Sequential Precedence Test Based On Sorted Set Early Failure Data

In medical research and industrial production,it is often necessary to compare different treatment methods or product quality.But sometimes there will be cost and moral problems,so researchers hope to use less samples to draw relatively reliable conclusions.In this article,based on the early failed ranked set samples and sequential procedure,one type of RSS sequential precedence test method is designed to save samples without losing too much test efficiency.In this article,we give the detailed process of this test method,including the ranked set sampling process and the sequential life-test process,and the test statistics as well as their exact distribution under the null hypothesis.We consider four types of-spending sequences and present the critical value and the corresponding significance level of the test statistics under the given set size and cycle size of ranked set samples.Next,we derive the exact power function of this test statistic under the Lehmann alternative₁:(1-(·))=(1-(·))with different.We then compare the power function with that of RSS non sequential precedence test.At the same time,we also compare expected number of failure samples and total test time of these two methods.Besides,Monte Carlo simulation method is used to compare the power,expected number of failure samples and total test time of sequential and non-sequential methods based on different forms of distributions under a location-shift alternative₁:()=(+).Finally,we investigate the effect of imperfect ranking on the performance of RSS sequential precedence test under the location-shift alternative.We use the imperfect ranking model with additional noise to obtain the power,expected number of failure samples and total test time of sequential and non-sequential methods under normal distribution and exponential distribution.After above study,conclusion got as follow,compared with the non-sequential method,the RSS sequential precedence test has a certain degree of reduction in the power,but it has obvious effect in saving samples and total test time,especially when the distribution of the two samples is quite different or the sample size is large.The effect is more obvious when the underlying distribution is right-skewed.In the case of imperfect ranking,the RSS sequential precedence test has a certain effect reduction,but it still has advantages over the non-sequential method.