Planning accelerated life tests with random effects of test chambers

Abstract

In accelerated life tests (ALTs), test units are often tested in multiple test chambers along with different stress conditions. The nonhomogeneity of test chambers precludes the complete randomized experiment and may affect the life-stress relationship of the test product. The chamber-to-chamber variation should be taken into account for ALT planning so as to obtain more accurate test results. In this paper, planning ALTs under a nested experimental design structure with random test chamber effects is studied. First, by a 2-phase approach, we illustrate to what extent different test chamber assignments to stress conditions may impact the estimation of unknown parameters. Then, D-optimal test plans with 2 test chambers are considered. To construct the optimal design, we establish the generalized linear mixed model for failure-time data and apply a quasi-likelihood method, where test chamber assignments, as well as other decision variables that are required for planning ALTs, are simultaneously determined. KEYWORDSaccelerated life tests, D-optimal design, generalized linear mixed model, nested experimental design, random effects, test chamber assignment 224

Data analysis for accelerated life tests via Weibull‐gamma frailty regression models

“…The gamma frailty Weibull regression model facilitates deriving the Fisher information matrix which makes us easily use the ACE algorithm to search for $$$ D $$$‐ and $$$ c $$$‐optimal designs. Our methods can be extended to the scenarios considered by Seo and Pan 11,22 …”

“…Nelson 3‐5 gave a comprehensive review of the literature on ALT planning from 1970 to 2015. Seo and Pan 11 proposed two methods including a 2‐phase approach and a quasi‐likelihood approach to construct $$$ D $$$‐optimal test plans under a nested experimental design structure with random test chamber effects. Seo and Pan 22 used a quasi‐likelihood approach to obtain $$$ D $$$‐optimal ALT test plan when there were multiple sources of random effects present in practical experiment.…”

“…Seo and Pan 22 used a quasi‐likelihood approach to obtain $$$ D $$$‐optimal ALT test plan when there were multiple sources of random effects present in practical experiment. The quasi‐likelihood approach adopted by Seo and Pan 11,22 depends on the GLMM framework to derive the approximate FIM which is the cornerstone in searching for the $$$ D $$$‐optimal ALT plans. Different from the approximation method advised by Seo and Pan, 20,22 we here use a direct method to derive the FIM, inspired by the work of Ueckert and Metntré 33 …”

“…Zhuang et al 21 proposed a fractional‐random‐weight bootstrap method to make interval estimation based on heavily censored interval data with batch effects. In addition to statistical inference, Seo and Pan 11 studied the optimal design problem for the ALT with a nested experimental design structure. Seo and Pan 22 developed a GLMM method to plan ALT with multiple sources of random effects.…”

Simulation-based search for optimal designs of accelerated life tests through response surface methodology

“…In recent research on ALT, more complex optimality criteria with various constraints are considered, e.g. (Han, 2015; Seo and Pan, 2018), that could make the traditional mathematical models based on the Fisher information matrix very complex and numerically intractable.…”