Based On The Generalized Exponential Distribution With Interval Data, Accelerated Life Testing

In many situations, and for many reasons, time-to-failure data of products, systems orcomponents is very difficult to obtain. Given this difficulty, and the need to observefailures of products to better understand their failure modes and their lifecharacteristics, accelerated life testing is a good method to force these products to failmore quickly than they would under normal use conditions. It can be carried out byusing constant stress, step-stress, or progressive stress. Over the years, the problem ofaccelerated life test has been studied by many authors. However, there are still somelimitations. On the one hand, there is a lack of effective methods to analyze the lifedata when the stress of the life test is circular-progressive stress. On the other hand,when the test units are inspected for failure intermittently during the life test, the dataobtained is interval-censored data and consist of only the number of failures in theinspecting intervals. Although many authors studied the interval-censored data of theaccelerated life test when the stress is constant, there are not available methods toestimate the parameters in step-stress situation.In this paper, we develop two models based on the existing research methods andresults. Firstly, we put forward a model of the accelerated life test which is carried outby circular-progressive stress and the life data is under generalized exponentialdistribution which is presented by Gupta and Kundu in 1999. At the same time, theBayesian estimation of the reliability function when the stress is constant is given. Inthis part, the probability density function of circular time of product is given.Moreover, we demonstrate the estimation procedure by combining MLE and LSEmethods and compare it with the MLE method by a simulated example. Secondly, wepresent a step-stress accelerated life testing model when the life time is followinglog-normal distribution and the failure data obtained is interval-censored data. On theassumption of cumulative exposure model, we make use of the exchange formula oftime and the EM algorithm to estimate the parameters.