A Class of Nearly Orthogonal Arrays

Abstract

Orthogonal arrays with mixed levels are very useful in factorial experiments when factors with different numbers of levels are to be investigated. However, one limitation associated with mixed-level orthogonal arrays is that many of them require a large number of runs. In such cases, nearly orthogonal arrays—which generally use fewer runs by slightly relaxing the requirement of orthogonality—may be useful. We propose a definition of nearly orthogonal arrays of strength m, extending the concept of orthogonal arrays of strength m. We focus on the nearly orthogonal arrays involving 2- and 3-level factors with small run sizes. Some useful arrays are tabulated for practical use. These designs are shown to have nice statistical and combinatorial properties.

• Nearly Orthogonal Array of Strength m
• Orthogonal Array
• Strength

Additional information

Notes on contributors

Xuan Lu

Dr. Lu is a Professor in the Department of Mathematical Science. His email address is [email protected].

William Li

Dr. Li is an Associate professor in the Operations and Management Science Department. His email address is [email protected].

Miao Xie

Ms. Xie is a Graduate Student in the Department of Mathematical Science. Her email address is [email protected].