The Optimal Design Of Step-stress Accelerated Life Test Plans Under Progressive Type Ⅰ Interval Censoring With Discrete Uniform Random Removals

We have studied the statistical analysis and optimal design for the accelerated life tests (ALT) of step-stress in this paper. The step-stress accelerated life tests have two advanced points:1. Less experiment time is needed comparing to the accelerated life tests with constant stress;2.The number of test units is reduced. Therefore, it is necessary for us to carry out the step-stress accelerated life tests if we want to know about quality information of the products with long life time during relatively short time. We investigate optimal accelerated life test plans of k step-stress for exponentially distributed lifetimes under progressive Type I censoring with random removals,where the number of units removed at failure time follows discrete uniform distribution.The joint likelihood function is derived based on the function model. Then the maximum likelihood estimated values of the life parameters are obtained.Furthermore Fisher information matrix and the asymptotic variance (AV) of the lifetime estimators are also derived. The optimal inspection interval is obtained by minimizing the AV under normal operating condition. Monte Carlo numerical simulations are conducted. Finally, we investigate the relationships among the life expectancy, stress level and optimal inspection interval by numerical study. It provides a meaningful reference for the practitioners when they design a step-stress accelerated life test.