Related papers: Recent Developments in Nonregular Fractional Facto…
Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the…
The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of…
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical…
We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and…
$2^K$ factorial designs are widely adopted by statisticians and the broader scientific community. In this short note, under the potential outcomes framework (Neyman, 1923; Rubin, 1974), we adopt the partial identification approach and…
Two-level factorial designs are widely used in industrial experiments. For processes involving \(n\) factors, the construction of designs comprising \(2^n\) and \(2^{n-p}\) factorials, arranged in blocks of size \(2^q\) is investigated. The…
We consider the design and analysis of multi-factor experiments using fractional factorial and incomplete designs within the potential outcome framework. These designs are particularly useful when limited resources make running a full…
Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…
This paper considers the construction of minimum aberration (MA) blocked factorial designs. Based on coding theory, the concept of minimum moment aberration due to Xu [Statist. Sinica 13 (2003) 691--708] for unblocked designs is extended to…
For unstructured experimental units, the minimum aberration due to Fries and Hunter (1980) is a popular criterion for choosing regular fractional factorial designs. Following which, many related studies have focused on multi-stratum…
We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and…
The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses…
Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
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…
Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment…
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…
In medical research, a scenario often entertained is randomized controlled $2^2$ factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. (2015) proposed a randomization-based causal inference…
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…
Chen and Cheng [Ann. Statist. 34 (2006) 546--558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for $9N/32\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$…