Orthogonal Arrays with Variable Numbers of Symbols
Open Access
- 1 March 1980
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 8 (2) , 447-453
- https://doi.org/10.1214/aos/1176344964
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.Keywords
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