A Bayesian Analysis of Unreplicated Two-Level Factorials Using Effects Sparsity, Hierarchy, and Heredity

Bergquist, Bjarne; Vanhatalo, Erik; Nordenvaad, Magnus Lundberg

doi:10.1080/08982112.2011.553760

Cited by 20 publications

(34 citation statements)

References 31 publications

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“…To calculate the critical values they use a method similar to that of Ye and Hamada, but it can be applied to a wide variety of designs, particularly those which are not orthogonal. Bergquist et al [1] propose a Bayesian procedure. They begin with a study of published cases to establish the a priori probabilities based on the principles of sparsity, hierarchy and heredity, and then illustrate their method by analyzing cases in the literature.…”

Section: Alternatives To the Lenth Methodsmentioning

confidence: 99%

Proposal of a Single Critical Value for the Lenth Method

Fontdecaba

Cintas

Tort‐Martorell

2015

Quality Technology & Quantitative Management

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Different critical values deduced by simulation have been proposed that greatly improve Lenth's original proposal. However, these simulations assume that all effects are zerosomething not realistic--producing bigger than desired critical values and thus significance levels lower that intended. This article, in accordance with George Box [2] well known idea that Experimental Design should be about learning and not about testing and based on studying how the presence of a realistic number and size of active effects affects critical values, proposes to use t = 2 for any number of runs equal or greater than 8. And it shows that this solution, in addition of being simpler, provides under reasonable realistic situations better results than those obtained by simulation.

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Section: Alternatives To the Lenth Methodsmentioning

confidence: 99%

Proposal of a Single Critical Value for the Lenth Method

Fontdecaba

Cintas

Tort‐Martorell

2015

Quality Technology & Quantitative Management

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“…The methods assume that the direction of the effects of the active variables tend to be monotonic. This regularity was seldom investigated in literature, and was proven to be valid when the system regularities of Bergquist et al (2011) and Li et al (2006) are present, as explained in Al Rashdan (2014. In addition, the methods evaluated the validity of this assumption at an early stage of their application.…”

Section: Introductionmentioning

confidence: 88%

“…If the variables were aligned in one direction, it was expected that the regularities studied in Bergquist et al, (2011) and Li et al, (2006) would reduce the confounded interactions, as was explained in Al Rashdan (2014).…”

Section: Directional Alignment Of Variablesmentioning

confidence: 97%

Parametric evaluation of an SMR design domain

Rashdan

Tsvetkov

2015

Annals of Nuclear Energy

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“…(7) to incorporate the strong and weak heredity principle, respectively. Bergquist et al (2011) reviewed some of the initial probabilities in an analysis of unreplicated twolevel factorials. However, in any case, it is difficult to explain the propriety of the initial tuning values.…”

Section: Strong and Weak Heredity Modelsmentioning

confidence: 99%

Bayesian Lasso with Effect Heredity Principle

Noguchi

Ojima

Yasui

2015

Frontiers in Statistical Quality Control 11

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The Bayesian Lasso is a variable selection method that can be applied in situations where there are more variables than observations; thus, both main effects and interaction effects can be considered in screening experiments. To apply the Bayesian framework to experiments involving the effect heredity principle, which governs the relationships between interactions and their corresponding main effects, several initial tunings of the Bayesian framework are required. However, it is rather unnatural to specify these tuning values before running an experiment. In this paper, we propose models that do not require the initial tuning values to be specified in advance. The proposed methods are demonstrated with screening examples such as Plackett-Burman and mixed-level design.

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A Bayesian Analysis of Unreplicated Two-Level Factorials Using Effects Sparsity, Hierarchy, and Heredity

Cited by 20 publications

References 31 publications

Proposal of a Single Critical Value for the Lenth Method

Proposal of a Single Critical Value for the Lenth Method

Parametric evaluation of an SMR design domain

Bayesian Lasso with Effect Heredity Principle

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