Planning accelerated life tests for censored two-parameter exponential distributions

We consider optimal test plans involving life distributions with failure-free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two-parameter exponential distribution and the stress–life relationship is given by the inverse power law model. Near-optimal test plans for constant-stress ALT under both failure-censoring and time-censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure-censored and time-censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near-optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal-allocation plan.