Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
01 Jan 1999-
TL;DR: In this paper, a generalized resolution criterion is defined and used for assessing non-regular fractional factorials, notably Plackett-Burman designs, which is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order fractional fractional factors under the assumption that higher order effects are negligible.
Abstract: Resolution has been the most widely used criterion for comparing regular fractional factorials since it was introduced in 1961 by Box and Hunter. In this pa- per, we examine how a generalized resolution criterion can be defined and used for assessing nonregular fractional factorials, notably Plackett-Burman designs. Our generalization is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order ef- fects under the assumption that higher order effects are negligible. Our generalized resolution provides a fruitful criterion for ranking different designs while Webb's resolution is mainly useful as a classification rule. An additional advantage of our approach is that the idea leads to a natural generalization of minimum aberration. Examples are given to illustrate the usefulness of the new criteria.
Citations
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TL;DR: The original definitive screening designs and the designs that were constructed from weighing matrices were investigated and compared and the generalized resolution and minimum aberration criteria as well as the projection estimation capacity criterion from the literature were used.
1 citations
TL;DR: In this paper , the authors developed a method of constructing space-filling designs using non-regular designs, which have very flexible run sizes compared to those constructed from regular designs, such as strong orthogonal arrays of strength two plus.
1 citations
TL;DR: In this article, the β-wordlength pattern was used to compare different fractional factorial designs with qualitative factors under an ANOVA model and for designs with quantitative factors under a polynomial regression model.
Abstract: Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aberration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the β-wordlength pattern can be employed to compare different fractional factorial designs. Although the β-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of β-wordlength pattern for four-level designs. These properties can help find better designs with quantitative factors.
1 citations
25 Jun 2012
TL;DR: Experimental results have demonstrated the effectiveness of the proposed approach, and optimizations regarding memory storage and transfer in NVIDIA's Compute Unified Device Architecture (CUDA) are explored, as well as advance features such as streams and multiple GPUs.
Abstract: The process of applying generalized minimum aberration criteria (GMAC) to non-regular fractional factorial designs is extremely computationally intensive. Constructing and ranking all designs can take hours if not days; therefore, exploitation of the massively parallel nature of modern graphics processing units (GPUs) are used to perform the task. The computation is not just ported to the GPU, but is implemented as to optimize performance based upon the modern GPU architecture. Optimizations include using bit operations and table lookups to reduce the number of addition and multiplication operations performed. Tables are housed in GPU constant memory with almost no latency for access. Using a statistical proof from previous research reduces the memory required for the calculation. Optimizations regarding memory storage and transfer in NVIDIA's Compute Unified Device Architecture (CUDA) are also explored, as well as advance features such as streams and multiple GPUs. Experimental results have demonstrated the effectiveness of the proposed approach.
1 citations
Cites background from "Generalized resolution and minimum ..."
...Each column represents a factor which has a potential effect on the response....
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TL;DR: In this paper, the generalized aliasing effect number pattern (G2-AENP) and generalized general minimum lower order confounding (G 2-GMC) were proposed for non-regular designs.
1 citations
References
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3,546 citations
TL;DR: In this paper, the problem of choosing a design such that the polynomial f(ξ) = f (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function over some region of interest R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R, is considered.
Abstract: The general problem is considered of choosing a design such that (a) the polynomial f(ξ) = f(ξ1, ξ2, · · ·, ξ k ) in the k continuous variables ξ' = (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function g(ξ1, ξ2, · · ·, ξ k ) over some “region of interest” R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R; and (b) subject to satisfaction of (a), there is a high chance that inadequacy of f(ξ) to represent g(ξ) will be detected. When the observations are subject to error, discrepancies between the fitted polynomial and the true function occur: i. due to sampling error (called here “variance error”), and ii. due to the inadequacy of the polynomial f(ξ) exactly to represent g(ξ) (called here “bias error”). To meet requirement (a) the design is selected so as to minimize J, the expected mean square error averaged over the region R. J contains two components, one associated entirely with varian...
697 citations
"Generalized resolution and minimum ..." refers result in this paper
...Finally, we note that our argument for minimizing biases is similar to that in Box and Draper (1959)....
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471 citations
"Generalized resolution and minimum ..." refers methods in this paper
...For a detailed discussion on the concept of resolution for regular factorials, we refer to Box and Hunter (1961)....
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TL;DR: The 2 k-p Fractional Factorial Designs Part I. as discussed by the authors is a collection of fractional fractional factorial designs with a focus on the construction of the construction.
Abstract: (2000). The 2 k—p Fractional Factorial Designs Part I. Technometrics: Vol. 42, No. 1, pp. 28-47.
449 citations
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
420 citations
"Generalized resolution and minimum ..." refers methods in this paper
...For results on minimum aberration designs, we refer to Fries and Hunter (1980), Franklin (1984), Chen and Wu (1991), Chen (1992), Tang and Wu (1996), Chen and Hedayat (1996) and Cheng, Steinberg and Sun (1999)....
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