Optimum test condition setting and sample allocation for accelerated degradation tests under the last-exit-time failure mode

Accelerated degradation tests (ADTs) have been widely adopted for products whose failure is defined as the first-passage-time (FPT) when the degradation path crosses a given threshold. However, for products whose failure is defined as the last-exit-time (LET), few studies related to ADT have been investigated. In this paper, we focus on designing an optimum test condition setting and sample allocation scheme for ADTs under the LET failure mode. In particular, the widely adopted Wiener process model and the generalized exponential acceleration model are used to describe the fluctuating degradation behaviors of products. By minimizing the asymptotic variance of mean-time-to-failure under the normal use condition, we design a two-level optimum test plan and a three-level compromise plan under the constraints of total sample size and stress region. The optimum plans are given in analytical forms, and we prove that the optimum plans under the FPT failure mode and LET failure mode are equivalent under some situations. Finally, a renewed selection method for the upper limit of the stress level in ADTs is proposed based on the prior ADT information from the perspective of accelerated mechanism equivalence. The proposed method is illustrated using a real-world application to rubber rings.