14.5 ORTHOGONAL ARRAYS (Updated Spring 2003)
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APPLICATION of the TAGUCHI METHOD to SENSITIVITY ANALYSIS of a MIDDLE- EAR FINITE-ELEMENT MODEL Li Qi1, Chadia S
APPLICATION OF THE TAGUCHI METHOD TO SENSITIVITY ANALYSIS OF A MIDDLE- EAR FINITE-ELEMENT MODEL Li Qi1, Chadia S. Mikhael1 and W. Robert J. Funnell1, 2 1 Department of BioMedical Engineering 2 Department of Otolaryngology McGill University Montréal, QC, Canada H3A 2B4 ABSTRACT difference in the model output due to the change in the input variable is referred to as the sensitivity. The Sensitivity analysis of a model is the investigation relative importance of parameters is judged based on of how outputs vary with changes of input parameters, the magnitude of the calculated sensitivity. The OFAT in order to identify the relative importance of method does not, however, take into account the parameters and to help in optimization of the model. possibility of interactions among parameters. Such The one-factor-at-a-time (OFAT) method has been interactions mean that the model sensitivity to one widely used for sensitivity analysis of middle-ear parameter can change depending on the values of models. The results of OFAT, however, are unreliable other parameters. if there are significant interactions among parameters. Alternatively, the full-factorial method permits the This paper incorporates the Taguchi method into the analysis of parameter interactions, but generally sensitivity analysis of a middle-ear finite-element requires a very large number of simulations. This can model. Two outputs, tympanic-membrane volume be impractical when individual simulations are time- displacement and stapes footplate displacement, are consuming. A more practical approach is the Taguchi measured. Nine input parameters and four possible method, which is commonly used in industry. It interactions are investigated for two model outputs. -
How Differences Between Online and Offline Interaction Influence Social
Available online at www.sciencedirect.com ScienceDirect Two social lives: How differences between online and offline interaction influence social outcomes 1 2 Alicea Lieberman and Juliana Schroeder For hundreds of thousands of years, humans only Facebook users,75% ofwhom report checking the platform communicated in person, but in just the past fifty years they daily [2]. Among teenagers, 95% report using smartphones have started also communicating online. Today, people and 45%reportbeingonline‘constantly’[2].Thisshiftfrom communicate more online than offline. What does this shift offline to online socializing has meaningful and measurable mean for human social life? We identify four structural consequences for every aspect of human interaction, from differences between online (versus offline) interaction: (1) fewer how people form impressions of one another, to how they nonverbal cues, (2) greater anonymity, (3) more opportunity to treat each other, to the breadth and depth of their connec- form new social ties and bolster weak ties, and (4) wider tion. The current article proposes a new framework to dissemination of information. Each of these differences identify, understand, and study these consequences, underlies systematic psychological and behavioral highlighting promising avenues for future research. consequences. Online and offline lives often intersect; we thus further review how online engagement can (1) disrupt or (2) Structural differences between online and enhance offline interaction. This work provides a useful offline interaction -
ARIADNE (Axion Resonant Interaction Detection Experiment): an NMR-Based Axion Search, Snowmass LOI
ARIADNE (Axion Resonant InterAction Detection Experiment): an NMR-based Axion Search, Snowmass LOI Andrew A. Geraci,∗ Aharon Kapitulnik, William Snow, Joshua C. Long, Chen-Yu Liu, Yannis Semertzidis, Yun Shin, and Asimina Arvanitaki (Dated: August 31, 2020) The Axion Resonant InterAction Detection Experiment (ARIADNE) is a collaborative effort to search for the QCD axion using techniques based on nuclear magnetic resonance. In the experiment, axions or axion-like particles would mediate short-range spin-dependent interactions between a laser-polarized 3He gas and a rotating (unpolarized) tungsten source mass, acting as a tiny, fictitious magnetic field. The experiment has the potential to probe deep within the theoretically interesting regime for the QCD axion in the mass range of 0.1- 10 meV, independently of cosmological assumptions. In this SNOWMASS LOI, we briefly describe this technique which covers a wide range of axion masses as well as discuss future prospects for improvements. Taken together with other existing and planned axion experi- ments, ARIADNE has the potential to completely explore the allowed parameter space for the QCD axion. A well-motivated example of a light mass pseudoscalar boson that can mediate new interactions or a “fifth-force” is the axion. The axion is a hypothetical particle that arises as a consequence of the Peccei-Quinn (PQ) mechanism to solve the strong CP problem of quantum chromodynamics (QCD)[1]. Axions have also been well motivated as a dark matter candidatedue to their \invisible" nature[2]. Axions can couple to fundamental fermions through a scalar vertex and a pseudoscalar vertex with very weak coupling strength. -
Orthogonal Arrays and Row-Column and Block Designs for CDC Systems
Current Trends on Biostatistics & L UPINE PUBLISHERS Biometrics Open Access DOI: 10.32474/CTBB.2018.01.000103 ISSN: 2644-1381 Review Article Orthogonal Arrays and Row-Column and Block Designs for CDC Systems Mahndra Kumar Sharma* and Mekonnen Tadesse Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia Received: September 06, 2018; Published: September 20, 2018 *Corresponding author: Mahndra Kumar Sharma, Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia Abstract In this article, block and row-column designs for genetic crosses such as Complete diallel cross system using orthogonal arrays (p2, r, p, 2), where p is prime or a power of prime and semi balanced arrays (p(p-1)/2, p, p, 2), where p is a prime or power of an odd columnprime, are designs derived. for Themethod block A designsand C are and new row-column and consume designs minimum for Griffing’s experimental methods units. A and According B are found to Guptato be A-optimalblock designs and thefor block designs for Griffing’s methods C and D are found to be universally optimal in the sense of Kiefer. The derived block and row- Keywords:Griffing’s methods Orthogonal A,B,C Array;and D areSemi-balanced orthogonally Array; blocked Complete designs. diallel AMS Cross; classification: Row-Column 62K05. Design; Optimality Introduction d) one set of F ’s hybrid but neither parents nor reciprocals Orthogonal arrays of strength d were introduced and applied 1 F ’s hybrid is included (v = 1/2p(p-1). The problem of generating in the construction of confounded symmetrical and asymmetrical 1 optimal mating designs for CDC method D has been investigated factorial designs, multifactorial designs (fractional replication) by several authors Singh, Gupta, and Parsad [10]. -
Orthogonal Array Experiments and Response Surface Methodology
Unit 7: Orthogonal Array Experiments and Response Surface Methodology • A modern system of experimental design. • Orthogonal arrays (sections 8.1-8.2; appendix 8A and 8C). • Analysis of experiments with complex aliasing (part of sections 9.1-9.4). • Brief response surface methodology, central composite designs (sections 10.1-10.2). 1 Two Types of Fractional Factorial Designs • Regular (2n−k, 3n−k designs): columns of the design matrix form a group over a finite field; the interaction between any two columns is among the columns, ⇒ any two factorial effects are either orthogonal or fully aliased. • Nonregular (mixed-level designs, orthogonal arrays) some pairs of factorial effects can be partially aliased ⇒ more complex aliasing pattern. This includes 3n−k designs with linear-quadratic system. 2 A Modern System of Experimental Design It has four branches: • Regular orthogonal arrays (Fisher, Yates, Finney, ...): 2n−k, 3n−k designs, using minimum aberration criterion. • Nonregular orthogonal designs (Plackett-Burman, Rao, Bose): Plackett-Burman designs, orthogonal arrays. • Response surface designs (Box): fitting a parametric response surface. • Optimal designs (Kiefer): optimality driven by specific model/criterion. 3 Orthogonal Arrays • In Tables 1 and 2, the design used does not belong to the 2k−p series (Chapter 5) or the 3k−p series (Chapter 6), because the latter would require run size as a power of 2 or 3. These designs belong to the class of orthogonal arrays. m1 mγ • An orthogonal array array OA(N,s1 ...sγ ,t) of strength t is an N × m matrix, m = m1 + ... + mγ, in which mi columns have si(≥ 2) symbols or levels such that, for any t columns, all possible combinations of symbols appear equally often in the matrix. -
Latin Squares in Experimental Design
Latin Squares in Experimental Design Lei Gao Michigan State University December 10, 2005 Abstract: For the past three decades, Latin Squares techniques have been widely used in many statistical applications. Much effort has been devoted to Latin Square Design. In this paper, I introduce the mathematical properties of Latin squares and the application of Latin squares in experimental design. Some examples and SAS codes are provided that illustrates these methods. Work done in partial fulfillment of the requirements of Michigan State University MTH 880 advised by Professor J. Hall. 1 Index Index ............................................................................................................................... 2 1. Introduction................................................................................................................. 3 1.1 Latin square........................................................................................................... 3 1.2 Orthogonal array representation ........................................................................... 3 1.3 Equivalence classes of Latin squares.................................................................... 3 2. Latin Square Design.................................................................................................... 4 2.1 Latin square design ............................................................................................... 4 2.2 Pros and cons of Latin square design................................................................... -
Contributions of the Taguchi Method
1 International System Dynamics Conference 1998, Québec Model Building and Validation: Contributions of the Taguchi Method Markus Schwaninger, University of St. Gallen, St. Gallen, Switzerland Andreas Hadjis, Technikum Vorarlberg, Dornbirn, Austria 1. The Context. Model validation is a crucial aspect of any model-based methodology in general and system dynamics (SD) methodology in particular. Most of the literature on SD model building and validation revolves around the notion that a SD simulation model constitutes a theory about how a system actually works (Forrester 1967: 116). SD models are claimed to be causal ones and as such are used to generate information and insights for diagnosis and policy design, theory testing or simply learning. Therefore, there is a strong similarity between how theories are accepted or refuted in science (a major epistemological and philosophical issue) and how system dynamics models are validated. Barlas and Carpenter (1992) give a detailed account of this issue (Barlas/Carpenter 1990: 152) comparing the two major opposing streams of philosophies of science and convincingly showing that the philosophy of system dynamics model validation is in agreement with the relativistic/holistic philosophy of science. For the traditional reductionist/logical empiricist philosophy, a valid model is an objective representation of the real system. The model is compared to the empirical facts and can be either correct or false. In this philosophy validity is seen as a matter of formal accuracy, not practical use. In contrast, the more recent relativist/holistic philosophy would see a valid model as one of many ways to describe a real situation, connected to a particular purpose. -
Interaction of Quantitative Variables
Regression Including the Interaction Between Quantitative Variables The purpose of the study was to examine the inter-relationships among social skills, the complexity of the social situation, and performance in a social situation. Each participant considered their most recent interaction in a group of 10 or larger that included at least 50% strangers, and rated their social performance (perf) and the complexity of the situation (sitcom), Then, each participant completed a social skills inventory that provided a single index of this construct (soskil). The researcher wanted to determine the contribution of the “person” and “situation” variables to social performance, as well as to consider their interaction. Descriptive Statistics N Minimum Maximum Mean Std. Deviation SITCOM 60 .00 37.00 19.7000 8.5300 SOSKIL 60 27.00 65.00 49.4700 8.2600 Valid N (listwise) 60 As before, we will want to center our quantitative variables by subtracting the mean from each person’s scores. We also need to compute an interaction term as the product of the two centered variables. Some prefer using a “full model” approach, others a “hierarchical model” approach – remember they produce the same results. Using the hierarchical approach, the centered quantitative variables (main effects) are entered on the first step and the interaction is added on the second step Be sure to check the “R-squared change” on the Statistics window SPSS Output: Model 1 is the main effects model and Model 2 is the full model. Model Summary Change Statistics Adjusted Std. Error of R Square Model R R Square R Square the Estimate Change F Change df1 df2 Sig. -
A Comparison of the Taguchi Method and Evolutionary Optimization in Multivariate Testing
A Comparison of the Taguchi Method and Evolutionary Optimization in Multivariate Testing Jingbo Jiang Diego Legrand Robert Severn Risto Miikkulainen University of Pennsylvania Criteo Evolv Technologies The University of Texas at Austin Philadelphia, USA Paris, France San Francisco, USA and Cognizant Technology Solutions [email protected] [email protected] [email protected] Austin and San Francisco, USA [email protected],[email protected] Abstract—Multivariate testing has recently emerged as a [17]. While this process captures interactions between these promising technique in web interface design. In contrast to the elements, only a very small number of elements is usually standard A/B testing, multivariate approach aims at evaluating included (e.g. 2-3); the rest of the design space remains a large number of values in a few key variables systematically. The Taguchi method is a practical implementation of this idea, unexplored. The Taguchi method [12], [18] is a practical focusing on orthogonal combinations of values. It is the current implementation of multivariate testing. It avoids the compu- state of the art in applications such as Adobe Target. This paper tational complexity of full multivariate testing by evaluating evaluates an alternative method: population-based search, i.e. only orthogonal combinations of element values. Taguchi is evolutionary optimization. Its performance is compared to that the current state of the art in this area, included in commercial of the Taguchi method in several simulated conditions, including an orthogonal one designed to favor the Taguchi method, and applications such as the Adobe Target [1]. However, it assumes two realistic conditions with dependences between variables. -
Design of Experiments (DOE) Using the Taguchi Approach
Design of Experiments (DOE) Using the Taguchi Approach This document contains brief reviews of several topics in the technique. For summaries of the recommended steps in application, read the published article attached. (Available for free download and review.) TOPICS: • Subject Overview • References Taguchi Method Review • Application Procedure • Quality Characteristics Brainstorming • Factors and Levels • Interaction Between Factors Noise Factors and Outer Arrays • Scope and Size of Experiments • Order of Running Experiments Repetitions and Replications • Available Orthogonal Arrays • Triangular Table and Linear Graphs Upgrading Columns • Dummy Treatments • Results of Multiple Criteria S/N Ratios for Static and Dynamic Systems • Why Taguchi Approach and Taguchi vs. Classical DOE • Loss Function • General Notes and Comments Helpful Tips on Applications • Quality Digest Article • Experiment Design Solutions • Common Orthogonal Arrays Other References: 1. DOE Demystified.. : http://manufacturingcenter.com/tooling/archives/1202/1202qmdesign.asp 2. 16 Steps to Product... http://www.qualitydigest.com/june01/html/sixteen.html 3. Read an independent review of Qualitek-4: http://www.qualitydigest.com/jan99/html/body_software.html 4. A Strategy for Simultaneous Evaluation of Multiple Objectives, A journal of the Reliability Analysis Center, 2004, Second quarter, Pages 14 - 18. http://rac.alionscience.com/pdf/2Q2004.pdf 5. Design of Experiments Using the Taguchi Approach : 16 Steps to Product and Process Improvement by Ranjit K. Roy Hardcover - 600 pages Bk&Cd-Rom edition (January 2001) John Wiley & Sons; ISBN: 0471361011 6. Primer on the Taguchi Method - Ranjit Roy (ISBN:087263468X Originally published in 1989 by Van Nostrand Reinhold. Current publisher/source is Society of Manufacturing Engineers). The book is available directly from the publisher, Society of Manufacturing Engineers (SME ) P.O. -
Interaction Graphs for a Two-Level Combined Array Experiment Design by Dr
Journal of Industrial Technology • Volume 18, Number 4 • August 2002 to October 2002 • www.nait.org Volume 18, Number 4 - August 2002 to October 2002 Interaction Graphs For A Two-Level Combined Array Experiment Design By Dr. M.L. Aggarwal, Dr. B.C. Gupta, Dr. S. Roy Chaudhury & Dr. H. F. Walker KEYWORD SEARCH Research Statistical Methods Reviewed Article The Official Electronic Publication of the National Association of Industrial Technology • www.nait.org © 2002 1 Journal of Industrial Technology • Volume 18, Number 4 • August 2002 to October 2002 • www.nait.org Interaction Graphs For A Two-Level Combined Array Experiment Design By Dr. M.L. Aggarwal, Dr. B.C. Gupta, Dr. S. Roy Chaudhury & Dr. H. F. Walker Abstract interactions among those variables. To Dr. Bisham Gupta is a professor of Statistics in In planning a 2k-p fractional pinpoint these most significant variables the Department of Mathematics and Statistics at the University of Southern Maine. Bisham devel- factorial experiment, prior knowledge and their interactions, the IT’s, engi- oped the undergraduate and graduate programs in Statistics and has taught a variety of courses in may enable an experimenter to pinpoint neers, and management team members statistics to Industrial Technologists, Engineers, interactions which should be estimated who serve in the role of experimenters Science, and Business majors. Specific courses in- clude Design of Experiments (DOE), Quality Con- free of the main effects and any other rely on the Design of Experiments trol, Regression Analysis, and Biostatistics. desired interactions. Taguchi (1987) (DOE) as the primary tool of their trade. Dr. Gupta’s research interests are in DOE and sam- gave a graph-aided method known as Within the branch of DOE known pling. -
Orthogonal Array Application for Optimized Software Testing
WSEAS TRANSACTIONS on COMPUTERS Ljubomir Lazic and Nikos Mastorakis Orthogonal Array application for optimal combination of software defect detection techniques choices LJUBOMIR LAZICa, NIKOS MASTORAKISb aTechnical Faculty, University of Novi Pazar Vuka Karadžića bb, 36300 Novi Pazar, SERBIA [email protected] http://www.np.ac.yu bMilitary Institutions of University Education, Hellenic Naval Academy Terma Hatzikyriakou, 18539, Piraeu, Greece [email protected] Abstract: - In this paper, we consider a problem that arises in black box testing: generating small test suites (i.e., sets of test cases) where the combinations that have to be covered are specified by input-output parameter relationships of a software system. That is, we only consider combinations of input parameters that affect an output parameter, and we do not assume that the input parameters have the same number of values. To solve this problem, we propose interaction testing, particularly an Orthogonal Array Testing Strategy (OATS) as a systematic, statistical way of testing pair-wise interactions. In software testing process (STP), it provides a natural mechanism for testing systems to be deployed on a variety of hardware and software configurations. The combinatorial approach to software testing uses models to generate a minimal number of test inputs so that selected combinations of input values are covered. The most common coverage criteria are two-way or pairwise coverage of value combinations, though for higher confidence three-way or higher coverage may be required. This paper presents some examples of software-system test requirements and corresponding models for applying the combinatorial approach to those test requirements. The method bridges contributions from mathematics, design of experiments, software test, and algorithms for application to usability testing.