Optimal Design Theory For Multiple Block Variables

Factorial designs are widely used in experiments. Randomization is one of the fun-damental principles in the design of an experiment. The randomization is based on the homogeneity of the experimental units. Due to the actual conditions and difficulties in con-trolling factors, it is difficult to guarantee the homogeneity of the experimental units, which will lead to the decline of the accuracy of experimental results. Then, peolple often choose the blocked design to run the experiment. Due to the wide range of applications of blocked design in our lives, it is all the time a hot topic in experimental design research field. At present, the investigation on blocked designs in the world is basically focused on those with a single block variable.The Minimum aberration (MA) criterion is a common criterion for selecting optimal designs. The current international research on the optimal blocked designs with multiple block variables under the MA criterion is almost blank. This article mainly studies the optimal theory of the blocked designs with multiple block variables. It first puts forward the effect hierarchy principle of blocked designs with multiple block variables and defines the corresponding word length pattern under the principle. Then it proposes the multiple blocked minimum aberration (MBMA) criterion for blocked designs with multiple block variables. The article mainly studies the construction methods of optimal blocked designs of full designs with two block variables and three block variables under the MBMA criterion.The MBMA designs of these two kinds of designs are constructed theoretically.