sample size,so that it can effectively reduce the test cost in production acceptance test.Especially,for the products with the higher quality,BTST performs better in reducing the expected test time and sample size.