Planning and Inference for a Sequential Accelerated Life Test

In planning accelerated life tests (ALTs), initial values of some unknown model parameters must be specified so as to derive a locally optimal test plan. Very often, the margin of specification error is high and the requisite level of statistical precision cannot be achieved as planned. In this paper, we propose a sequential test plan for single-variable constant-stress accelerated life test. Under the sequential scheme, a test at the highest stress level is first planned and conducted. Using the information obtained at the highest stress level, a Bayesian framework is proposed to optimally determine both the sample allocation and stress combinations at lower stress levels of subsequent accelerated tests. This is done by minimizing the preposterior expectation of the posterior variance of the estimated life percentile of interest at use conditions. For illustration purposes, the proposed scheme is applied to ALTs with two and three constant stress levels and a comprehensive simulation study is presented to compare the performance of the sequential ALT with that of nonsequential static testing. Our results suggest that the proposed approach not only enhances the robustness of an ALT plan against misspecification of model parameters but also improves its statistical efficiency.