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

Several industrial experiments are set up using second-order splitplot designs (SPDs). These experiments have two types of factors: whole-plot (WP) factors and sub-plot (SP) factors. WP factors, also called hard-to-change factors are factors whose levels are hard or expensive to change. SP factors, also called easy-to-change factors are factors whose levels are easy or less expensive to change. In a splitplot 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 which produce 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 & Goos (2010) and Jones & Goos (2012).