The Construction of Trend-Free Experimental Plans on Two-Level Split-Plot Designs

In most experimental designs, the standard procedure involves randomization of the factor level combination run order. There are cases, however, where it is known that a time or position trend that can seriously compromise the results of the experiment may be present. These trends include wear of tooling and equipment, learning curves, change in temperatures, etc; and may show up as linear, quadratic or even higher order trends. All previously published work [2-9] has dealt with various methods of constructing trend-resistant run order plans on full and fractional factorial designs. The objective of this work is to establish the foundations of a generalized method for constructing linear and quadratic trend-resistant plans in two-level split-plot designs that addresses all dimensions along which these trends may occur. The methodology involves development of a hybrid approach combining the Foldover Method and the Daniel and Wilcoxon (D-W) Method in each of the dimensions of interest and embedding these in a non-linear integer programming model in the search for a feasible solution. Feasibility of this approach is shown for the particular case of a split-plot design (2^sup 5^ whole-plot factors and 3^sup 1^ × 2^sup 1^ split-plot factors) performed on abrasive machining. In this case study, an experimental plan that is robust against all linear trends and most quadratic trends was achieved.