# A-ComVar: A Flexible Extension of Common Variance Design

## TL;DR

This paper introduces A-ComVar, an efficient numerical method for designing experiments with equal variance in estimates of interactions, improving upon traditional common variance designs for factorial experiments.

## Contribution

It proposes A-ComVar, a novel extension of common variance designs, with a computational approach that simplifies finding optimal designs for complex factorial experiments.

## Key findings

- A-ComVar designs achieve more balanced variance estimates.
- The method outperforms exhaustive searches in efficiency.
- A-ComVar designs are competitive with existing popular designs.

## Abstract

We consider nonregular fractions of factorial experiments for a class of linear models. These models have a common general mean and main effects, however they may have different 2-factor interactions. Here we assume for simplicity that 3-factor and higher order interactions are negligible. In the absence of a priori knowledge about which interactions are important, it is reasonable to prefer a design that results in equal variance for the estimates of all interaction effects to aid in model discrimination. Such designs are called common variance designs and can be quite challenging to identify without performing an exhaustive search of possible designs. In this work, we introduce an extension of common variance designs called approximate common variance, or A-ComVar designs. We develop a numerical approach to finding A-ComVar designs that is much more efficient than an exhaustive search. We present the types of A-ComVar designs that can be found for different number of factors, runs, and interactions. We further demonstrate the competitive performance of both common variance and A-ComVar designs using several comparisons to other popular designs in the literature.