Using JMP Pro 12 to Investigate Designs Produced by the DOE Custom Design Platform
Mark Johnson, Professor of Statistics, University of Central Florida
Tokyo University of Science, Faculty of Science and Technology, Department of Industrial Engineering and Management
The JMP Pro12 DOE custom design platform can generate 27 different 16-run two-level fractional factorial designs. This presentation uses JMP to explore the properties of various designs and provides some JSL scripts to facilitate their analysis. One of these properties concerns the space spanned by vectors of all main effects and two-factor interactions in a given design (i.e., vectors I, A, B, ..., F, AB, AC, ..., EF). Somewhat surprisingly, the "gold standard" Resolution IV design (generators E=ABC, F=BCD) spans only 14 dimensions of the space out of a maximum of 16. This deficiency means that the gold standard design is unable to model some response vectors (specifically, in this case, in the space spanned by vectors ABD and ACD). In contrast, the "inferior" Resolution III design based on generators E = AB and F = CD can span the 16-dimensional space of possible response vectors, making it superior to the gold standard in certain circumstances. Some of the nonregular designs among the 27 possible custom designs also satisfy the full dimensionality potential with properties of other designs (E(s2) and trace(AA')), as pointed out by Lou Johnson and Anderson Cook (Quality Engineering, 2014). For example, generators E = ABC and F = 1/2 [CD + ACD + BCD - ABCD] span a 16-dimensional space. When examining the nonregular designs generated from the custom designs, it is important to identify all factorial projection designs from the main effects columns. A JSL script is presented to facilitate this effort. It will be shown that the spanning property deficiency also occurs in the Resolution V design with 32 runs.
