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Related papers: Uniform fractional factorial designs

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The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…

Statistics Theory · Mathematics 2011-05-16 Runchu Zhang , Frederick K. H. Phoa , Rahul Mukerjee , Hongquan Xu

We develop $D$-optimal designs for linear models with first-order interactions on a subset of the $2^K$ full factorial design region, when both the number of factors set to the higher level and the number of factors set to the lower level…

Statistics Theory · Mathematics 2019-05-14 Fritjof Freise , Rainer Schwabe

Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have been commonly used for obtaining optimal designs. For a given statistical model, standard criteria assume the error variance is known at the design stage. However, in…

Methodology · Statistics 2017-01-27 Md. Shaddam Hossain Bagmar , Wasimul Bari , A. H. M. Mahbub Latif

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…

Statistics Theory · Mathematics 2013-12-19 Rahul Mukerjee , Boxin Tang

In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We focus on the notion of regular fraction and we introduce methods to check whether a given symmetric orthogonal array can…

Methodology · Statistics 2017-05-04 Fabio Rapallo , Maria Piera Rogantin

Tang and Xu [Biometrika 101 (2014) 333-350] applied the minimum $\beta$-aberration criterion to selecting optimal designs for screening quantitative factors. They provided a statistical justification showing that minimum $\beta$-aberration…

Statistics Theory · Mathematics 2014-09-04 Po Yang , Chang-Yun Lin

Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean…

Statistics Theory · Mathematics 2026-03-05 Douglas P. Wiens

We develop $D$-optimal designs for linear main effects models on a subset of the $2^K$ full factorial design region, when the number of factors set to the higher level is bounded. It turns out that in the case of narrow margins only those…

Statistics Theory · Mathematics 2019-07-08 Fritjof Freise , Heinz Holling , Rainer Schwabe

Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribution function is one such transformation. The discrepancy is…

Computation · Statistics 2026-05-12 Yiou Li , Lulu Kang , Fred J. Hickernell

Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs…

Methodology · Statistics 2019-09-25 Neil A. Spencer , Pritam Ranjan , Franklin Mendivil

Given an Orthogonal Array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the…

Statistics Theory · Mathematics 2018-09-12 Roberto Fontana , Fabio Rapallo

Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…

Methodology · Statistics 2018-02-21 Maria Umlauft

A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine…

Methodology · Statistics 2009-07-22 Satoshi Aoki , Akimichi Takemura

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and…

Statistics Theory · Mathematics 2007-06-13 Hongquan Xu , C. F. J. Wu

In this paper we make a first attempt at understanding how to build an optimal approximate normal factor analysis model. The criterion we have chosen to evaluate the distance between different models is the I-divergence between the…

Probability · Mathematics 2023-02-27 Lorenzo Finesso , Peter Spreij

Given a two-level regular fractional factorial design of resolution IV, the method of doubling produces another design of resolution IV which doubles both the run size and the number of factors of the initial design. On the other hand, the…

Statistics Theory · Mathematics 2007-06-13 Hegang H. Chen , Ching-Shui Cheng

We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each with binary response. Our focus is primarily on the 2^2 experiment. In this paper, we derive analytic…

Methodology · Statistics 2015-03-13 Abhyuday Mandal , Jie Yang , Dibyen Majumdar

Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…

Networking and Internet Architecture · Computer Science 2018-04-24 Bestoun S. Ahmed , Amin S. Mohammad , Hemin T. Essa

We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the…

Applications · Statistics 2008-12-18 Tathagata Banerjee , Rahul Mukerjee

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Statistics Theory · Mathematics 2022-02-17 Jack Noonan , Anatoly Zhigljavsky