D-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor

Oluwole A Nuga,Shobanke Emmanuel Omobola Kayode,Abba Zakirai Abdulhamid

doi:10.5539/ijsp.v11n1p1

Oluwole A Nuga, Shobanke Emmanuel Omobola Kayode + Show 1 more

Open Access

https://doi.org/10.5539/ijsp.v11n1p1

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Abstract

This study examines design preference in Completely Randomized (CR) split-plot experiments involving random whole plot factor effect and fixed sub-plot factor effect. Many previous works on optimally designing split-plot experiments assumed only factors with fixed levels. However, the cases where interests are on random factors have received little attention. These problems have similarities with optimal design of experiments for fixed parameters of non-linear models because the solution rely on the unknown parameters.&nbsp; Design Space (DS) containing exhaustive list of balanced designs for a fixed sample size were compared for optimality using the product of determinants of derived information matrices of the Maximum Likelihood (ML) estimators equivalent to random and fixed effect in the model. Different magnitudes of components of variance configurations where variances of factor effects are larger than variances of error term were empirically used for the comparisons. The results revealed that the D-optimal designs are those with whole plot factor levels greater than replicates within each level of whole plot.

Highlights

1.1 Introduce the ProblemSplit-plot designs are applied when there is restricted randomization of the factor-levels of whole-plots
The first vector on table 2 assumes that 84% of the total variation in observation is accounted for by the variation in the whole-plot factor, while only 6%, 5% and 5% is accounted for by the interaction variance, the whole plot error variance and the sub-plot error variance respectively
The second vector assumes that 46% of the total variation in observation is accounted for by the whole plot factor variance while 44%, 5% and 5% is accounted for by the interaction variance, the whole plot error variance and the sub-plot error variance respectively

Summary

Introduction

1.1 Introduce the ProblemSplit-plot designs are applied when there is restricted randomization of the factor-levels of whole-plots. Computer procedures for constructing D-optimal split-plot design was given by Goos and Vanderbroek (2001, 2003) These algorithms are useful in several experimental situations that allow the combinations of factor levels. The algorithm requires specifying the type of factors, size of the whole-plot, size of the easy-to-change factor, ratio of error variances, model and starting design size The constructions of these entire algorithms were based on the assumptions that factor levels are fixed. Most of the works in this area of research were published in the sixties and seventies and were limited to some certain models These problems have similarities with optimal experimental design for fixed parameters of non-linear models because the solution depends on the magnitude of unknown parameters. The solution depends on the model and the method of estimation

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