Statistical Analysis Of Step-and-step Life Testing Based On Improved Chen's Life Distribution

In recent years,with the development of technology,more and more products have high life property.In order to estimate this type products' lifetime,we cannot choose traditional ways,it will cost a lot of time and money.However,accelerated life test can avoid this defects,therefore,it is important for Manufacturing Industry.Zhenmin Chen raised a new two-parameter life time distribution with bathtub-shape or increasing failure rate function in 2000,it can be used to model bathtub-shaped failure rate,but it does not contain a scale parameter and hence not flexible in modeling real data.Base on it,M.Xie had added scale parameter to this distribution,and made this distribution more universal applicability.This article is mainly discussing about the statistical analysis of step stress accelerated life test and step down accelerated life test on the distribution that proposed by M.Xie.The main work are as follows:1?First this paper introduces the basic concepts of step stress accelerated life test,step down accelerated life test and the background of the distribution.In addition,this distribution's basic statistical properties are described.2?According to the Nelson assumption,converting failure time under different stress levels to the same level by time conversion,and hence the failure distribution function can be obtained.The maximum likelihood estimations of the parameters under the inverse power law model and Arrhenius model are derived.Since the equations are transcendental equations,solve the parameter estimation by numerical method.This paper use Monte Carlo simulation to simulate failure time and to solve the estimations of parameters.The accuracy of the simulations is investigated through500 Monte Carlo simulations and it can be proved that the feasibility of this method.3?Mainly focusing on the estimating the parameters of the accelerate equation under step down stress accelerated life test.Since this test's stress sequence is opposite to step stress accelerated life test,the way of time conversion changes.Therefore,the failure distribution function which had been calculated by timeconversion should be used to structure likelihood function,and then deduce the maximum likelihood estimations.Finally,the estimation of parameters which has be calculated by Monte Carlo simulation can illustrate the feasibility of the method.