Optimal Design of Blocked and Split-Plot Experiments for Fixed Effects and Variance Component Estimation

TY - JOUR

T1 - Optimal Design of Blocked and Split-Plot Experiments for Fixed Effects and Variance Component Estimation

AU - Mylona, Kalliopi

AU - Goos, Peter

AU - Jones , Bradley

PY - 2013/9/20

Y1 - 2013/9/20

N2 - In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. The resulting designs allow for a more powerful statistical inference than traditional optimal designs. In our algorithm for generating optimal blocked and split-plot designs, we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion. Supplementary materials for this article are available online.

AB - In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. The resulting designs allow for a more powerful statistical inference than traditional optimal designs. In our algorithm for generating optimal blocked and split-plot designs, we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion. Supplementary materials for this article are available online.

U2 - 10.1080/00401706.2013.818579

DO - 10.1080/00401706.2013.818579

M3 - Article

SN - 0040-1706

SP - 132

EP - 144

JO - TECHNOMETRICS

JF - TECHNOMETRICS

ER -