(M, S)-OPTIMALITY CRITERION FOR REGULAR FRACTIONAL FACTORIAL DESIGNS

Abstract

The performance of (M, S)-optimality criterion on Regular two-level fractional factorial designs (FFD’s) is studied. The criterion has good estimation capacity and easy to compute. In the past, researchers have used (M, S)-optimality criterion on Regular two-level fractional factorial designs up to two factor interactions (2fi’s). This study is the extension of previous work and (M, S)-optimality criterion is used on Regular two-level FFD’s to two factor interactions (2fi’s) as well as three factor interactions (3fi’s). Models for three factor interactions are used to determine maximum trace Cd and minimum trace for the best designs. New formulae for two factor interactions and three factors interactions are developed and used. Two components of the (M, S) criterion, i.e., trace Cd and trace are derived as explicit functions of the numbers of three- and four-letter words. Generally, (M, S)-optimal designs are not Minimum Aberration MA designs but all MA designs up to 64 runs are (M, S)-optimal. Although main effects, 2fi’s and 3fi’s are focused in this study, but the (M, S) criterion is to be used when 3fis or more than three factors are available.

Keywords

• Alias sets
• fractional factorial designs
• minimum aberration
• (M, S)-Optimality
• regular fractional factorial design