In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We code the s levels of a factor with the s-th roots of the unity. We focus on the notion of regular fraction in the complex coding, called C-regularity. We introduce methods to check whether a given symmetric orthogonal array can or cannot be transformed into a regular fraction by means of suitable permutations of the factor levels. The proposed techniques take advantage of the complex coding of the factor levels and of some tools from polynomial algebra. Several examples are described, mainly involving factors with five levels.
Algebraic Characterization of C-Regular Fractions Under Level Permutations
Maria Piera Rogantin;Fabio Rapallo
2019-01-01
Abstract
In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We code the s levels of a factor with the s-th roots of the unity. We focus on the notion of regular fraction in the complex coding, called C-regularity. We introduce methods to check whether a given symmetric orthogonal array can or cannot be transformed into a regular fraction by means of suitable permutations of the factor levels. The proposed techniques take advantage of the complex coding of the factor levels and of some tools from polynomial algebra. Several examples are described, mainly involving factors with five levels.File | Dimensione | Formato | |
---|---|---|---|
Rapallo-Rogantin2018_Article_AlgebraicCharacterizationOfMat.pdf
accesso chiuso
Tipologia:
Documento in versione editoriale
Dimensione
1.19 MB
Formato
Adobe PDF
|
1.19 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.