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A polynomial indicator function of designs is first introduced by Fontana, Pistone and Rogantin (2000) for two-level designs. They give the structure of the indicator function of two-level designs, especially from the viewpoints of the…
A polynomial indicator function of designs is first introduced by Fontana {\it et al}. (2000) for two-level cases. They give the structure of the indicator functions, especially the relation to the orthogonality of designs. These results…
In a general fractional factorial design, the $n$-levels of a factor are coded by the $n$-th roots of the unity. This device allows a full generalization to mixed-level designs of the theory of the polynomial indicator function which has…
Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order…
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…
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main…
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…
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…
Suppose several two-valued input-output systems are designed by setting the levels of several controllable factors. For this situation, Taguchi method has proposed to assign the controllable factors to the orthogonal array and use ANOVA…
Factorial designs are widely used in agriculture, engineering, and the social sciences to study the causal effects of several factors simultaneously on a response. The objective of such a design is to estimate all factorial effects 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 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…
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 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…
We consider nonregular fractions of factorial experiments for a class of linear models. These models have a common general mean and main effects, however they may have different 2-factor interactions. Here we assume for simplicity that…
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…
An {\em $m\times n$ row-column factorial design} is an arrangement of the elements of a factorial design into a rectangular array. Such an array is used in experimental design, where the rows and columns can act as blocking factors. If for…
Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let $F = \sum_\alpha b_\alpha X^\alpha$ be the…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when…