On the Analysis of Balanced Two-Level Factorial Whole-Plot Saturated Split-Plot Designs

This paper considers an experimentation strategy when resource constraints permit only a single design replicate per time interval, and one or more design variables are hard-to-change. The experimental designs considered are two-level full or fractional factorial designs run as balanced split-plots. These designs are common in practice and appropriate for fitting a main effects plus interactions model, while minimizing the number of times the whole-plot treatment combination is changed. Depending on the postulated model, single replicates of these designs can result in the inability to estimate error at the whole-plot level, suggesting formal statistical hypothesis testing on the whole-plot effects is not possible. We refer to these designs as balanced two-level whole-plot saturated split-plot designs. In this paper we show that, for these designs, it is appropriate to use ordinary least squares (OLS) to analyze the subplot factor effects at the “intermittent” stage of the experiments (i.e., after a single design replicate is run); however, formal inference on the whole-plot effects may or may not be possible at this point. We exploit the sensitivity of OLS in detecting whole-plot effects in a split-plot design and propose a data-based strategy for determining whether to run an additional replicate following the intermittent analysis, or whether to simply reduce the model at the whole-plot level to facilitate testing. The performance of the proposed strategy is assessed using Monte Carlo simulation. The method is then illustrated using wind tunnel test data obtained from a NASCAR Winston Cup Chevrolet Monte Carlo stock car.