Two-Level Multifactor Designs for Detecting the Presence of Interactions

Abstract

A design optimality criterion, tr (L)-optimality, is applied to the problem of designing two-level multifactor experiments to detect the presence of interactions among the controlled variables. We give rules for constructing tr (L)-optimal foldover designs and tr (L)-optimal fractional factorial designs. Some results are given on the power of these designs for testing the hypothesis that there are no two-factor interactions. Augmentation of the tr (L)-optimal designs produces designs that achieve a compromise between the criteria of D-optimality (for parameter estimation in a first-order model) and tr (L)-optimality (for detecting lack of fit). We give an example to demonstrate an application to the sensitivity analysis of a computer model.

KEY WORDS:

• Compromise design
• D-optimality
• Experimental design
• First order design
• Foldover design
• Fractional factorial design
• Main effects design
• Minimum aberration
• Optimal design
• Orthogonal array
• Resolution IV design
• Screening design
• Sensitivity analysis
• Tr (L)-optimality