Statistical Analysis Of Accelerated Life Testing Under The Two Parameter Exponential Distribution With Grouped Data

The reliability theory which mainly research on life characteristics is used widely.Accelerated life test is an important branch in the research field of reliability which refers to test by lifting stress accelerated failure in the premise of keeping constant failure mechanism. We often require products not failure before a certain time in practical application,it requires consideration of threshold parameter estimates.This paper studies the basic concepts and statistical analysis of accelerated life test in two parameter exponential distribution with grouped data. The main contents are as follows:The first part introduced the research background, research status and basic theory of accelerated life test, including the basic knowledge of grouped data, accelerated life test types, acceleration model, two parameter life distribution.In the second part, under the two case with the threshold parameter is the same and different, we do the statistical analysis in view of the constant stress accelerated life test and step stress accelerated life test : give the likelihood function, the likelihood equation of the Single stress- Arrhenius,Single stress- Polynomial and double stress- Eyring with the quantity of the stress level is k and built a model of the threshold parameter,derive the one order and two order guide.At the same time, taking the Arrhenius model as the example, prove the existence and uniqueness of solution of the constant stress accelerated life test and step stress accelerated life test’s likelihood equation in two parameter exponential distribution.The last part of this paper using Matlab software to do the optimization of log likelihood function of the single stress accelerated life test and get the numerical simulation results of unknown parameter estimation value and standard error. The results show that: 1. when the other conditions are the same, with the increase of the sample size n or standard stress life, the parameter estimates are more close to the true value, the standard error is smaller and smaller, the precision is more and more high.2. The same test type and accelerated model that can guarantee that the precision of the same threshold parameters is as the same as the different threshold parameters.3.The precision of Arrhenius is slightly higher than the Polynomial model.4. The simulation accuracy of step test is slightly higher than constant acceleration test, and the simulation time of step test is shorter, the sample is only 1/k of the constant stress tests.