Construction of optimal run order in design of experiments

Abstract

It is sometimes favorable to conduct experiments in a systematic run order rather than the conventional random run order. In this article, we propose an algorithm to construct the optimal run order. The algorithm is very flexible: it is applicable to any design and works whenever the optimality criterion can be represented as distance between any two experimental runs. Specifically, the proposed method first formulates the run order problem into a graph, then makes use of the existing traveling salesman problem-solver to obtain the optimal run order. It can always reach the optimal result in an efficient manner.

A special case where level change is used as the distance criterion is investigated thoroughly. The optimal run orders for popular two-level designs are obtained and tabulated for practical use. For higher- or mixed-level designs a generic table is not possible, although the proposed algorithm still works well for finding the optimal run order. Some supporting theoretical results are derived.

Keywords:

• design of experiments
• distance
• level changes
• run order
• traveling salesman problem

About the authors

Mr. Jiayu Peng is a PhD student in the Department of Statistics. His email address is [email protected].

Dr. Dennis K. J. Lin is a distinguished professor in the Department of Statistics. He is a fellow of ASQ. His email address is [email protected].

Acknowledgments

The authors greatly thank the helpful comments by the editor and two anonymous referees. This work was supported by the National Security Agency, via Grant H-98-230-15-1-0253.