Statistical Analysis Of Step-and-step Tests And Step-down Tests For Half-logistic Distributions With Shape Parameters

Assessing product reliability in the industry is an important issue.Actually,in order to evaluate the reliability of a product,we have to do life experiment to collect the failure time data of the product,and the unknown parameters can be estimated by using the failure data,then you can know the life distribution of the product and the performance of the product are derived.In order to evaluate the reliability of products with lower cost,people introduce accelerated life test,which helps to obtain the product failure data in a short time,and then use the acceleration equation to extrapolate the estimated value of the product under normal environments,in a shorter time and the lower cost.In this paper,we assume that the product's life is subject to a half-logistic distribution with shape parameters.The inverse power model and the Arrhenius model are used as the acceleration model.When the sample data is the time-series censored data and the accelerated life test is step-stress or step-down stress,the unknown parameter can be estimated by using the maximum likelihood method.The first chapter is an explanation of the current status of life test development and references.The second chapter introduces the theoretical basis of the study,including the life test and the half-logistic distribution.In the third chapter,the statistical analysis of the simple step-by-step experiment is performed firstly,and then analyzed in two cases: the inverse power law model and the Arrhenius model.The maximum likelihood estimation method is used to estimate the unknown parameters;then,it is extended to multiple steps.The additive test is still performed under the inverse power law and Arrhenius model.Finally,the Monte-Carlo method is used for numerical simulation to evaluate the effect of maximum likelihood estimation.In the fourth chapter,the statistical analysis of the step-down test is carried out.The idea of the step-down test and the current development status are first introduced.It is consistent with the research ideas in the third chapter.Steps are statistically analyzed from two to many;finally,numerical simulations are performed to evaluate the results of the maximum likelihood estimation of step-down tests.The fifth chapter explains the application of research content in practice and summarizes the research work of this article.The sixth chapter puts forward the outlook based on the research content of this paper.