Iterative Regression Algorithm for Parameter Estimation for Nondestructive One-Shot Devices under Cyclic Accelerated Life Test with Adaptive Proportion of Failure Design

One-shot devices, such as automotive airbags, fire extinguishers and ammunitions, pose significant challenges in their reliability analysis due to their inherently unobservable lifespans. Nondestructive one-shot devices, in particular, offer additional information when they have not failed prior to inspection, yielding interval-censored failure time data. This article addresses the limitations of traditional testing designs for such devices by introducing an adaptive proportion of failure approach within the context of cyclic accelerated life tests, a variant of accelerated life tests characterized by continuously varying stress levels in the operating environment. Using the Norris-Landzberg model for thermal cycling-induced stresses, we propose here an iterative regression algorithm for statistical inference under this adaptive design. Our algorithm provides estimators that possess consistency and asymptotic normality, demonstrating robustness against initial value sensitivity, a common issue with traditional numerical methods used for maximum likelihood estimation. A simulation study and an illustrative example are presented to exemplify the merits of the proposed approach.