Simulation-based Bayesian optimal ALT designs for model discrimination

Abstract

Accelerated life test (ALT) planning in Bayesian framework is studied in this paper with a focus of differentiating competing acceleration models, when there is uncertainty as to whether the relationship between log mean life and the stress variable is linear or exhibits some curvature. The proposed criterion is based on the Hellinger distance measure between predictive distributions. The optimal stress-factor setup and unit allocation are determined at three stress levels subject to test-lab equipment and test-duration constraints. Optimal designs are validated by their recovery rates, where the true, data-generating, model is selected under the DIC (Deviance Information Criterion) model selection rule, and by comparing their performance with other test plans. Results show that the proposed optimal design method has the advantage of substantially increasing a test plan's ability to distinguish among competing ALT models, thus providing better guidance as to which model is appropriate for the follow-on testing phase in the experiment.

Advances in Bayesian decision making in reliability

“…For example, Erkanli and Soyer (20 0 0) use MCMC methods with nonparametric surface estimation to find optimal ALT designs and Zhang and Meeker (2006) consider large sample results for Bayesian ALT designs, as well as simulation-based methods. Nasir and Pan (2015) present simulation-based ALT designs for model discrimination.…”

Design of step‐stress accelerated life tests for estimating the fatigue reliability of structural components based on a finite‐element approach

“…In previous years a number of review articles on this topic were published, that is, Escobar and Meeker, 4 Ma, 5 and Chen et al 6 while a handbook with a comprehensive description of the ALT methods was published by Nelson in 2004 7 . The methods were developed to cope with a wide range of engineering challenges, from single‐failure‐mode cases (e.g., Cheon et al 8 ), competing‐failure‐mode cases (e.g., Bunea & Mazzuchi, 9 Luo et al 10 ) ), optimal ALT designs for model discrimination (Nassir & Pan 11 ), progressive ALT designs (Sha 12 ), and so on. Applications of ALT testing on real‐case structures have been reported in the field of agriculture (Mattetti et al 13 Paraforos et al 14 ), the automotive (Putra et al 15 Shafiullah & Wu 16 ), and railway industries (Lu et al 17 ).…”

Statistical inference for the Arrhenius-Weibull accelerated life testing model with imprecision based on the likelihood ratio test

“…Sha and Pan [27] introduced step-stress ALT with Bayesian analysis for the Weibull proportional hazard model. Nasir and Pan [22] posited a Bayesian optimal design criterion and presented acceleration model selection ALT studies, while Han [16] conducted research into temporally and financially constrained constant-stress and step-stress ALT.…”