Optimal design of cyclic-stress accelerated life tests for lognormal lifetime distribution

ABSTRACT Accelerated life tests (ALTs) have frequently been used in industry to assess the reliability of products within an affordable amount of time and cost. Most of the previous works on designing ALT plans have dealt with the case of constant-, step- or progressive-stress loading, which may not be adequate for products operating under cyclic-stress loading at the use condition. In this paper, optimal and compromise ALT plans are developed under the assumptions of cyclic-stress loading, lognormal lifetime distribution, log-linear relationship between the scale parameter of the lifetime distribution and stress variable and the cumulative exposure model for the effect of changing stress levels. In particular, the common floor level and the proportion of units assigned to two (for optimal plans) or three (for compromise plans) cyclic-stress conditions are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized. In addition, a sample size determination method is developed, and sensitivity analysis procedures are presented to evaluate the robustness of the proposed ALT plans in the face of uncertainty in the pre-estimation of a model parameter. The whole process is illustrated with an example.