Aportaciones metodológicas al diseño de productos robustos

Se propone una nueva metodología que facilita la selección de los valores óptimos de los factores de diseño para llegar a una solución de compromiso entre la distancia al óptimo y la varianza de la respuesta, de acuerdo con los intereses del diseñador. La novedad del método no reside en el planteamiento del diseño experimental (aunque no se usa la típica matriz producto de Taguchi), sino en el análisis que se realiza a partir del modelo obtenido para la respuesta. Dicho análisis se basa en la realización de un diagrama bivariante de la varianza de la respuesta frente a la distancia al óptimo en el que cada punto representa una determinada combinación de valores de los factores de diseño. La aplicación de estemétodo es especialmente sencillo, tanto desde un punto de vista conceptual como práctico, si se utiliza una hoja de cálculo para ordenador personal. A lo largo de la Tesis se van presentando ejemplos que sirven para ilustrar lasposibilidades y forma de utilización de la metodología propuesta.Postprint (published version

Fent servir l'estadística: què és i per a què serveix l'estadística a través de casos pràctics basats en projectes final de carrera

Descripció de setze casos tractats en projectes de final de carrera que donen una visió general de les possibilitats d’aplicació de l’estadística

Estadística en acción: qué es y para qué sirve la estadística a través de casos prácticos basados en proyectos final de carrera

Descripció de setze casos tractats en projectes de final de carrera que donen una visió general de les possibilitats d’aplicació de l’estadística

Visualizing type II error in normality tests

This is an Accepted Manuscript of an article published by Taylor & Francis in “Visualizing type II error in normality tests” on 19th January 2017, available online: http://www.tandfonline.com/doi/full/10.1080/00031305.2016.1278035A Skewed Exponential Power Distribution, with parameters defining kurtosis and skewness, is introduced as a way to visualize Type II error in normality tests. By varying these parameters a mosaic of distributions is built, ranging from double exponential to uniform or from positive to negative exponential; the normal distribution is a particular case located in the center of the mosaic. Using a sequential color scheme, a different color is assigned to each distribution in the mosaic depending on the probability of committing a Type II error. This graph gives a visual representation of the power of the performed test. This way of representing results facilitates the comparison of the power of various tests and the influence of sample size. A script to perform this graphical representation, programmed in the R statistical software, is available online as supplementary material.Peer ReviewedPostprint (author's final draft

The time has come: Statistics in bestselling books

Beyond textbooks, statistics is also present in bestselling books, those that appear on the top 10 lists of bookshops and online bookstores. This paper discusses five of those books, highlighting the role of statistics in each one. Besides describing the general topics of the books, we want to show that the knowledge of the world around us – and also the knowledge on ourselves – advances thanks to the application of the scientific method of which statistics is a key element. The paper finishes with some thoughts on the desirability of a practical approach to teaching statisticsPostprint (published version

El histograma como un instrumento para la comprensión de las funciones de densidad de probabilidad

Tradicionalmente los profesores de Estadística de nivel medio y superior hemos mirado la Estadística Descriptiva como una temática divorciada de la probabilidad y de la Inferencia. Cuando llega el momento de explicar el histograma, generalmente se construyen intervalos de igual tamaño y el eje de las ordenadas representa directamente la frecuencia relativa. Sin embargo, cuando trata la temática de las funciones de densidades en probabilidad, para calcular la probabilidad, que conceptualmente es el homólogo de la frecuencia relativa, si se mira como una extensión del concepto a la población entera, debe calcularse un área, ya no son las ordenadas las que proporcionan esta información. La pregunta que surge es ¿Por qué si el concepto de probabilidad es una extensión de la frecuencia relativa a la población, en un caso se calcula un área y en el otro una altura? Esto parece conceptualmente incoherente. En el presente trabajo se plantea una estrategia para lograr coherencia, definiendo el histograma como un gráfico de la densidad empírica. Esto tiene una doble función, ganar potencial intuitivo para dar sentido real a la idea de densidad, logrando que la definición de variable aleatoria continua no suene artificial para los estudiantes y por otro lado resolver la mencionada incoherencia. En este trabajo se ilustra con un ejemplo la estrategia que se plantea.Postprint (published version

Reducing variability of a critical dimension

Peer ReviewedPostprint (author's final draft

Consequences of using estimated response values from negligible interactions in factorial designs

This article analyzes the increase in the probability of committing type I and type II errors in assessing the significance of the effects when some properly selected runs have not been carried out and their responses have been estimated from the interactions considered null from scratch. This is done by simulating the responses from known models that represent a wide variety of practical situations that the experimenter will encounter; the responses considered to be missing are then estimated and the significance of the effects is assessed. Through comparison with the parameters of the model, the errors are then identified. To assess the significance of the effects when there are missing values, the Box-Meyer method has been used. The conclusions are that 1 missing value in 8 run designs and up to 3 missing values in 16 run designs experiments can be estimated without hardly any notable increase in the probability of error when assessing the significance of the effects.Peer ReviewedPostprint (author's final draft

Blocking versus robustness in industrial contexts

This is the peer reviewed version of the following article: “Grima, P, Marco, L, Tort-Martorell, X. (2017) Blocking versus robustness in industrial contexts, (2017)1-13.” which has been published in final form at [doi: 10.1002/qre.2173]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."The paper discusses the similarities and differences between blocking factors (blocked designs) and noise factors (robust designs) in industrial two-level factorial experiments. The discussion covers from the objectives of both design types and the nature of blocking and noise factors to the types of designs and the assumptions needed in each case. The conclusions are as follows: the nature and characteristics of noise and blocking factors are equal or very similar; the designs used in both situations are also similar; and the main differences lie in the assumptions and the objectives. The paper argues that the objectives are not in conflict and can easily be harmonized. In consequence, we argue in favor of a unified approach that would clarify the issue, especially for students and practitioners.Peer ReviewedPostprint (author's final draft

Selecting significant effects in factorial designs: Lenth’s method versus the Box-Meyer approach

The Lenth method is conceptually simple and probably the most common approach to analyzing the significance of the effects in factorial designs. Here, we compare it with a Bayesian approach proposed by Box and Meyer and which does not appear in the usual software packages. The comparison is made by simulating the results of 4, 8 and 16 run designs in a set of scenarios that mirror practical situations and analyzing the results provided by both methods. Although the results depend on the number of runs and the scenario considered, the use of the Box and Meyer method generally produces better results. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.Peer ReviewedPostprint (author's final draft