Ranking Non-Regular Design
Fractional factorial designs are commonly used in industrial and experiments to iden- tify factors affecting a response or process. The focus of this thesis is on two-level orthogonal designs, however, the methods we consider can be generalized to non- orthogonal designs. Orthogonal designs can be classified into two broad categories: regular designs, which have a simple aliasing structure, in that any two effects are orthogonal or fully aliased; and non-regular designs which have a complex aliasing structure, in that there exist effects that are neither orthogonal nor fully aliased. This thesis focuses on the study of non-regular designs.
In many industrial settings robust parameter designs are performed as a strategy for variance reduction. In these situations the experimenter is mainly interested in the estimation of control-by-noise interactions. For non-regular fractional factorial designs, the goodness of the design can be judged using the generalized aberration criteria. We extend the definitions of generalized aberration to emphasize the control- by-noise interactions. Theoretical results are used to show how one can construct the set of all non-isomorphic multi-factor designs from the existing set of all non- isomorphic designs. We then use the set of all non-isomorphic multi-factor designs to construct a catalog of generalized minimum aberration robust parameter designs.
Next, we focus attention on factorial designs and introduce the projection estimation capacity sequence and use this new criterion to select good non-regular designs. Two theoretical results are presented that will be practically useful when searching for good designs. Based on these results, a simple search procedure is implemented to find such designs. Catalogues of designs are constructed for 20, 24 and 28 runs. Finally, we discuss topics for future research. Firstly, we show how projection estimation capacity can be modified and used to rank robust parameter designs. Secondly, we show how one could use the projection estimation capacity to select follow-up runs in a factorial experiment. The selection of additional runs is briefly discussed and it is shown how one can select follow-up runs to ensure the overall design is orthogonal.
This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact Jason Loeppky (jloeppkystat.sfu.ca) or his supervisor Randy Sitter (sitterstat.sfu.ca).