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.
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01 Jan 2013
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2 citations
TL;DR: A variety of designs are included, such as the definitive screening designs and designs from weighing matrices, and their performance is presented in tables.
Abstract: In this paper, the properties of three-level screening designs are studied. A variety of designs are included, such as the definitive screening designs and designs from weighing matrices. These are...
2 citations
Cites background from "Generalized resolution and minimum ..."
...Deng and Tang (1999) and Tang and Deng (1999) studied Plackett-Burman and other non-regular factorial designs....
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TL;DR: In this article, a generalized wordlength pattern (GWLP) is used as the base of the AENP and the GMC criterion for non-regular orthogonal designs.
Abstract: In this paper, we extend the AENP and the GMC criterion proposed by Zhang et al. (2008) to the case of nonregular orthogonal designs. A G-AENP and correspondingly a G-GMC criterion are proposed. The confounding frequency vector (CFV) and the generalized wordlength pattern (GWLP), as the base of MGA and GMA criteria, are shown to be functions of the G-AENP. Some optimal properties of G-GMC designs are obtained. At the last, we give an efficient algorithm for finding optimal designs and tabulate some G-GMC designs with 16- and 18-run for application and comparison with GMA and MGA designs.
2 citations
Dissertation•
01 Jan 2009
TL;DR: A computational algorithm is developed based on theoretical results from Tang and Zhou (2009) for finding optimal orthogonal arrays for estimating main effects and some specified two-factor interactions and a useful collection of optimal orthogsonal arrays with small run sizes is presented.
Abstract: We consider the problem of finding optimal orthogonal arrays for estimating main effects and some specified two-factor interactions. Based on theoretical results from Tang and Zhou (2009), we develop a computational algorithm for this purpose. The D-efficiency and bias are considered as the criteria for design optimality. The performance of the algorithm is evaluated by comparing the results obtained by the algorithm with those from complete search. Finally, we present a useful collection of optimal orthogonal arrays with small run sizes.
2 citations
Additional excerpts
...34 8 2(a) II {1,2,3,4,6,7,8,9} (6,9) (7,8) 0....
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...94 2(b) II {1, 2, 3, 4, 15, 16, 17, 18, 19} (5,6) (5,7) 0....
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...08 2(b) II {5,6,7,8,9,10,11,12,13} (5,6) (5,7) 0....
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...12 9 2(a) II {5,6,7,8,9,10,11,12,13} (5,6) (10,12) 0....
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...62 10 II {1, 2, 3, 4, 15, 16, 17, 18, 19} (5,6) 0....
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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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