Orthogonal Arrays: A Review

TL;DR

Orthogonal arrays are vital statistical tools with rich mathematical foundations, extensively used across industries and increasingly applied in modern fields like AI and big data for efficient data collection and experimental design.

Contribution

This paper provides a comprehensive review of orthogonal arrays, covering fundamental concepts, recent developments, and their diverse applications across multiple disciplines.

Findings

Detailed overview of orthogonal arrays' properties and theory

Recent applications in computer experiments and AI

Connections with combinatorics and error-correcting codes

Abstract

Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and beautiful mathematical theory. Their connections with combinatorics, finite fields, geometry, and error-correcting codes are profound. Orthogonal arrays have been widely used in agriculture, engineering, manufacturing, and high-technology industries for quality and productivity improvement experiments. In recent years, they have drawn rapidly growing interest from various fields such as computer experiments, integration, visualization, optimization, big data, machine learning/artificial intelligence through successful applications in those fields. We review the fundamental concepts and statistical properties and report recent developments. Discussions of recent applications and connections with various fields are presented.