## The Annals of Statistics

### Orthogonal Arrays with Variable Numbers of Symbols

Ching-Shui Cheng

#### Abstract

Orthogonal arrays with variable numbers of symbols are shown to be universally optimal as fractional factorial designs. The orthogonality of completely regular Youden hyperrectangles ($F$-hyperrectangles) is defined as a generalization of the orthogonality of Latin squares, Latin hypercubes, and $F$-squares. A set of mutually orthogonal $F$-hyperrectangles is seen to be a special kind of orthogonal array with variable numbers of symbols. Theorems on the existence of complete sets of mutually orthogonal $F$-hyperrectangles are established which unify and generalize earlier results on Latin squares, Latin hypercubes, and $F$-squares.

#### Article information

Source
Ann. Statist. Volume 8, Number 2 (1980), 447-453.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176344964

Digital Object Identifier
doi:10.1214/aos/1176344964

Mathematical Reviews number (MathSciNet)
MR560740

Zentralblatt MATH identifier
0431.62048

JSTOR