Open Access
Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
Lih-Yuan Deng,Boxin Tang +1 more
TLDR
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.read more
Citations
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Minimum moment aberration for nonregular designs and supersaturated designs
TL;DR: In this paper, a new combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs, which is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2).
Journal ArticleDOI
Uniform designs limit aliasing
Fred J. Hickernell,Min-Qian Liu +1 more
TL;DR: In this article, it is shown that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together, while robust experimental designs guard against inaccurate estimates caused by model misspecification.
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An Algorithm for Constructing Orthogonal and Nearly Orthogonal Arrays with Mixed Levels and Small Runs
TL;DR: This article describes a simple and effective algorithm for constructing mixed-level orthogonal and nearly-orthogonal arrays that can construct a variety of small-run designs with good statistical properties efficiently.
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A quality by design (QbD) case study on liposomes containing hydrophilic API: II. Screening of critical variables, and establishment of design space at laboratory scale.
TL;DR: Two statistical designs were used in this case study as part of an investigation into the feasibility and the advantages of applying QbD concepts to liposome-based complex parenteral controlled release systems containing a hydrophilic active pharmaceutical ingredient (API).
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Indicator function and its application in two-level factorial designs
TL;DR: In this paper, a polynomial indicator function is used to generalize the aberration criterion of a regular two-level fractional factorial design to all 2-level factorial designs and an important identity of generalized aberration is proved.
References
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Journal ArticleDOI
Some Results on $s^{n-k}$ Fractional Factorial Designs with Minimum Aberration or Optimal Moments
Jiahua Chen,C. F. J. Wu +1 more
TL;DR: In this paper, it was shown that the resolution criterion and the minimum aberration criterion have a periodicity property in fractional factorial designs for any fixed n = 3, 4, and any n ≥ 4.
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Saturated Fractions of 2 n and 3 n Factorial Designs
TL;DR: In this article, saturated fractions of 2 n and 3 n factorial designs which permit the estimation of both main effects and first order interactions are described, and a simple method of generating these particular designs is given.
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Balanced Optimal 2m Fractional Factorial Designs of Resolution V, m ? 6
J. N. Srivastava,D. V. Chopra +1 more
TL;DR: In this article, balanced optimal fractional factorial designs of 2 m series which allow the estimation of the general mean, main effects and two factor interactions are described, and covariance matrices of the estimates of the effects are also presented for each design.
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Some Results on $2^{n - k}$ Fractional Factorial Designs and Search for Minimum Aberration Designs
TL;DR: In this paper, an upper bound for the length of the longest word in the defining contrasts subgroup is given for fractional factorial designs with minimum aberration for any n = 5.