The D-optimal design of blocked and split-plot experiments with mixture components.

So far, the optimal design of blocked and split-plot experiments involving mixture components has received scant attention. In this paper, an easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. It is also shown that orthogonally blocked mixture experiments are highly inefficient compared to D-optimal designs. Finally, the design of a split-plot mixture experiment with process variables is discussed.Design; Fixed and random blocks; Minimum support design; Mixture experiment; Optimal; Optimal design; Orthogonal blocking; Process variables; Processes; Qualitative variables; Split-plot experiment; Variables;

Incomplete split-plots in variety trials - based on a-designs

Incomplete split-plots based on a-designs are proposed as alternative to traditional split-plot designs. The purpose of the incomplete split-plot designs is to increase the efficiency of the treatment (whole plot factor) comparisons especially for specific varieties. The designs are constructed in 4 different methods, but in all methods the unit for the treatments are the incomplete blocks (in stead of whole plots with all varieties in traditional split-plots). The designs are compared with each other and with traditional split-plot and randomised complete block designs using generated data with known covariance structure and using data from 5 uniformity trials. The comparisons showed that these designs in almost all cases were more efficient than the traditional designs and that they were never considerably less efficient that these. Designs where the incomplete blocks are grouped so that each group contain all treatments (one incomplete block with each treatment) were more efficient that when the incomplete blocks were randomised independently (in one step)

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;

Split-plot designs: What, why, and how

The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications

How to establish a perennial legume-grass sward?

In 2002, a field experiment with split-plot design was established in Juva in order to compare the use of nurse crop to establish perennial legume grass sward in organic farming

Incomplete Data in Split-Plot, Split-Block, and Other Similar Designs

15 pages, 1 article*Incomplete Data in Split-Plot, Split-Block, and Other Similar Designs* (Federer, W. T.) 15 page