DOCSLIB.ORG

STATISTICAL PLANNING of EXPERIMENTS Seppo Tenitz FOOD-601 Extrusion 2019

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
STATISTICAL PLANNING of EXPERIMENTS Seppo Tenitz FOOD-601 Extrusion 2019 STATISTICAL PLANNING OF EXPERIMENTS Seppo Tenitz FOOD-601 Extrusion 2019 1 1. FUNDAMENTALS AND RECAPITULATION • Experimental research finds out how different treatments affect the experimental units to be studied. The treatments differ from one another by different combinations of levels in independent (also predicting, or explanatory) variables. • An experimental unit is that something, independent of oth- er experimental units, which a certain treatment is focused on. A certain treatment leads to a certain observation about dependent (also predicted, or explained) variables. • A plan of experiments determines how treatments decided in advance (a priori) are focused on the experimental units, and in which order the treatments will be put into practice. • The aim is to produce as trustful and convincing information as possible about the effects of the treatments on the pre- dicted variables. 2 1 The alternative to experimental research is observational re- search: • no controlled experiments but direct observations are col- lected about the experimental units • the state of the experimental units are not affected active- ly but it is followed how the units react the variables pre- dicting their state • the experimental units are chosen randomly from a larger population or the universe (perusjoukko) of those units • a trustful final result usually requires more observations than what is needed in experimental studies • a natural approach e.g. in economical, social, environmen- tal or behavioural research 3 • In all experimentation there is usually in the backgound some implicit or abreast preconception about the pat- tern how the values of the predicted variables are de- termined by the predicting variables and their levels • If that preconception can be shaped into a form of an informative set of experiments the result of the test se- ries is often a mathematical equation or a set of such ones that precisely decribes that pattern and by which it is possible by calculations to predict the results of future experiments • Such a mathematical description of a real system is called an experimental mathematical model (system) of the real system if it can be seen to have some gen- eral validity and not just to be a mere simplification of a bunch of results 4 2 • One frequently applied experimental model type is a by statistical means obtained polynomial of one or several (predicting) variables • The question in the application of such a model structure with systems based on physics and chemistry is whether the polynomials describe in a scientifically and meaningly correct way the relationship between the predicting vari- ables and the response variables • The answer is very often no, but the polynomial is an ade- quate choice because any continuous, differentiable and scientifically valid model function y = f(x) can be approxi- mated using a Taylor series, if the scrutinity is restricted to a narrow region of x. The new function is in the form of y 2 p-1 = bo + b1x + b2x + ... + bp-1x + , i.e. a polynomial. • The relation enlarges also to functions of several variables 5 For a researcher who performs experiments to obtain such a metamodel (a ”model of a model”) as a polynomial, there are three main types of variables to consider: controlled, indepen- dent and dependent: Controlled variables (whose values are kept constant, e.g. sample temperature in a measurement) Predicting variables Response variables (whose values can (whose values are be chosen freely dependent on the and which are in system values of the pre- that way indepen- dicting variables) dent but controlled) Other variables These must be avoided or their influence must be minimized! 6 3 Different types of errors are inevitably connected with experimental studies: • Usual sources of coarse or systematic errors are, for instance • an incorrect or unsuitable experimental design • an error in experimental working made by a researcher • an error in the observation of the measured quantity • an error in writing down the measured quantity • an error in calculation or • limitations of the measuring equipment used: accuracy (ul- koinen tarkkuus), precision (sisäinen tarkkuus), measuring range (mittausalue) • The always inherent random fluctuation in the measured value of a variable becomes apparent in studies as a statistical exper- imental error, the magnitude of which can be stated as the vari- ance of a set of repeated measurements or trials. 7 Bricks of the statistical planning of experiments by which the influences of errors are tackled are • replication of an experiment in similar conditions • the experimental error can be evaluated • an exact evaluation of the experimental effect is enabled • randomization of the experimental units or the order of experiments • the effects of unanticipated sources of variation on the ob- servations are made smaller • blocking of the experimental units • the effects of unavoidable but predictable sources of varia- tion on the observations are made smaller • subgrouping of experiments e.g. by differences in batches of ingredients, type of soil, human beings, points in time, sex, ... 8 4 The nature of the variables connected with the research problem largerly determines the sta- tistical analysis method of the results. e.g.: Predicted / dependent Variable Categorical Continuous Logistic analysis Analysis of Categorical of variance variance Predicting / independent Continuous Logistic regres- Regression sion analysis analysis 9 • From the point of view of the regression analysis, in the design of experiments (DoE) either the uncertainty of the coefficients bi of a polynomial model or the predictions obtained for y by that (which both are dependent on both the error variance of the measured values of y and the experimental design) are tried to be minimized. • Other objectives: • it is ensured that enough informative events arises as a result of the experiments • it is ensured that the effects of predicting variables can be studied apart from one another (to avoid aliasing) • it is ensured that the interactions between the predict- ing variables can be found out trustfully • the amount of experiments is minimized, if needed 10 5 A good experimental design for e.g. preliminary experiments: the 22 full factorial design + center points → ŷ = bo + b1x1 + b2x2 + b12x1x2 x2 40 min 1 3 replicates from which the 0 error variance time 20 min -1 x -1 0 1 1 100oC temperature 120oC 11 Terms and concepts: constant, intercept regression coeffi- predicting cients, slopes variables ŷ = bo + b1x1 + b2x2 2 2 ŷ = bo + b1x1 + b2x2 + b12x1x2 + b11x1 + b22x2 MAIN EFFECTS, i.e. LINEAR PREDICTORS: predictors are made up of pre- dicting variables or, alterna- x1, x2 tively, are such ones already NONLINEAR EFFECTS: the constant and the regression x 2, x 2, x x coefficients together are often 1 2 1 2 called regression parameters INTERACTIONS: the effect of x1 on the value of y is dependent on the value of x2 and vice versa: x1x2 12 6 Graphically, e.g. in the case of two predicting variables: X2 = u1 Y X2 = u2 the value of X2 is fixed, the values of Y on different val- ues of X1 are measured X1 13 Applications of the results of regression analysis: • Identification of statistically significant predictors • Comparison of alternatives: Is there e.g. any difference be- tween the influence of two optional ingredients? If not, the cheaper one is chosen. • Obtaining an optimal result: Which levels of which predict- ing variables should be chosen. Fitting several simultane- ous objectives together. Taking the bounds associated with the predicting variables into consideration. • Reducing variability: Is it e.g. possible to reduce the varia- tion in some quality attribute by changing the recipe. • Improving robustness: By which recipe e.g. replacing the baking oven used with a new one would affect as little as possible some quality attribute. 14 7 Hands-on questions: • what kind of model and what kind of experimental design? • an experimental design of certain type → a regression model of certain structure! • which of the all possible predicting variables are included in the model? • screening experiments, the Pareto principle, scientific literature, causal analysis + practical experience, ... • are qualitative variables taken along and which would be their values? • should there be used transformed variables instead of the actual ones (log xi, y, …)? • yes, if the presuppositions associated with the analysis methods to be used are not otherwise fulfilled 15 • Two important properties characterizing an experi- mental design are its orthogonality and rotatability (kiertosymmetrisyys tai kierrettävyys) • a design matrix X is orthogonal if its condition number (kuntoisuusluku) = 1 • Every rotatable experimental design is also ortho- gonal but not necessarily vice versa • E.g. a 23 factorial design, Matlab: • X = twon(3); cond(X) = 1 → orthogonal • X = [X; [2.5 0.13 6]]; cond(X) = 2.5067 → this is not; instead there is multicolliarity in the data 16 8 Similar partial multicollinearity in a D-optimal design whose condition number = 1.583, i.e. quite small: one variable Yet the Pearson’s correlation coefficient between the last two variables is remarkably -1 -1 1 high (-0.474) → the rule of thumb is 0.30 so like multi- 0.5 1 -1 collinear designs should not -1 1 -1 be applied without a careful preconsideration 0.5 -1 1 one experiment 0.5 1 1 -1 1 1 coded i.e. nor- malized values 0.25 0 0 17 Consequences of multicollinearity: • The basis: perfect multicollinearity – let x2 = x1 in the regression model ŷ = bo + b1x1 + b2x2 – by substituting ŷ = bo + (b1 + b2)x1 = bo + x1 → the coefficients b1, b2 and stick together so the effects of the predictors x1 and x2 on ^the response variable ŷ cannot be separated from one anotherb → also the OLS calculation of the model breaks down ... • The practice: partial multicollinearity • the variance inflation factor VIFj of the j:th coefficient bj of 2 2 the model = 1/(1-Rj ) in which Rj is the coefficient of deter- mination in linear regression of a predictor on all the other 2 predictors of the model (here e.g.
Load more

Recommended publications
  • Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization
    Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization Li Wang Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Statistics Geoff Vining, Chair Scott Kowalski, Co-Chair John P. Morgan Dan Spitzner Keying Ye August 15, 2006 Blacksburg, Virginia Keywords: Response Surface Designs, Central Composite Design, Split-plot Designs, Rotatability, Orthogonal Blocking. Copyright 2006, Li Wang Recommendations for Design Parameters for Central Composite Designs with Restricted Randomization Li Wang ABSTRACT In response surface methodology, the central composite design is the most popular choice for fitting a second order model. The choice of the distance for the axial runs, α, in a central composite design is very crucial to the performance of the design. In the literature, there are plenty of discussions and recommendations for the choice of α, among which a rotatable α and an orthogonal blocking α receive the greatest attention. Box and Hunter (1957) discuss and calculate the values for α that achieve rotatability, which is a way to stabilize prediction variance of the design. They also give the values for α that make the design orthogonally blocked, where the estimates of the model coefficients remain the same even when the block effects are added to the model. In the last ten years, people have begun to realize the importance of a split-plot structure in industrial experiments. Constructing response surface designs with a split-plot structure is a hot research area now. In this dissertation, Box and Hunters’ choice of α for rotatablity and orthogonal blocking is extended to central composite designs with a split-plot structure.
    [Show full text]
  • Split-Plot Designs and Response Surface Designs
    Chapter 8: Split-Plot Designs Split-plot designs were originally developed by Fisher (1925,Statistical Methods for Research Workers) for use in agricultural experiments where factors are differentiated with respect to the ease with which they can be changed from experimental run to experimental run. This may be due to the fact that a particular treatment is expensive or time-consuming to change or it may be due to the fact that the experiment is to be run in a large batches and batches can be subdivided later for additional treatments. A split-plot design may be considered as a special case of the two-factor randomized design where one wants to obtain more precise information about one factor and also about the interaction between the two factors. The second factor being of secondary importance to the experimenter. Example 1 Consider a study of the effects of four irrigation methods (A1, A2, A3, and A4) and three fertilizers (B1, B2, and B3). Two replicates are planned to carried out for each of the 12 combinations. A completely randomized design will randomly assign a combination of irrigation and fertilization methods to one of the 24 fields. This may be easy for fertilization but it is hard for irrigation where sprinklers are arranged in a certain way. What is usually done is to use just eight plots of land, chosen so that each can be irrigated at a set level without affecting the irrigation of the others. These large plots are called the whole plots. Randomly assign irrigation levels to each whole plot so that each irrigation level is assigned to exactly two plots.
    [Show full text]
  • Interventions for Controlling Myopia Onset and Progression Report
    Special Issue IMI – Interventions for Controlling Myopia Onset and Progression Report Christine F. Wildsoet,1 Audrey Chia,2 Pauline Cho,3 Jeremy A. Guggenheim,4 Jan Roelof Polling,5,6 Scott Read,7 Padmaja Sankaridurg,8 Seang-Mei Saw,9 Klaus Trier,10 Jeffrey J. Walline,11 Pei-Chang Wu,12 and James S. Wolffsohn13 1Berkeley Myopia Research Group, School of Optometry and Vision Science Program, University of California Berkeley, Berkeley, California, United States 2Singapore Eye Research Institute and Singapore National Eye Center, Singapore 3School of Optometry, The Hong Kong Polytechnic University, Hong Kong 4School of Optometry and Vision Sciences, Cardiff University, Cardiff, United Kingdom 5Erasmus MC Department of Ophthalmology, Rotterdam, The Netherlands 6HU University of Applied Sciences, Optometry and Orthoptics, Utrecht, The Netherlands 7School of Optometry and Vision Science and Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia 8Brien Holden Vision Institute and School of Optometry and Vision Science, University of New South Wales, Sydney, Australia 9Saw Swee Hock School of Public Health, National University of Singapore, Singapore 10Trier Research Laboratories, Hellerup, Denmark 11The Ohio State University College of Optometry, Columbus, Ohio, United States 12Department of Ophthalmology, Kaohsiung Chang Gung Memorial Hospital and Chang Gung University College of Medicine, Kaohsiung, Taiwan 13Ophthalmic Research Group, Aston University, Birmingham, United Kingdom Correspondence: Christine F. Wild- Myopia has been predicted to affect approximately 50% of the world’s population based soet, School of Optometry, Universi- on trending myopia prevalence figures. Critical to minimizing the associated adverse ty of California Berkeley, 588 Minor visual consequences of complicating ocular pathologies are interventions to prevent or Hall, Berkeley, CA 94720-2020, USA; delay the onset of myopia, slow its progression, and to address the problem of mechanical [email protected].
    [Show full text]
  • The Usefulness of Optimal Design for Generating Blocked and Split-Plot Response Surface Experiments Peter Goos
    The Usefulness of Optimal Design for Generating Blocked and Split-Plot Response Surface Experiments Peter Goos Universiteit Antwerpen Abstract This article provides an overview of the recent literature on the design of blocked and split-plot experiments with quantitative experimental variables. A detailed literature study introduces the ongoing debate between an optimal design approach to constructing blocked and split-plot designs and approaches where the equivalence of ordinary least squares and generalized least squares estimates are envisaged. Examples where the competing approaches lead to totally different designs are given, as well as examples in which the proposed designs satisfy both camps. Keywords: equivalence of OLS and GLS, ordinary least squares, generalized least squares, orthogonal blocking, D-optimal design 1 Introduction Blocked experiments are typically used when not all the runs of an experiment can be conducted under homogeneous circumstances. In such experiments, the runs are par- titioned in blocks so that the within-block variability is considerably smaller than the between-block variability. Split-plot experiments are used for a different reason, that is because the levels of some of the experimental variables are not independently reset for every experimental run as this is often impractical, costly or time-consuming. As a con- sequence, the runs of a split-plot experiment are also partitioned in groups, and within each group the levels of the so-called hard-to-change variables are constant. Split-plot experiments can thus be interpreted as special cases of blocked experiments. Despite the similarity between the two types of experiments, the terminology utilized in the context of blocked and split-plot experiments is different: the groups of observations in a blocked experiment are called blocks, whereas those in split-plot experiments are named whole plots.
    [Show full text]
  • Experiment Design and Analysis Reference
    Experiment Design & Analysis Reference ReliaSoft Corporation Worldwide Headquarters 1450 South Eastside Loop Tucson, Arizona 85710-6703, USA http://www.ReliaSoft.com Notice of Rights: The content is the Property and Copyright of ReliaSoft Corporation, Tucson, Arizona, USA. It is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. See the next pages for a complete legal description of the license or go to http://creativecommons.org/licenses/by-nc-sa/4.0/legalcode. Quick License Summary Overview You are Free to: Share: Copy and redistribute the material in any medium or format Adapt: Remix, transform, and build upon the material Under the following terms: Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. See example at http://www.reliawiki.org/index.php/Attribution_Example NonCommercial: You may not use this material for commercial purposes (sell or distribute for profit). Commercial use is the distribution of the material for profit (selling a book based on the material) or adaptations of this material. ShareAlike: If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. Generation Date: This document was generated on April 29, 2015 based on the current state of the online reference book posted on ReliaWiki.org. Information in this document is subject to change without notice and does not represent a commitment on the part of ReliaSoft Corporation.
    [Show full text]
  • Graphical Tools, Incorporating Cost and Optimizing Central Composite Designs for Split- Plot Response Surface Methodology Experiments
    GRAPHICAL TOOLS, INCORPORATING COST AND OPTIMIZING CENTRAL COMPOSITE DESIGNS FOR SPLIT- PLOT RESPONSE SURFACE METHODOLOGY EXPERIMENTS by Li Liang Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in fulfillment of the requirements for the degree of Doctor of Philosophy in Statistics C.M. Anderson-Cook, Co-Chair T.J. Robinson, Co-Chair E.P. Smith G.G. Vining K. Ye March 28, 2005 Blacksburg, Virginia Keywords: 3-dimensional variance dispersion graph, fraction of design space, cost penalized evaluation, multiple criteria, optimal factorial levels, central composite structure GRAPHICAL TOOLS, INCORPORATING COST AND OPTIMIZING CENTRAL COMPOSITE DESIGNS FOR SPLIT- PLOT RESPONSE SURFACE METHODOLOGY EXPERIMENTS Li Liang (Abstract) In many industrial experiments, completely randomized designs (CRDs) are impractical due to restrictions on randomization, or the existence of one or more hard-to-change factors. Under these situations, split-plot experiments are more realistic. The two separate randomizations in split-plot experiments lead to different error structure from in CRDs, and hence this affects not only response modeling but also the choice of design. In this dissertation, two graphical tools, three-dimensional variance dispersion graphs (3-D VDGs) and fractions of design space (FDS) plots are adapted for split-plot designs (SPDs). They are used for examining and comparing different variations of central composite designs (CCDs) with standard, V- and G-optimal factorial levels. The graphical tools are shown to be informative for evaluating and developing strategies for improving the prediction performance of SPDs. The overall cost of a SPD involves two types of experiment units, and often each individual whole plot is more expensive than individual subplot and measurement.
    [Show full text]
  • Design and Analysis of Experiments Course Notes for STAT 568
    Design and Analysis of Experiments Course notes for STAT 568 Adam B Kashlak Mathematical & Statistical Sciences University of Alberta Edmonton, Canada, T6G 2G1 March 27, 2019 cbna This work is licensed under the Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/ by-nc-sa/4.0/. Contents Preface1 1 One-Way ANOVA2 1.0.1 Terminology...........................2 1.1 Analysis of Variance...........................3 1.1.1 Sample size computation....................6 1.1.2 Contrasts.............................7 1.2 Multiple Comparisons..........................8 1.3 Random Effects..............................9 1.3.1 Derivation of the F statistic................... 11 1.4 Cochran's Theorem............................ 12 2 Multiple Factors 15 2.1 Randomized Block Design........................ 15 2.1.1 Paired vs Unpaired Data.................... 17 2.1.2 Tukey's One DoF Test...................... 18 2.2 Two-Way Layout............................. 20 2.2.1 Fixed Effects........................... 20 2.3 Latin Squares............................... 21 2.3.1 Graeco-Latin Squares...................... 23 2.4 Balanced Incomplete Block Designs................... 24 2.5 Split-Plot Designs............................ 26 2.6 Analysis of Covariance.......................... 30 3 Multiple Testing 33 3.1 Family-wise Error Rate......................... 34 3.1.1 Bonferroni's Method....................... 34 3.1.2 Sidak's Method.......................... 34 3.1.3 Holms' Method.......................... 35 3.1.4 Stepwise Methods........................ 35 3.2 False Discovery Rate........................... 36 3.2.1 Benjamini-Hochberg Method.................. 37 4 Factorial Design 39 4.1 Full Factorial Design........................... 40 4.1.1 Estimating effects with regression................ 41 4.1.2 Lenth's Method.......................... 43 4.1.3 Key Concepts..........................
    [Show full text]
  • Visual Performance of Center-Distance Multifocal Contact Lenses Fit Using a Myopia Control Paradigm
    VISUAL PERFORMANCE OF CENTER-DISTANCE MULTIFOCAL CONTACT LENSES FIT USING A MYOPIA CONTROL PARADIGM By Hannah R. Gregory, BS A thesis submitted to the Graduate Program, University of Houston College of Optometry In partial fulfillment of the requirements for the degree of MASTER OF SCIENCES In PHYSIOLOGICAL OPTICS & VISION SCIENCE Chair of Committee: Eric R. Ritchey, OD, PhD Co-chair of Committee: David A. Berntsen, OD, PhD Committee Member: Han Cheng, PhD, OD University of Houston May 2021 Acknowledgments I would like to thank my advisor, Dr. Eric Ritchey, for his many hours of teaching and directing me throughout this entire process. His passion for teaching and research is evident in all that he does. He welcomed me into his new lab when it first began and made sure I understood what it really meant to be a researcher, explaining how it is relevant to the optometric world, especially in the field of myopia progression. My research project would not be where it is without all of his help. He always made himself available when I needed help, especially when aiming for deadlines throughout this process. His guidance truly pushed me to become the professional I am today. I am also so thankful for the support of his wife, Dr. Moriah Chandler, and his children. I would also like to thank my co-advisor, Dr. David Berntsen, for his support and help throughout my schooling. He also spent countless hours, aiding in analyzing data and explaining it in a way that I could understand to utilize in my project. His dedication to the field of myopia management is inspiring and has made me want to pursue this throughout my career.
    [Show full text]
  • Fitting Success for Three Multifocal Designs Multicentre Randomised Trial
    Contact Lens and Anterior Eye xxx (xxxx) xxx–xxx Contents lists available at ScienceDirect Contact Lens and Anterior Eye journal homepage: www.elsevier.com/locate/clae Fitting success for three multifocal designs: Multicentre randomised trial ⁎ Emilia Novillo-Díaza, , César Villa-Collarb, Mónica Narváez-Peñac, José Luis R. Martínc a María Cristina Optometry Center, Tomelloso, Ciudad Real, Spain b Universidad Europea de Madrid, Madrid, Spain c Simplifying Research Institute, Layos, Toledo, Spain ARTICLE INFO ABSTRACT Keywords: Purpose: To determine if the discontinuation of commercially-available simultaneous vision Multifocal Soft Multifocal design Contact Lenses is independent from the multifocal design. To determine causes for discontinuation and psy- Simultaneous vision chosocial factors involved. Discontinuation Methods: Multicentre single-blinded randomised controlled trial with external blinded evaluation for a three Psychosocial factors months follow-up period for three intervention groups. 150 single-vision soft wearers were randomly assigned a Quality of life spherical near centred lens (S-CN), distance centred lens (CD) or aspherical near centred lens (A-CN). Cases of discontinuation, anxiety and quality of life were measured at one week and one month. Results: 120 females and 30 males were included with an age range of 40–62 (48.79 ± 5.23). At one month, the S-CN design had a statistically significant higher risk of discontinuation than the other two OR: 6.12 (95%CI 2.5–14.9). Twenty-eight subjects discontinued wearing S-CN at first week (56%), while discontinuation of CD and A-CD were 15 (30%) and 11 (22%), with a statistically significant difference between S-CN design and the other two (p = 0.001).
    [Show full text]
  • Spherical Designs and Non-Convex Minimization for Recovery of Sparse Signals on the Sphere∗
    SPHERICAL DESIGNS AND NON-CONVEX MINIMIZATION FOR RECOVERY OF SPARSE SIGNALS ON THE SPHERE∗ XIAOJUN CHENy AND ROBERT S. WOMERSLEYzz Abstract. This paper considers the use of spherical designs and non-convex minimization for 2 recovery of sparse signals on the unit sphere S . The available information consists of low order, 2 potentially noisy, Fourier coefficients for S . As Fourier coefficients are integrals of the product of a function and spherical harmonics, a good cubature rule is essential for the recovery. A spherical 2 t-design is a set of points on S , which are nodes of an equal weight cubature rule integrating exactly all spherical polynomials of degree ≤ t. We will show that a spherical t-design provides a sharp error bound for the approximation signals. Moreover, the resulting coefficient matrix has orthonormal 2 rows. In general the `1 minimization model for recovery of sparse signals on S using spherical harmonics has infinitely many minimizers, which means that most existing sufficient conditions for sparse recovery do not hold. To induce the sparsity, we replace the `1-norm by the `q-norm (0 < q < 1) in the basis pursuit denoise model. Recovery properties and optimality conditions are discussed. Moreover, we show that the penalty method with a starting point obtained from the re- weighted `1 method is promising to solve the `q basis pursuit denoise model. Numerical performance on nodes using spherical t-designs and t-designs (extremal fundamental systems) are compared with tensor product nodes. We also compare the basis pursuit denoise problem with q = 1 and 0 < q < 1.
    [Show full text]
  • Design and Analysis of Response Surface Designs with Restricted Randomization Wayne R
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2006 Design and Analysis of Response Surface Designs with Restricted Randomization Wayne R. Wesley Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING DESIGN AND ANALYSIS OF RESPONSE SURFACE DESIGNS WITH RESTRICTED RANDOMIZATION By Wayne R. Wesley A Dissertation submitted to the Department of Industrial Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Summer Semester, 2006 Copyright © 2006 Wayne R. Wesley All Rights Reserved The members of the Committee approve the dissertation of Wayne R. Wesley defended on July 6, 2006. ______________________________ James R. Simpson Professor Directing Dissertation ______________________________ Anuj Srivastava Outside Committee Member ______________________________ Peter A. Parker Outside Committee Member ______________________________ Joseph J. Pignatiello, Jr. Committee Member Approved: _________________________________ Chuck Zhang, Chair, Department of Industrial and Manufacturing Engineering _________________________________ Ching-Jen Chen, Dean, College of Engineering The Office of Graduate Studies has verified and approved the above named committee members. ii I dedicate this dissertation to my son and daughter Jowayne and Jowaynah Wesley. iii ACKNOWLEDGEMENTS I must first give thanks to the almighty God for good health, strength and wisdom to successfully complete my dissertation. It is with a deep sense of gratitude that I express my sincere appreciation to Dr. James Simpson and Dr. Peter Parker for their invaluable advice and contributions in directing the dissertation. Special thanks to Dr. Joseph Pignatiello and Dr. Anuj Srivastava for their meaningful comments and suggestions that helped to improve the quality of the dissertation.
    [Show full text]
  • 2004/12/31-Sandia Report No. SAND2004-6258, "Guidance On
    SANDIA REPORT SAND2004-6258 Unlimited Release Printed December 2004 Guidance on Risk Analysis and Safety Implications of a Large Liquefied Natural Gas (LNG) Spill Over Water Mike Hightower, Louis Gritzo, Anay Luketa-Hanlin, John Covan, Sheldon Tieszen, Gerry Wellman, Mike Irwin, Mike Kaneshige, Brian Melof, Charles Morrow, Don Ragland Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors.
    [Show full text]