A class of response surface split-plot designs

There are many situations in industrial experimentation where departures from the fundamental principles of experimentation-randomization, replication, and local control of error-are commonplace. For instance, complete randomization is not always feasible when factor level settings are hard, impractical, or inconvenient to change, or when the resources available to execute the experiment under homogeneous conditions are limited. These restrictions in randomization lead to split-plot designs. Often, we are also interested in fitting higher-order statistical models, which calls for response surface split-plot designs. In this article we explore the systematic construction of a class of response surface split-plot design we call response surface Cartesian product split-plot designs. This collection of design alternatives offers an effective and efficient addition to the split-plot design repertoire available currently in the engineering, manufacturing, quality control, and test and evaluation communities. These designs are generally competitive in size relative to other standard designs, easy to construct, can be executed sequentially, have good coverage, low prediction variances, minimal aliasing between the model terms, and are suitable for cuboidal and spherical regions of the factor space. When evaluated with well-accepted design evaluation criteria, response surface Cartesian product split-plot designs perform as well as designs that have been standards in the response surface split-plot methodology community such as equivalent estimation designs, minimum whole plot designs, and optimal designs.