Abstract
Let D1 and D2 be the same run size 2-level factorial design matrix, respectively, and D1(r) is a design matrix which obtained by D1 through some row permutation r.We merge D1(r) and D2 row-wise and then get a design matrix D(r), called the row-wise merged design. In this work, we transform design matrix D1 and D2 through a similar Yates order conversion. Each design point with a value of the real number line to replace, respectively. Through this transformation, D1 and D2 converted into two vectors V1 and V2, respectively, which dimension equal to the run size of D1 and D2. And V1(r) represents D1(r) conversion after the resulting vector. We can investigate the property of the row-wise merged design D(r) by the sample correlation coefficient between V1(r) and V2. We found that when the strength of D(r) is 2, the sample correlation coefficient of V1(r) and V2 must be 0, and we also generalized this nature such that strength greater than 2. In addition, if D1(r) and D2 more consider the transformation of column permutation, we can develope conditions that the sample correlation coefficient of V1(r) and V2 is equal to 0 if and only if D(r) is a design of strength 2. Finally, we propose a positional notation coefficient selection method that perform a faster way to detect whether the strength of D(r) is 2 than column permutation. Furthermore, we through a combination between V1 and V2 to present a row permutation algorithm that perform a row permutation such that D(r) is strength 2 design.