Simulation-based Bayesian optimal ALT designs for model discrimination

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.NOTICE: this is the author's version of a work that was accepted for publication in RELIABILITY ENGINEERING & SYSTEM SAFETY. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in RELIABILITY ENGINEERING & SYSTEM SAFETY, 134, 1-9. DOI: 10.1016/j.ress.2014.10.00

Study of efficiency time of recombinant DNA insulin via accelerated life testing and interval censoring.

This paper aims to study the efficiency of recombinant DNA insulin via models for accelerated life tests. The potency loss of these insulin products was evaluated periodically, subject to the conditions of temperature of 8?C, 25?C and 37?C. Insulin samples with potency at less than 100% were considered unfit for consumption, which characterizes the event of interest. Samples suitable for consumption were considered to be censored. The response variable was observed periodically for 736 days. For data analysis, statistical models of stress-response regression were used. The deterministic part of these models is the Arrhenius model because the stress variable is the temperature, while the probabilistic part was comprised of the Exponential, Weibull, and Log-normal models. The techniques of accelerated life tests proved adequate to address the time of potency loss of the insulin for the various temperature levels. The times of occurrence of the events were treated in three different ways, which were compared in this study. First, interval censoring was considered, or only the upper and lower limits of the interval in which the failure occurred were known. Then, the midpoint of this interval was considered as a failure time. Finally, only the lower limit of the interval in which the failure occurred was considered. According to the results, it is concluded that the use of the interval lower limit is more appropriate for estimating the reliability curves, as the estimates are closer to those using interval censoring then using the midpoint of the interval. For the specific case of the recombinant DNA insulin data, it was observed that the Arrhenius-Weibull model and the Arrhenius-lognormal are suitable for adjusting the data. It follows also that the temperature affects the power of the insulin: The higher the temperature are, the lesser the efficiency

Data Analysis and Experimental Design for Accelerated Life Testing with Heterogeneous Group Effects

abstract: In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects. Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship. The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201