Design of Experiments for Screening

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 of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Regression Models and Experimental Designs: A Tutorial for Simulation Analaysts

This tutorial explains the basics of linear regression models. especially low-order polynomials. and the corresponding statistical designs. namely, designs of resolution III, IV, V, and Central Composite Designs (CCDs).This tutorial assumes 'white noise', which means that the residuals of the fitted linear regression model are normally, independently, and identically distributed with zero mean.The tutorial gathers statistical results that are scattered throughout the literature on mathematical statistics, and presents these results in a form that is understandable to simulation analysts.metamodels;fractional factorial designs;Plackett-Burman designs;factor interactions;validation;cross-validation

Application of flexible recipes for model building, batch process optimization and control

Unlike the traditionally fixed recipes in batch process operation, flexible recipes allow the adjustment of some of its relevant recipe items. These adjustments can either be predefined in cases of planned experimentation, or suggested by a formal process optimization or control algorithm on the basis of actual information. In both the response surface methodology and the simplex evolutionary operation (EVOP), some well-known methods for empirical model building and process optimization, flexible recipes are involved. Another application of flexible recipes arises in a feedforward quality control strategy of batch processes when variations in market or process conditions are known a priori. The experimental results of these strategies are presented for the batchwise production of benzylalcohol on a pilotplant scale. Experiments have been performed to obtain a reliable model of the yield. On the basis of this model, better process conditions have been suggested, which substantially deviate from the final simplex resulted from experiments within simplex EVOP. Finally, an adaptive feedforward control strategy has been applied for a priori known disturbances in the process inputs

A response surface approach to noise optimization of engine structures

The work presented within this thesis concerns the optimization of finite element models of engine structures to reduce radiated noise. For many engineering problems, current methods of structural optimization provide an efficient means by which to identify an optimum design, subject to a set of imposed bounds and constraints. They do not, however, have the flexibility to carry out efficient investigation of a range of different constraint criteria, and this is often a requirement of a noise optimization study. In order to address this restriction, an alternative method of noise optimization is developed, which is based on the techniques of experimental design theory and response, surface methodology. The main feature of this approach is that values of the response functions of interest are calculated at a number of selected points Within the design variable space, from which an approximating mathematical model is generated. It is this analytical model of the original responses which is used as the basis of the optimization procedure. Experimental design theory is employed in order to ensure that a sufficiently accurate model can be generated With the minimum number of function evaluations. A number of competing experimental designs and mathematical models are considered, and numerical trials are carried out to evaluate their performance in representing the noise function. A quadratic model is found to perform well throughout the design region, and can be estimated efficiently using a particular class of economic second-order designs. A number of detailed noise optimization studies are presented, involving up to seven design variables, which illustrate the ways in which the requirements of the noise optimization problem can be met using the response surface approach

Experiments : design, parametric and nonparametric analysis, and selection

Some general remarks for experimental designs are made. The general statistical methodology of analysis for some special designs is considered. Statistical tests for some specific designs under Normality assumption are indicated. Moreover, nonparametric statistical analyses for some special designs are given. The method of determining the number of observations needed in an experiment is considered in the Normal as well as in the nonparametric situation. Finally, the special topic of designing an experiment in order to select the best out of k(\geq 2) treatments is considered

Practical inference from industrial split-plot designs.

Many industrial response surface experiments are deliberately not conducted in a completely randomized fashion. This is because some of the factors investigated in the experiment are hard to change. The resulting experimental design then is of the split-plot type and the observations in the experiment are in many cases correlated. A proper analysis of the experimental data therefore is a mixed model analysis involving generalized least squares estimation. Many people, however, analyze the data as if the experiment was completely randomized, and estimate the model using ordinary least squares. The purpose of the present paper is to quantify the differences in conclusions reached from the two methods of analysis and to provide the reader with guidance for analyzing split-plot experiments in practice. The problem of choosing the number of degrees of freedom for significance tests in the mixed model analysis is discussed as well.Containment method; Data; Design; Experimental design; Factors; Fashion; Generalized least squares; Least-squares; Method of Kenward and Roger; Methods; Model; Ordinary least squares; Residual method; Satterthwaite's method; Split-plot experiment; Squares;

A VON LIEBIG MODEL FOR WATER AND NITROGEN CROP RESPONSE

The century-old “law of the minimum” proposed by von Liebig was tested using five independent sets of crop response data on wheat, corn, cotton, silage, and sugar beets. The rival models were polynomial functions reported in the literature as the most suitable models for interpreting those data. Overall, the von Liebig model performed very well. While the nonnested hypothesis test was inconclusive with regard to silage and sugar beets, the von Liebig model rejected the polynomial specifications for wheat, corn and cotton.Crop Production/Industries,