Fractional Factorial Designs That Restrict the Numbers of Treatment Combinations for Factor Subsets

Designs are constructed that limit the number of treatment combinations within subsets of factors. Such designs came to our attention in the context of machine assembly experiments [1,2]. For example, to improve a stepper motor, we plan a 2 design to investigate four rotor factors and a similar 2 design to investigate four stator factors. The product of these two arrays to study the eight factors of these motors would involve 64 combinations. However, a resolution IV design is possible in only 16 treatment combinations. Others have cited the benefits of such design efficiencies for assembly experiments. We propose two methods for constructing restricted subset designs and catalog the possible designs with factors partitioned into two or more subsets. We also suggest alternative applications of these designs and cite related literature.