Searching for D-Efficient Equivalent-Estimation Second-Order Split-Plot Designs

Abstract

Several industrial experiments are set up using second-order split-plot designs (SPDs). These experiments have two types of factors: whole-plot (WP) factors and subplot (SP) factors. WP factors, also called hard-to-change factors, are factors for which levels are hard or expensive to change. SP factors, also called easy-to-change factors, are factors for which levels are easy or less expensive to change. In a split-plot experiment, the WP factors are confounded with blocks. Certain SPDs possess the equivalent-estimation property. For SPDs with this property, ordinary least-squares estimates of the model parameters are equivalent to the generalized least-squares estimates.This paper describes a fast and simple algorithm that produces D-efficient equivalent-estimation SPDs by interchanging the levels of the SP factors within each WP. The performance of this algorithm is evaluated against the 111 SPD scenarios reported in Macharia and Goos (2010) and Jones and Goos (2012).