Generation of Fractional Factorial Designs

TL;DR

This paper introduces a new methodology combining counting functions, Hilbert basis, and Markov basis to generate all fractional factorial designs satisfying specific orthogonality constraints, including mixed level designs.

Contribution

It develops a comprehensive method for generating fractional factorial designs with mixed levels without restrictions on the number of levels per factor.

Findings

Successfully applied to mixed level orthogonal arrays

Generates all feasible fractional factorial designs under given constraints

Extends existing methods to non-prime and non-prime power level factors

Abstract

The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs, without restrictions on the number of levels of each factor (like primes or power of primes) is studied. This new methodology has been experimented on some significant classes of fractional factorial designs, including mixed level orthogonal arrays.