QPRC 2016

Design and Analysis of Order-of-Addition Experiments

Joseph G. Voelkel
Rochester Institute of Technology

The order in which components are added in a chemical batch, film, food product, or a study of protein transport may be a primary consideration in an experiment, especially in its earliest stages.

Little work has been done for the design of such order-of-addition (OofA) experiments. We define a reference standard of OofA experiments by extending the idea of orthogonal arrays. For strength 2 designs, upon which we focus most of our attention, we find that OofA orthogonal arrays require N = 0 mod 12 runs when the number m of components exceeds 3. We consider a chi-square criterion to measure the balance of an OofA array, and show that for strength 2 designs, OofA OA’s (corresponding to chi-suqare = 0) are essentially equivalent to D-optimal designs (using a special set of columns in the model matrix). In many situations, a number of non-isomorphic designs exist; in such cases we use a Hamming-distance criterion among the rows of the design as a finer measure of its quality. We then extend these optimal OofA designs to incorporate standard process variables as well so that, for example, temperature or mixing speeds may be included. Our methods can also take into account natural restrictions that the experimenter may have, such as requiring that one component is always added before another. Our main emphasis is on the design of OofA experiments, but we also provide suggestions and examples for analysis.