J2 optimality and Multi-level Minimum Aberration Criteria in fractional factorial design

Abstract

The desirable properties of fractional factorial design: Balance and orthogonal; was examined for near balance and near orthogonal using the balance coefficient and J₂ optimality criteria respectively. Efficient orthogonal arrays with three factors having two, three and four levels were constructed with balance and orthogonal property for lowest common multiples of runs. The two forms of balance coefficient were used for classifying the designs into two and multi level minimum aberration criteria were used to determine designs with lesser aberration. It was observed that designs constructed using the maximum form of balance coefficient has the lesser aberration in both the generalized minimum aberration and minimum moment aberration criteria. The J₂ – optimality criterion reveals that the higher the run of a design, the lesser it’s optimality value.

Keywords: Balance Coefficient, fractional factorial, Generalized Minimum Aberration (GMA), J₂ optimality and Minimum Moment Aberration (MMA).