EVALUACIÓN DE LAS FRACCIONES DEL MÉTODO NOBA CONTRA EL FACTORIAL COMPLETO MEDIANTE LA GENERACIÓN DE DATOS POR SIMULACIÓN (EVALUATION OF THE FRACTIONS OF THE NOBA METHOD AGAINST THE COMPLETE FACTORIAL BY GENERATING SIMULATION DATA)

Resumen Este trabajo pretende mostrar los tres tipos de errores que se pueden presentar en un diseño fraccionado. Para esto se pretende comparar las fracciones del método NOBA frente a un factorial completo. La principal contribución de esta investigación es la identificación de los tipos de errores que pueden presentarse al fraccionar un diseño para generar conocimiento acorde a las condiciones que existen hoy de mejora de procesos y productos en el sector industrial. Palabras Clave: Diseño fraccionado, factorial completo, identificación de los tipos de errores, método NOBA. Abstract This work tries to show the three types of errors that can appear in a fractional design. For this, the intention is to compare the fractions of the NOBA method against a full factorial. The main contribution of this research is the identification of the types of errors that can occur when fractioning a design to generate knowledge according to the conditions that exist today for the improvement of processes and products in the industrial sector. Keywords: Fractional design, full factorial, identification of the types of errors, NOBA method

Gestión del conocimiento. Perspectiva multidisciplinaria. Volumen 17

El libro “Gestión del Conocimiento. Perspectiva Multidisciplinaria”, Volumen 17 de la Colección Unión Global, es resultado de investigaciones. Los capítulos del libro, son resultados de investigaciones desarrolladas por sus autores. El libro es una publicación internacional, seriada, continua, arbitrada, de acceso abierto a todas las áreas del conocimiento, orientada a contribuir con procesos de gestión del conocimiento científico, tecnológico y humanístico. Con esta colección, se aspira contribuir con el cultivo, la comprensión, la recopilación y la apropiación social del conocimiento en cuanto a patrimonio intangible de la humanidad, con el propósito de hacer aportes con la transformación de las relaciones socioculturales que sustentan la construcción social de los saberes y su reconocimiento como bien público

PLANEACIÓN PARA EL DESARROLLO DE UN PROGRAMA PARA DESBALANCEAR MATRICES DE DISEÑO EN DISEÑOS FACTORIALES 2k (PLANNING FOR THE DEVELOPMENT OF A PROGRAM TO UNBALANCE DESIGN MATRICES IN FACTORY DESIGNS 2k)

Resumen Generalmente los diseños de experimentos son desarrollados a partir de matrices de diseño balanceadas ya que de acuerdo a la literatura se sabe que el desbalance en las matrices de diseño ocasiona efectos negativos y cierto grado de error en los diferentes términos del modelo. Debido a que los efectos negativos, así como el grado de error que ocasiona el desbalance, no han sido estudiados a fondo ni cuantificados. El propósito de esta investigación es plantear el desarrollo de un programa que ayude a desbalancear en tres distintos grados a las matrices de diseño utilizadas en los diseños experimentales. Para posteriormente identificar y cuantificar las consecuencias del desbalance. Las categorías de desbalance que dicho programa manejará son: bajo, medio y alto estas categorias serán determinadas a partir de los resultados obtenidos después de la aplicación del método GBM por sus siglas en ingles “General Balance Metric”. El cual únicamente nos indica el grado de balance de una determinada matriz de diseño. Palabras Clave: Matrices de diseño, Algoritmo, General Balance Metric, balance. Abstract Generally, the experimental designs are developed from balanced design matrices since, according to the literature, it is known that the imbalance in the design matrices causes negative effects and a certain degree of error in the different terms of the model. Since the negative effects, as well as the degree of error caused by the imbalance, have not been thoroughly studied or quantified. The purpose of this research is to propose the development of a program that helps to unbalance the design matrices used in experimental designs in three different degrees. To later identify and quantify the consequences of the imbalance. The imbalance categories that said program will handle are: low, medium and high. These categories will be determined from the results obtained after the application of the GBM method for its acronym in English “General Balance Metric”. Which only tells us the degree of balance of a certain design matrix. Keywords: Balanced design matrices, Algorithm, General Balance Metric, experimental design, Balance

APLICACIÓN DEL MÉTODO NOBA PARA LA GENERACIÓN DE DISEÑOS FRACCIONADOS DE DOS NIVELES (APPLICATION OF THE NOBA METHOD FOR THE GENERATION OF TWO-LEVEL FRACTIONAL DESIGNS)

Resumen El diseño de experimentos es una herramienta crucial en la optimización de cualquier proceso, su uso ya es indispensable en cualquier empresa que busca resolver problemas, sin embargo en ocasiones el diseño puede llegar a ser muy grande, es por lo que se utiliza un diseño factorial fraccionado, que permite analizar una fracción del diseño completo. El método NOBA es un método diseñado para fraccionar diseños de niveles mixtos. El propósito de esta investigación es mediante la aplicación del método NOBA comprobar si se pueden generar diseños fraccionados de dos niveles y a su vez esos diseños compararlos con diseños factoriales fraccionados de dos niveles, utilizando el criterio D-óptimo escalado. Palabras Clave: Diseño de experimentos, diseño fraccionado, diseño de dos niveles, método NOBA. Abstract The design of experiments is a crucial tool in the optimization of any process, its use is already indispensable in any company that seeks to solve problems, however sometimes the design can become very large, which is why a fractional factorial design is used, which allows to analyze a fraction of the complete design. The NOBA method is a method designed to fractionate mixed-level designs. The purpose of this research is to test, by applying the NOBA method, whether fractional two-level designs can be generated and to compare these designs with fractional two-level factorial designs, using the scaled D-optimal criterion. Keywords: Design of experiments, fractional design, two-level design, NOBA method

APLICACIÓN DEL MÉTODO NOBA A DISEÑOS FACTORIALES DE TRES NIVELES (APPLICATION OF THE NOBA METHOD TO THREE-LEVEL FACTORIAL DESIGNS)

Resumen El diseño de experimentos es una herramienta estadística que ayuda a las empresas a realizar mejoras a sus productos, pero cuando los factores y niveles a evaluar incrementan, las corridas que se generan también incrementan drásticamente, así como sus costos. En la literatura existen varias técnicas y métodos ya establecidos y comprobados para reducir el número de corridas unos más sofisticados que otros. Actualmente han surgido varias metodologías para fraccionar este tipo de experimentos, uno de ellos es el método NOBA que fue aplicado a diseños factoriales de niveles mixtos obteniendo buenos resultados. En este escrito se investiga la capacidad del método NOBA para generar fracciones en los diseños factoriales completos 3^k y evaluar si los resultados generados son igual de satisfactorios como en los diseños de niveles mixtos.Palabras Clave: Diseño de experimentos, diseños factoriales de tres niveles, diseños factoriales fraccionados, diseños de niveles mixtos, método NOBA. Abstract The design of experiments is a statistical tool that helps companies to make improvements to their products, but when the factors and levels to be evaluated increase, the runs that are generated also increase drastically, as well as their costs. In the literature there are several techniques and methods already established and proven to reduce the number of runs, some more sophisticated than others. Currently, several methodologies have emerged to fractionate this type of experiments, one of them is the NOBA method, which was applied to mixed-level factorial designs, obtaining good results. In this paper, the ability of the NOBA method to generate fractions in 3^k full factorial designs are investigated and to evaluate whether the results generated are as satisfactory as in mixed-level designs.Keywords: Design of experiments, three-level factorial designs, fractional factorial designs, mixed-level designs, NOBA method

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

Experimental designs are built by using orthogonal balanced matrices. Balance is a desirable property that allows for the correct estimation of factorial effects and prevents the identity column from aliasing with factorial effects. Although the balance property is well known by most researchers, the adverse effects caused by the lack or balance have not been extensively studied or quantified. This research proposes to quantify the effect of the lack of balance on model term estimation errors: type I error, type II error, and type I and II error as well as R2, R2adj, and R2pred statistics under four balance conditions and four noise conditions. The designs considered in this research include 24–28 factorial experiments. An algorithm was developed to unbalance these matrices while maintaining orthogonality for main effects, and the general balance metric was used to determine four balance levels. True models were generated, and a MATLAB program was developed; then a Monte Carlo simulation process was carried out. For each true model, 50,000 replications were performed, and percentages for model estimation errors and average values for statistics of interest were computed

Alias Structures and Sequential Experimentation for Mixed-Level Designs

Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation

One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple

Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels are multiples of each other, which we have called pure asymmetrical arrays. For this subgroup we present two algorithms of zero computational cost: the first with capacity to build fractions of a desired size; and the second, a strategy to increase these fractions with M additional new runs determined by the experimenter; this is an advantage over the folding methods presented in the literature in which at least half of the initial runs are required. In both algorithms, the constructed fractions are comparable to those showed in the literature as the best in terms of balance and orthogonality

Alias Structures and Sequential Experimentation for Mixed-Level Designs

Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation