Sequential Procedures In The Life Test Data

Sequential procedures were first developed by Wald(1947), it mostly contains sequential probability ratio test and sequential estimation. Sequential procedures is an important branch of applications of statistics which tells us how to obtain sequential samples and how to carry out statistical inference, it has ever been provided with"the most power of statistical ideas in the world". Generally speaking, sequential procedures have two essential features: one is a rule for terminational of the experiment ; the other is a terminal decision rule. The former says the time when the sampling should be stopped during a sequence of observations one (or a fixed number) at a time; the latter how to draw a conclusion according to the sequential sample. Sequential procedures have been widely used in the life test data , in this thesis, sequential analysis methods are discussed under the complete life experiment data.Firstly, we concerned the sequential probability ratio test (SPRT) for a simple versus simple hypothesis-testing problem in the exponential distribution, and the SPRT can be extended to test a composite hypothesis against a composite alternative. By comparing with Neyman-Pearson test, theoretical estimator and simulation results indicate the optimal properties of SPRT.Secondly, We constructed N-truncated SPRT of the exponential distribution based on the SPRT. The problem was discussed in this thesis, which we try to search for a method of selecting an embedded point C, such as probability weighted method according to prior information. Simulated results shows that the appropriate selection of C can greatly improve the efficiency of testing.Thirdly, we worked over two-stage procedure of sequential interval estimation for the lognormal distribution. Making use of Bayes statistics, we obtain Bayes sequential interval estimation of the parameter under different prior distributions. And these estimations are better than classical interval estimation.At last, all the works in this thesis are summarized and some prospects are also proposed.