Equitable $(d,m)$-edge designs

TL;DR

This paper develops systematic procedures for creating equitable $(d,m)$-edge designs, enabling better classification of input factors in multivariate functions through polynomial-based hypercube subgraph representations.

Contribution

It introduces constructive methods to complete clustered designs for any number of factors, enhancing the analysis of function derivatives and their behaviors.

Findings

Designs can be generated systematically for arbitrary factors.

Verification of design properties is formalized via polynomial representations.

Enhanced discrimination in classifying input factors is achievable.

Abstract

The paper addresses design of experiments for classifying the input factors of a multi-variate function into negligible, linear and other (non-linear/interaction) factors. We give constructive procedures for completing the definition of the clustered designs proposed Morris 1991, that become defined for arbitrary number of input factors and desired clusters' multiplicity. Our work is based on a representation of subgraphs of the hyper-cube by polynomials that allows the formal verification of the designs' properties. Ability to generate these designs in a systematic manner opens new perspectives for the characterisation of the behaviour of the function's derivatives over the input space that may offer increased discrimination.