Designs and Comparison of Step and Constant-Stress ALTs for Acceleration Factor and Lognormal Lifetime Distributions

This paper considers designing the simple (2-level) constant-and step-stress ALTs minimizing the asymptotic variance of the maximum likelihood estimator of the accelaeration factor, which is defined as the ratio of the 100qth percentile at use stress to that a specified stress, for items having lognormally-distributed lives. It is assumed that (i) the log-linear relationship exists between the stress and the mean log life, (ii) the standard deviation of the log life is constant, and (iii) the cumulative exposure model holds for the effect of changing stress. For the constant-stress ALT the low stress and the sample proportion allocated to low stress are determined and for two modes of stress loading of step-stress ALTs, the low-to-high and high-to-low, the low stress and the stress change time are determined. For selected values of the design parameters the optimum plans are figured, two modes of step-stress ALTs and the constant-stress ALT are compared to each other, and the effects of the incorrect pre-estimates of the design parameters are investigated.