Three-level Factorials Research Articles

A Three-Level Factorial Model for Maximising Protein Extraction from Rice Bran with Choline Chloride: Glycerol

A Three-Level Factorial Model for Maximising Protein Extraction from Rice Bran with Choline Chloride: Glycerol

Optimal fractions of three-level factorials under a baseline parameterization

The paper proposes the minimum aberration (MA) criterion for three-level designs under a baseline parameterization. An algorithm is put forward to search the MA designs. A catalogue of MA 18-run and 27-run three-level baseline designs is tabulated.

Uniformity pattern of mixed two- and three-level factorials under average projection mixture discrepancy

The issue of the projection uniformity of mixed two- and three-level factorials measured by mixture discrepancy is investigated in this paper. The average projection mixture discrepancy is defined to measure the uniformity for low-dimensions projection designs. Moreover, the relationship between uniformity pattern and generalized minimum aberration is established. Two numerical examples are provided to illustrate the theoretical results.

A new extension strategy on three-level factorials under wrap-around L2-discrepancy

ABSTRACTSequential experiment is an indispensable strategy and is applied immensely to various fields of science and engineering. In such experiments, it is desirable that a given design should retain the properties as much as possible when few runs are added to it. The designs based on sequential experiment strategy are called extended designs. In this paper, we have studied theoretical properties of such experimental strategies using uniformity measure. We have also derived a lower bound of extended designs under wrap-around L2-discrepancy measure. Moreover, we have provided an algorithm to construct uniform (or nearly uniform) extended designs. For ease of understanding, some examples are also presented and a lot of sequential strategies for a 27-run original design are tabulated for practice.

A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

The objective of this article is to study the issue of employing the uniformity criterion measured by wrap-around L2-discrepancy to assess the optimal foldover plans. For mixed two- and three-level fractional factorials as the original designs, general foldover plan and combined design under a foldover plan are defined, and the equivalence between any foldover plan and its complementary foldover plan is investigated. A lower bound of wrap-around L2-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Properties of gypsum composites containing vermiculite and polypropylene fibers: Numerical and experimental results

We have added expanded vermiculite and polypropylene fibers with low thermal conductivity to lightweight gypsum. Thermal conductivity of the composites decreases on addition of vermiculite as pore-maker. Physical and mechanical properties of the composites are improved by incorporating polypropylene fibers. A nonlinear finite element model of a three point bending model and a design of experiments analysis have been developed to evaluate and optimize the additive concentrations and also to understand the effects provided by the additives on the mechanical strength. Statistical response surface method with three-level factorial was employed to evaluate the effect of addition of vermiculite and polypropylene fibers on gypsum composites. Our methodology can be applied to other nonlinear materials for property optimization.

A Lower Bound for the Centered L 2-Discrepancy on Asymmetric Factorials and its Application

The role of uniformity measured by the centered L2-discrepancy (Hickernell 1998a) has been studied in fractional factorial designs. The issue of a lower bound for the centered L2-discrepancy is crucial in the construction of uniform designs. Fang and Mukerjee (2000) and Fang et al. (2002, 2003b) derived lower bounds for fractions of two- and three-level factorials. In this paper we report some new lower bounds for the centered L2-discrepancy for a set of asymmetric fraction factorials. Using these lower bounds helps to measure uniformity of a given design. In addition, as an application of these lower bounds, we propose a method to construct uniform designs or nearly uniform designs with asymmetric factorials.

Bayes Optimal Designs for Two- and Three-Level Factorial Experiments

Abstract Two- and three-level factorial designs are often used for exploratory experiments with many independent variables. The purpose of such experiments is to estimate the effects of all active independent variables and their interactions. For reasons of economy or other constraints, only a fraction of the full number of experimental settings of the independent variables may be run, precluding the separate data-based estimation of all the effects. In this situation of relatively sparse data and many unknown parameters, the benefits of reliable prior information, used in the estimation and experimental design, can be especially significant. In this article, exact Bayes-optimal designs of two- and three-level fractional factorial experiments and of blocked two- and three-level factorial experiments are derived. The optimality criteria used in this process are versions of the Bayes ψ criterion introduced by Duncan and DeGroot. It is shown that the classical fractional factorial designs for the 2k experime...

Bayes Optimal Designs for Two- and Three-Level Factorial Experiments

Abstract Two- and three-level factorial designs are often used for exploratory experiments with many independent variables. The purpose of such experiments is to estimate the effects of all active independent variables and their interactions. For reasons of economy or other constraints, only a fraction of the full number of experimental settings of the independent variables may be run, precluding the separate data-based estimation of all the effects. In this situation of relatively sparse data and many unknown parameters, the benefits of reliable prior information, used in the estimation and experimental design, can be especially significant. In this article, exact Bayes-optimal designs of two- and three-level fractional factorial experiments and of blocked two- and three-level factorial experiments are derived. The optimality criteria used in this process are versions of the Bayes ψ criterion introduced by Duncan and DeGroot. It is shown that the classical fractional factorial designs for the 2k experiment are usually optimal, whereas those for the 3k experiment are not. Further, the classical blocked 2k and 3k designs are Bayes ψ optimal.