Related papers: $Q_B$-Optimal Two-Level Designs
We have established the association matrix that expresses the estimator of effects under baseline parameterization, which has been considered in some recent literature, in an equivalent form as a linear combination of estimators of effects…
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…
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…
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…
In this paper we study optimality aspects of a certain type of designs in a multi-way heterogeneity setting. These are ``duals" of plans orthogonal through the block factor (POTB). Here by the dual of a main effect plan (say $\rho$) we mean…
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…
The concept of orthogonality through the block factor (OTB), defined in Bagchi (2010), is extended here to orthogonality through a set (say S) of other factors. We discuss the impact of such an orthogonality on the precision of the…
Follow-up experimental designs are popularly used in industry. In many follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the first…
We improve the existing results of optimal partial profile paired choice designs and provide new designs for situations where the choice set sizes are greater than two. The optimal designs are obtained under the main effects models and the…
The analysis of screening experiments is often done in two stages, starting with factor selection via an analysis under a main effects model. The success of this first stage is influenced by three components: (1) main effect estimators'…
Acquiring information on spatial phenomena can be costly and time-consuming. In this context, to obtain reliable global knowledge, the choice of measurement location is a crucial issue. Space-lling designs are often used to control…
A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are…
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…
Recent researches on designs for computer experiments with both qualitative and quantitative factors have advocated the use of marginally coupled designs. This paper proposes a general method of constructing such designs for which the…
For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are…
Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each…
Row-column factorial designs that provide unconfounded estimation of all main effects and the maximum number of two-factor interactions (2fi's) are called 2fi-optimal. This issue has been paid great attention recently for its wide…
Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis…
Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and…