Constructing orthogonal fractional factorial designs with the same confounding structure

摘要

ORTHOGONAL arrays (OAs) have important applications to many fields. A lot of OAs and their construction methods have been introduced in the experimental design literature (for example, Box, Hunter and Dey ). These OAs are used for an experimenter to choose in practice. But it often happens that any existing OA is not suitable for a given experiment, i.e. any existing OA contains some infeasible factor-level combinations for the experiment to be executed. In this case, it is necessary to consider a flexible method to generate a suitable OA. Cheng and Li and Wang and Zhang give a necessary and sufficient condition, of existence of OA debarring some infeasible combinations and some construction methods. But these methods need large computation and it is difficult to carry out in practice. It fact, there are many OAs with the same defining relations, but in the existing literature usually only one is given and not debarring the specific infeasible factorlevel combinations. It is possible to find a suitable one from all the OAs with the same defining relations. With this consideration, we can reduce the computations to pick up an OA debarring the infeasible factor-level combinations. This note will give a method of constructing such OAs from all the OAs with the same confounding structure.