Optimal Design of Experiments for Dual-Response Systems

abstract: The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work. The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

ISBIS 2016: Meeting on Statistics in Business and Industry

This Book includes the abstracts of the talks presented at the 2016 International Symposium on Business and Industrial Statistics, held at Barcelona, June 8-10, 2016, hosted at the Universitat Politècnica de Catalunya - Barcelona TECH, by the Department of Statistics and Operations Research. The location of the meeting was at ETSEIB Building (Escola Tecnica Superior d'Enginyeria Industrial) at Avda Diagonal 647. The meeting organizers celebrated the continued success of ISBIS and ENBIS society, and the meeting draw together the international community of statisticians, both academics and industry professionals, who share the goal of making statistics the foundation for decision making in business and related applications. The Scientific Program Committee was constituted by: David Banks, Duke University Amílcar Oliveira, DCeT - Universidade Aberta and CEAUL Teresa A. Oliveira, DCeT - Universidade Aberta and CEAUL Nalini Ravishankar, University of Connecticut Xavier Tort Martorell, Universitat Politécnica de Catalunya, Barcelona TECH Martina Vandebroek, KU Leuven Vincenzo Esposito Vinzi, ESSEC Business Schoo

Contributions to industrial statistics

This thesis is about statistics' contributions to industry. It is an article compendium comprising four articles divided in two blocks: (i) two contributions for a water supply company, and (ii) significance of the effects in Design of Experiments. In the first block, great emphasis is placed on how the research design and statistics can be applied to various real problems that a water company raises and it aims to convince water management companies that statistics can be very useful to improve their services. The article "A methodology to model water demand based on the identification of homogeneous client segments. Application to the city of Barcelona", makes a comprehensive review of all the steps carried out for developing a mathematical model to forecast future water demand. It pays attention on how to know more about the influence of socioeconomic factors on customer's consumption in order to detect segments of customers with homogenous habits to objectively explain the behavior of the demand. The second article -related to water demand management, "An Approach to disaggregating total household water consumption into major end-uses" describes the procedure to assign water consumption to microcomponents (taps, showers, cisterns, washer machines and dishwashers) on the basis of the readings of water consumption of the water meter. The main idea to accomplish this is, to determine which of the devices has caused the consumption, to treat the consumption of each device as a stochastic process. In the second block of the thesis, a better way to judge the significance of effects in unreplicated factorial experiments is described. The article "Proposal of a Single Critical Value for the Lenth Method" analyzes the many analytical procedures that have been proposed for identifying significant effects in not replicated two level factorial designs. Many of them are based on the original "Lenth Method and explain and try to overcome the problems that it presents". The article proposes a new strategy to choose the critical values to better differentiate the inert from the active factors. The last article "Analysing DOE with Statistical Software Packages: Controversies and Proposals" review the most important and commonly used in industry statistical software with DOE capabilities: JMP, Minitab, SigmaXL, StatGraphics and Statistica and evaluates how well they resolve the problem of analyzing the significance of effects in unreplicated factorial design

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Design of Experiments

This book is a research publication that covers original research on developments within the Design of Experiments - Applications field of study. The book is a collection of reviewed scholarly contributions written by different authors and edited by Dr. Messias Borges Silva. Each scholarly contribution represents a chapter and each chapter is complete in itself but related to the major topics and objectives. The target audience comprises scholars and specialists in the field

Estimation and Inference for 2k-p Experiments with Beta Response

Fractional factorial experiments are widely used in industry and engineering. The most common interest in these experiments is to identify a subset of the factors with the greatest effect on the response. With respect to data analysis for these experiments, the most used methods include linear regression, transformations, and the Generalized Linear Model (GLM). This thesis focuses on experiments whose response is measured continuously in the (0,1) interval (if y ∈(a,b), then (y-a)/(b-a) ∈ (0,1)). Analyses for factorial experiments in (0,1) are rarely found in the literature. In this work, advantages and drawbacks of the three mentioned methods for analyzing data from experiments in (0,1) are described. Here, as the beta distribution assumes values in (0,1), the beta regression model (BRM) is proposed for analyzing these kinds of experiments. More specifically, the necessity of considering variable dispersion (VD) and using linear restrictions on parameters are justified in data from 2k and 2k and 2k-p experiments. Thus, the first result in this thesis is to propose, develop, and apply a restricted VDBRM. The restricted VDBRM is developed from frequentist perspective: a penalized likelihood (by means of Lagrange multipliers), restricted maximum likelihood estimators with their respective Fisher Information Matrix, hypothesis tests, and a diagnostic measure. Upon applying the restricted VDBRM, good results were obtained for simulated data, and it is shown that the hypothesis related to 2k and 2k-p experiments are a special case of the restricted model. The second result of this thesis is to explore an integrated Bayesian/likelihood proposal for analyzing data from factorial experiments using the (Bayesian and frequentist) simple BRM's. This was done upon employing at prior distributions in the Bayesian BRM. Thus, comparisons between confidence intervals (frequentist case) and credibility intervals (Bayesian case) on the mean response are done with good and promisory results in real experiments. This work also explores a technique for choosing the best model among several candidates which combine the Half-normal plots (given by the BRM) and the inferential results. Starting from the active factors chosen from each plot, subsequently the respective regression models are fitted and, finally, by means of information criteria, the best model is chosen. This technique was explored with the following models: normal, transformation, generalized linear, and simple beta regression for real 2k and 2k- p experiments: into the greater part of the examples considered for the Bayesian and frequentist BRM's, results were very similar (using at prior distributions). Moreover, four link functions for the mean response in the BRM are compared: results highlight the importance to study each problem at hand.Resumen. Los experimentos factoriales fraccionados se usan ampliamente en la industria y en la Ingeniería. El interés más común en estos experimentos es identificar el subconjunto de factores que tiene mayor efecto sobre la respuesta. Con respecto al análisis de datos de dichos experimentos, los métodos más usados incluyen regresión lineal, transformaciones y Modelo Lineal Generalizado (MLG). Esta Tesis se enfoca en experimentos cuya respuesta está medida continuamente en el intervalo (0,1), (si y ∈ (a,b), entonces y (y-a)/(b-a) ∈ (0,1)). En la literatura se encuentran pocos análisis de experimentos con esta respuesta. En este trabajo, se describen ventajas y desventajas de las tres metodologías mencionadas en experimentos con esta respuesta. Acá, como la distribución beta asume valores en (0,1), se propone el modelo de regresión beta (MRB) para analizar estos datos. Más específicamente, se justifica la necesidad de modelar la dispersión variable y usar restricciones sobre los parámetros se justifican en datos de experimentos 2k y 2k-p. De este modo, el primer resultado de esta Tesis es proponer, desarrollar y aplicar un modelo de regresión beta con dispersión variable y restricciones en los parámetros (MRBDV restringido). El modelo es desarrollado desde la perspectiva clásica: una función de verosimilitud penalizada (con multiplicadores de Lagrange), estimadores de máxima verosimilitud restringidos con su respectiva matriz de Información de Fisher, tests de hipótesis y una medidad de bondad de ajuste. Al aplicar el MRBDV restringido, se obtuvieron buenso resultados para datos simulados y se mostró que las hipótesis asociadas con experimentos 2k y 2k-p son un caso especial del modelo restringido. El segundo resultado de esta Tesis es explorar una propuesta integrada bayesiana/verosimil para analizar datos de experimentos factoriales usando los dos MRB (bayesiano y clásico). Esto se hizo al emplear distribuciones a priori planas (poco informativas) en el modelo bayesiano. Así, las comparaciones entre intervalos de confianza y de credibilidad presentaron buenos resultados y promisorios en experimentos factoriales reales. Esta Tesis tambien explora una técnica para elegir el mejor modelo entre varios candidatos, el cual combina los Half-normal plots (dados por el BRM) y resultados inferenciales. Partiendo de los efectos activos según cada gráfico, posteriormente se ajustan los modelos de regresión respectivos y, finalmente, por medio de criterios de información, se escoge el mejor modelo. Esta técnica fue explorada con los siguientes modelos: normal, transformaciones, MLG y MRB simple para datos reales de experimentos 2k y 2kDoctorad

Multivoxel codes for representing and integrating acoustic features in human cortex

Using fMRI and multivariate pattern analysis, we determined whether acoustic features are represented by independent or integrated neural codes in human cortex. Male and female listeners heard band-pass noise varying simultaneously in spectral (frequency) and temporal (amplitude-modulation [AM] rate) features. In the superior temporal plane, changes in multivoxel activity due to frequency were largely invariant with respect to AM rate (and vice versa), consistent with an independent representation. In contrast, in posterior parietal cortex, neural representation was exclusively integrated and tuned to specific conjunctions of frequency and AM features. Direct between-region comparisons show that whereas independent coding of frequency and AM weakened with increasing levels of the hierarchy, integrated coding strengthened at the transition between non-core and parietal cortex. Our findings support the notion that primary auditory cortex can represent component acoustic features in an independent fashion and suggest a role for parietal cortex in feature integration and the structuring of acoustic input. Significance statement A major goal for neuroscience is discovering the sensory features to which the brain is tuned and how those features are integrated into cohesive perception. We used whole-brain human fMRI and a statistical modeling approach to quantify the extent to which sound features are represented separately or in an integrated fashion in cortical activity patterns. We show that frequency and AM rate, two acoustic features that are fundamental to characterizing biological important sounds such as speech, are represented separately in primary auditory cortex but in an integrated fashion in parietal cortex. These findings suggest that representations in primary auditory cortex can be simpler than previously thought and also implicate a role for parietal cortex in integrating features for coherent perception

Computer aids for the design of large scale integrated circuits.

The work described in this thesis is concerned with the development of CADIC (Computer Aided Design of Integrated Circuits), a suite of computer programs which allows the user to design integrated circuit layouts at the geometric level. Initially, a review of existing computer aids to integrated circuit design is carried out. Advantages and disadvantages of each computer aid is discused, and the approach taken by CADIC justified in the light of the review. The hardware associated with a design aid can greatly influence its performance and useability. For this reason, a critical review of available graphic terminals is also undertaken. The requirements, logistics, and operation of CADIC is then discussed in detail. CADIC provides a consise range of features to aid in the design and testing of integrated circuit layouts. The most important features are however CADIC's high efficiency in processing layout data, and the implementation of complete on-line design rule checking. Utilization of these features allows CADIC to substantially reduce the lengthy design turnaround time normally associated with manual design aids. Finally, the performance of CADIC is presented. Analysis of the results show that CADIC is very efficient at data processing, especially when small sections of the layout are considered. CADIC can also perform complete on-line design rule checking well within the time it takes the designer to start adding the next shape