How to Handle Hard-to-Change Factors or Components in a Designed Experiment

By Mark J. Anderson

The traditional approach to experimentation—often referred to as the “scientific method”— requires changing only one factor at a time (OFAT). Unfortunately, the relatively simplistic OFAT approach falls flat when users are faced with factor or component interactions, for example, the combined impact of time and temperature on a process, or two reactants in a mixture. Because inter-actions abound in the coatings industry, the multifactor and multicomponent test matrices provided by the design of experiments (DOE) approach appeal greatly to process engineers and formulators.¹ However, carrying out DOE correctly requires that runs be randomized whenever possible to counteract the bias that may be introduced by time-related trends, such as aging of materials, increasing humidity, and the like.

But what if complete randomization proves to be so inconvenient that it becomes impossible to run a statistically designed experiment? In this case, a specialized form of design called “split plot” becomes attractive, because of its ability to effectively group hard-to-change (HTC) factors.² A split plot accommodates both HTC factors, for instance, the conditions in an electrostatic powder-coating chamber, and those factors that are easy to change (ETC), such as the part precleaning and preparation. Split-plot designs originated in the field of agriculture, where experimenters applied one treatment to a large area of land, called a whole plot, and other treatments to smaller areas of land within the whole plot, called subplots.

For example, Figure 1 shows two alternative experiments that were carried out on six varieties of sugar beets (Number 1 through 6) that were sown either early (E) or late (L) in the growing season:

• A completely randomized design in one field shown on the top row versus
• The bottom row where the whole plot (single field) has been split into two subplots (in this case, sown early vs late)