The joint use of counting functions, Hilbert basis, and Markov basis allows to define a procedure to generate all the fractional factorial designs that satisfy a given set of constraints in terms of orthogonality [Fontana, Pistone and Rogantin (JSPI, 2000), Pistone and Rogantin (JSPI, 2008)]. The general case of mixed level designs without restrictions on the number of levels of each factor (such as power of prime number) is studied. The generation problem is reduced to finding positive integer solutions of a linear system of equations [e.g., Carlini and Pistone (JSTP, 2007)]. This new methodology has been experimented on some significant classes of fractional factorial designs, including mixed level orthogonal arrays and sudoku designs [Fontana and Rogantin in Algebraic and Geometric Methods in Statistics, CUP (2009)]. For smaller cases the complete generating set of all the solutions can be computed. For larger cases we resort to the random generation of a sample solution.

Algebraic Generation of Orthogonal Fractional Factorial Designs / Fontana R.; Pistone G.. - STAMPA. - (2013), pp. 61-71.

Algebraic Generation of Orthogonal Fractional Factorial Designs

FONTANA, ROBERTO;PISTONE, Giovanni
2013

Abstract

The joint use of counting functions, Hilbert basis, and Markov basis allows to define a procedure to generate all the fractional factorial designs that satisfy a given set of constraints in terms of orthogonality [Fontana, Pistone and Rogantin (JSPI, 2000), Pistone and Rogantin (JSPI, 2008)]. The general case of mixed level designs without restrictions on the number of levels of each factor (such as power of prime number) is studied. The generation problem is reduced to finding positive integer solutions of a linear system of equations [e.g., Carlini and Pistone (JSTP, 2007)]. This new methodology has been experimented on some significant classes of fractional factorial designs, including mixed level orthogonal arrays and sudoku designs [Fontana and Rogantin in Algebraic and Geometric Methods in Statistics, CUP (2009)]. For smaller cases the complete generating set of all the solutions can be computed. For larger cases we resort to the random generation of a sample solution.
9783642355875
Advances in Theoretical and Applied Statistics
File in questo prodotto:
File Dimensione Formato  
cap7_rev0.pdf

non disponibili

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 255.41 kB
Formato Adobe PDF
255.41 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2509921
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo