A D-Optimal Design for Estimation of Parameters of an Exponential-Linear Growth Curve of Nanostructures

Zhu, Lei; Dasgupta, Tirthankar; Huang, Qiang

doi:10.1080/00401706.2013.866600

Cited by 12 publications

(6 citation statements)

References 27 publications

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“…A sequential design approach to deal with the problem of dependence on parameters has also been proposed and studied. Zhu et al (2014) proposed a Bayesian sequential algorithm for obtaining D-optimal designs and a geometric approach to compute locally D-optimal designs.…”

Section: Discussionmentioning

confidence: 99%

Optimal Experimental Designs in the Flow Rate of Particles

2016

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This paper focuses on analysing the process of jam formation during the discharge by gravity of granular material stored in a 2D silo. The aim of the paper is twofold. Firstly, optimal experimental designs are computed, in which four approaches are considered: D−optimality, a combination of D−optimality and a cost/gain function, Bayesian D−optimality and sequential designing. These results reveal that the efficiency of the design used by the experimenters can be improved dramatically. A sensitivity analysis with respect to the most important parameter is also performed. Secondly, estimation of the unknown parameters is done using least squares, i.e. assuming normality, and also via maximum likelihood assuming the exponential distribution. Simulations for the designs considered in this paper show that the variance, the mean square error and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares.

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Section: Discussionmentioning

confidence: 99%

Optimal Experimental Designs in the Flow Rate of Particles

2016

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“…This is known as "Bayesian D-posterior precision"; e.g. see [29,30]. However, if one is interested in the precision of the marginal posterior distributions of the model parameters, the trace of the posterior covariance matrix, instead of its determinant, can be used to obtain the "Bayesian A-posterior precision".…”

Section: Bayesian Model Identification and The Ranking Of Materials Rementioning

confidence: 99%

On the value of test data for reducing uncertainty in material models: Computational framework and application to spherical indentation

Asaadi

Heyns

Haftka

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…Roy et al [17] and Zhu et al [18] proved convergence properties of the Bayesian sequential D-optimal designs for different forms of models.…”

Section: Related Literaturementioning

confidence: 99%

Bayesian Sequential Design Based on Dual Objectives for Accelerated Life Tests

Lee

Hong

2019

Statistical Quality Technologies

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Traditional accelerated life test plans are typically based on optimizing the C-optimality for minimizing the variance of an interested quantile of the lifetime distribution. The traditional methods rely on some specified planning values for the model parameters, which are usually unknown prior to the actual tests. The ambiguity of the specified parameters can lead to suboptimal designs for optimizing the intended reliability performance. In this paper, we propose a sequential design strategy for life test plans based on considering dual objectives. In the early stage of the sequential experiment, we suggest to allocate more design locations based on optimizing the D-optimality to quickly gain precision in the estimated model parameters. In the later stage of the experiment, we can allocate more samples based on optimizing the C-optimality to maximize the precision of the estimated quantile of the lifetime distribution.We compare the proposed sequential design strategy with existing test plans considering only a single criterion and illustrate the new method with an example on fatigue testing of polymer composites.

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A D-Optimal Design for Estimation of Parameters of an Exponential-Linear Growth Curve of Nanostructures

Cited by 12 publications

References 27 publications

Optimal Experimental Designs in the Flow Rate of Particles

Optimal Experimental Designs in the Flow Rate of Particles

On the value of test data for reducing uncertainty in material models: Computational framework and application to spherical indentation

Bayesian Sequential Design Based on Dual Objectives for Accelerated Life Tests

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