Optimal Design of a Two-Block Experiment Using Contrasts of a Four-Level Categorical Factor

• Activity Number: 78
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Greg Piepel*+ and Joe Westsik, Jr. and Alex Cozzi and Dave Swanberg
• Companies: Pacific Northwest National Laboratory and Pacific Northwest National Laboratory and Savannah River National Laboratory and Washington River Protection Solutions
• Keywords: Optimal design ; Blocking ; Categorical factors ; Contrasts ; Four-level factor

Abstract

The optimal design of an experiment in two blocks is presented for an application involving four two-level factors (two of which are categorical) and a four-level categorical factor. The goal was to screen the factors, hopefully to reduce the number of levels of the four-level categorical factor and to choose a level of at least one of the two-level categorical factors. The screening experiment was designed in two blocks in case funding was not available for the second block. The first block was designed to assess the main effects of the five factors. The second block was designed to augment the first block to provide for assessing selected two-factor interactions thought to be more likely to exist by subject-matter experts. Specific hypotheses of interest for the four-level factor were expressed as contrasts, with only some of the contrasts involved in the selected interactions. Main effects and main effects-plus-interactions models were specified and used in constructing the two-block optimal experimental design, which involved some challenges because of the 4-level categorical factor and the use of contrasts.