MULTI-LEVEL FACTORIAL DESIGNS WITH MINIMUM NUMBERS OF LEVEL CHANGES

Abstract

The order of experimental runs in a fractional factorial experiment is essential when the cost of level changes in factors is considered. The generalized foldover scheme given by [1]gives an optimal order to experimental runs in an experiment with specified defining contrasts. An experiment can be specified by a design requirement such as resolution or estimation of some interactions. To meet such a requirement, we can find several sets of defining contrasts. Applying the generalized foldover scheme to these sets of defining contrasts, we obtain designs with different numbers of level changes and then the design with minimum number of level changes. The difficulty is to find all the sets of defining contrasts. An alternative approach is investigated by [2]for two-level fractional factorial experiments. In this paper, we investigate experiments with all factors in slevels.

Keywords:

• Run order
• Resolution
• Generalized foldover scheme
• Orthogonal arrays

ACKNOWLEDGMENT

The authors are grateful to the referees for many helpful suggestions which improved the presentation of the paper. The research of M. H. Chen and P. C. Wang was supported in part by NSC grant NSC89-2118-M-130-005 and NSC86-2115-M-008-028.