Step-stress life-testing with random stress-change times for exponential data

This paper studies statistical models in step-stress accelerated life-testing when the stress-change times are random. The marginal lifetime distribution of a test unit under a step-stress test plan when the stress change times are random variables is presented. Maximum likelihood estimates for model parameters based on both the marginal and conditional life distributions are considered. An optimum test plan is explored for simple step-stress test when the stress change time is an order statistic from the exponential lifetime under the low-stress level.