A method for construction of mixed‐level fractional designs

Abstract

This research presents a new method to generate near-orthogonal balanced mixed-level fractional designs. The proposed method showed that it is possible to create near-orthogonal balanced fractions of economic size. The method is based in the analysis of the behavior of the genetic algorithm used to generate the efficient arrays (EAs) developed by Guo; a pattern was detected, and this led to the generation of an algorithm capable of constructing fractions in a simple way. These fractions were called near-orthogonal balanced arrays (NOBAs). To analyze the properties of the NOBAs and the capabilities of the proposed method, a series of performance indicators were defined. The NOBAs were compared with the EAs developed by Guo; results are provided.

Quantitative Analysis of the Balance Property in Factorial Experimental Designs 24 to 28

“…Secondly, in a balanced factorial experiment, the effect of each factor can be evaluated independently from other factors [5]. Pantoja et al (2009), point out that balance is an important property because it prevents the main effects and interactions from aliasing with the interception column β 0 [6]. Balance also plays another important role; it leads to a considerable simplification of the calculations [7].…”

“…Orthogonality can be estimated separately and without confusion [27]. In other words, orthogonality ensures that effects can be estimated independently so each column provides different information to the design [6].…”

Alias Structures and Sequential Experimentation for Mixed-Level Designs

“…This difference may not seem significant, but on an industrial level, it could be a competitive advantage. To construct mixed-level fractions, we recommended the approach proposed by [34,35] to produce a near orthogonal balanced design. To achieve more orthogonality, we recommended the use of the sequential experimentation algorithm, presented in Section 5, or D-optimal augmentation.…”

Programa computacional para generar estructuras de alias de diseños factoriales fraccionados de niveles mixtos

“…Se han propuesto diferentes métodos para construir diseños de niveles mixtos, algunos métodos utilizan algoritmos y técnicas complejas de programación. Para una discusión detallada de métodos de construcción, véase Wang & Wu (1991), Wang & Wu (1992), Wang (1996), Nguyen (1996), DeCock & Stufken (2000), Xu (2002), Guo et al (2007) y Pantoja et al (2019). A diferencia de los diseños tradicionales de dos niveles, los diseños fraccionados de niveles mixtos no tienen relación definidora y no se construyen mediante generadores.…”

“…La propiedad de balance se refiere a que cada nivel de un factor se ejecute el mismo número de veces en un experimento, de esta forma se obtiene una distribución uniforme de la información para cada nivel de factor. La ortogonalidad implica la independencia lineal por pares de columnas y es útil para evaluar la importancia del factor (Pantoja et al, 2019). Se han propuesto criterios para evaluar dichas propiedades para diseños de niveles mixtos (Xu & Wu, 2001;Xu, 2002;Xu, 2003;Xu & Deng, 2005;Guo et al, 2007;Guo et al, 2009a).…”