Planning gamma accelerated degradation tests with two accelerating variables

Abstract

Gamma accelerated degradation tests (ADT) are widely used to assess timely lifetime information of highly reliable products with degradation paths that follow a gamma process. In the existing literature, there is interest in addressing the problem of deciding how to conduct an efficient, ADT that includes determinations of higher stress‐testing levels and their corresponding sample‐size allocations. The existing results mainly focused on the case of a single accelerating variable. However, this may not be practical when the quality characteristics of the product have slow degradation rates. To overcome this difficulty, we propose an analytical approach to address this decision‐making problem using the case of two accelerating variables. Specifically, based on the criterion of minimizing the asymptotic variance of the estimated q quantile of lifetime distribution of the product, we analytically show that the optimal stress levels and sample‐size allocations can be simultaneously obtained via a general equivalence theorem. In addition, we use a practical example to illustrate the proposed procedure.

Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

“…Based on prior researches (Duan & Wang, 2019; Tung & Tseng, 2019), the optimal number of stress levels is typically equal to the number of parameters in the drift parameter, which would be four in this study. In addition, the stress levels are usually allocated at the boundaries of the design region.…”

“…Similarly, Limon et al (2020) assumed equal termination times for testing at each stress level, whereas higher stress levels typically require shorter testing times. Tung and Tseng (2019) considered a generalized Eyring model to the drift parameter of the gamma process, and analytically showed that the $$$ V $$$‐optimal approximate design only allocates test units at four stress levels. The result offers an intuitive insight for practitioners.…”

Optimization Design of Step Stress Accelerated Degradation Test for Motorized Spindle Based on Ds-Optimality

“…In order to further improve test efficiency, reduce the test sample size and apply to more kinds of products, scholars have expanded the research content from single stress level selection to more test factors. Tsai [17] and Tung [18] researched the ADT optimization method for the degradation process following a gamma process. Mosavebi [19] researched an optimal sample ratio under each sample size and the influence of each stress on the objective function.…”