Minimum Aberration Regular Two-Level Designs in the Presence of Dispersion Factors

Abstract

In practice, the variance of the response variable may change as some specific factors change from one setting to another in a factorial experiment. These factors affecting the variation of the response are called dispersion factors, which can violate the usual assumption of variance homogeneity. In this study, we modify the conventional minimum aberration criterion to take the impact of dispersion factors into account. The situations of one or two dispersion factors are investigated. As a result, we present regular 2^{n − p} designs with run sizes equal to 16 and 32 using the modified minimum aberration criterion.

Keywords:

• Fractional factorial design
• Dispersion effect
• Location effect
• Optimal design

Mathematics Subject Classification:

• Primary 62K15; Secondary 62K05