On the aberrations of mixed level Orthogonal Arrays with removed runs

TL;DR

This paper investigates how removing runs from mixed level Orthogonal Arrays affects their aberrations, providing formulas and methods to identify optimal sub-fractions with minimal aberration.

Contribution

It introduces formulas for computing aberrations of sub-fractions and a simple method to select the best sub-fractions after removing points, applicable to any mixed level Orthogonal Array.

Findings

Formulas for Generalized Word-Length Pattern of sub-fractions.

Methodology to identify best sub-fractions after removing points.

Analysis of the impact of removing 1, 2, or 3 points on aberrations.

Abstract

Given an Orthogonal Array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the deletion of one single point, we provide a simple methodology to find which the best sub-fractions are according to the Generalized Minimum Aberration criterion. We also study the effect of the deletion of 1, 2 or 3 points on some examples. The methodology does not put any restriction on the number of levels of each factor. It follows that any mixed level Orthogonal Array can be considered.