DOCSLIB.ORG

Interaction Graphs for a Two-Level Combined Array Experiment Design by Dr

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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. Bisham received his Ph.D. (Statistics) and Mas- linear graphs associated with orthogo- as classical methods, it is possible for ter of Science in Mathematics from the University of Windsor, Canada in 1972 and 1969 respectively. He nal arrays to facilitate the planning of experimenters to make use of their also received his Master of Science in Mathematics such experiments. Since then the graph- technical skills and in-depth knowledge and Statistics in 1964 and Bachelor of Science in Mathematics in 1962 from Punjab University, India. aided method has been enhanced by of their particular industrial operations various authors such as Li et al (1991), to design more effective, less expensive Wu and Chen (1992), Robinson (1993), experiments using non-isomorphic and Wu and Hamada (2000). In this interaction graphs. Accordingly, in this paper, we propose an algorithm for paper the authors will provide for developing all possible non-isomorphic readers a context for the application of interaction graphs for combined arrays. non-isomorphic interaction graphs, formally define and describe these Introduction graphs as valuable tools, provide an Industrial Technologists (IT’s) are algorithm for developing all possible frequently required to use designed graphs for combined arrays, provide for experiments as problem solving and readers a detailed example developing process improvement tools in their roles and using these graphs, explain how to as “…technical and/or management read and interpret the graphs, and pose oriented professionals…in business, the argument that IT’s and other Dr. H. Fred Walker, CQMgr, CQE, CQA, CSIT is the industry, education, and government.” interested professionals can use non- Department Chair and Graduate Coordinator in the Department of Technology at the University of South- (The National Association of Industrial isomorphic interaction graphs to do their ern Maine. Fred develops and teaches graduate Technology, 1997, [Online]). In fact, it jobs more effectively and efficiently. courses in Applied Research Methods, Engineering Economy, Quality Systems, Manufacturing Strategies, is common practice for IT’s to work and Project Management. He also develops and teaches undergraduate courses Quality, Industrial Sta- with other communities of technical and Background tistics, Cost Analysis and Control, Human Resource managerial professionals as experiment- In planning a 2k-p fractional facto- Management, Project Management, and Technical Writing. Dr. Walker’s industrial experience includes ers in the application of designed rial experiment, prior knowledge may 12 years with airborne weapons systems integration experiments in discrete part manufactur- enable experimenters to pinpoint and automation, supervision and administration, project management, and program management in ing, assembly, and process industries. interactions which should be estimated countries throughout the Pacific Rim, Australia, and Of primary importance to these experi- free of main effects and any other Africa. Fred’s consulting experience includes ten years of continual involvement with internationally-based menters is working with design, desired interactions. While working on manufacturers from electronics, pulp and paper, bio- production, and quality personnel to applications of classical DOE methods, medical equipment, printing, farm implements, and machined component industries. This experience has identify and understand the many Taguchi (1987) introduced a graph- enabled Fred to earn Certified Quality Manager, Cer- variables or factors associated with any aided technique known as linear graphs tified Quality Engineer, Certified Quality Auditor, Cer- tified Manufacturing Technologist, and Certified Se- type of industrial operation. It is associated with orthogonal arrays to nior Industrial Technologist designations. Dr. Walker particularly interesting to these experi- facilitate the planning of such experi- received his Ph.D. (Industrial Education and Technol- ogy) and Master of Science in Systems Engineering menters to pinpoint those variables that ments, and as such, Taguchi’s graph from Iowa State University. He also received his Mas- ter of Business Administration (MBA) and Bachelor of most significantly influence or impact aided technique is not to be confused Science in Industrial Technology from California State their industrial operations as well as any with what is commonly known as University – Fresno. 2 Journal of Industrial Technology • Volume 18, Number 4 • August 2002 to October 2002 • www.nait.org Taguchi Methods. Linear graphs are tions, properties of raw materials and achieved by using interaction graphs graphical representations of the any other factors that are hard-to- for two-level combined arrays. allocation of main effects and desired control. Taguchi’s technique, also In this paper, we give an algorithm two-factor interactions to the columns known as Taguchi methods, uses an for developing all possible non- of orthogonal arrays. Linear graphs experimental design consisting of a isomorphic interaction graphs for a facilitate the selection of an aliasing cross product of two arrays, an inner combined array of various two level pattern that in turn enables experiment- array containing the control factors and fractional factorial designs. We do this ers to estimate all main effects and an outer array containing the noise in the context of classical DOE appli- desired two-factor interactions. And it factors. The cross product of the inner cations even though the topic could be should be noted it is important for and outer array often leads to a large applied to Taguchi Methods. These experimenters to be able to quantify the number of observations that are interaction graphs enable one to existence and magnitude of these main generally very expensive to complete. allocate the factors to the columns of effects and interactions to support fact- In an attempt to reduce the number orthogonal arrays, along with the based decision making regarding the of observations needed to support an estimation of main effects and desired experiment design and application. experiment, and thus reduce costs, control-to-control, control-to-noise Since 1987, researchers such as Li, Welch et al (1990), Shoemaker et al interactions assuming all other interac- Washio, Iida and Tanimoto (1991) have (1991), Montgomery (1991), and tions to be negligible. extended Taguchi’s work on classical Borkowski and Lucas (1997) suggested DOE applications of linear graphs by independently an alternative design to “Non-Isomorphic” Defined developing non-isomorphic linear study both the control and noise factors Having introduced the concept of graphs for an experiment involving by using a single array, called a linear interaction graphs in the preced- eight (8) factors. In this scenario, a 2k combined array. A combined array ing paragraphs, it is time to explain the experiment design was crafted wherein structure enables experimenters to nature and meaning of the concepts of no main effect was confounded with estimate both control-to-control and isomorphic and non-isomorphic as they any other main effect or with any two- control-to-noise interactions with fewer relate to interaction graphs. Figure 1 factor interactions, while two-factor observations. Miller et al (1993) used below is provided to help readers interactions were confounded with a combined array in an automobile visualize the explanation. each other. This type of experiment is experiment and demonstrated similar As can be seen in Figure 1 (page 4), commonly referred to as a resolution results could be obtained using the graph “A” depicts interactions among IV design and, in this case, the re- combined array approach and a much factorsV1-5,
Recommended publications
  • 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

    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

    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
  • Industrial and Systems Engineering (ISE)

    Industrial and Systems Engineering (ISE)

    Lehigh University 2021-22 1 Industrial and Systems Engineering (ISE) Courses ISE 224 Information Systems Analysis and Design 3 Credits ISE 100 Industrial Employment 0 Credits An introduction to the technological as well as methodological Usually following the junior year, students in the industrial engineering aspects of computer information systems. Content of the course curriculum are required to do a minimum of eight weeks of practical stresses basic knowledge in database systems. Database design and work, preferably in the field they plan to follow after graduation. A evaluation, query languages and software implementation. Students report is required. Must have sophomore standing. that take CSE 241 cannot receive credit for this course. ISE 111 Engineering Probability 3 Credits ISE 226 Engineering Economy and Decision Analysis 3 Credits Random variables, probability models and distributions. Poisson Economic analysis of engineering projects; interest rate factors, processes. Expected values and variance. Joint distributions, methods of evaluation, depreciation, replacement, breakeven covariance and correlation. analysis, aftertax analysis. decision-making under certainty and risk. Prerequisites: MATH 022 or MATH 096 or MATH 032 or MATH 052 Prerequisites: ISE 111 or MATH 231 or IE 111 Can be taken Concurrently: ISE 111, MATH 231, IE 111 ISE 112 Computer Graphics 1 Credit Introduction to interactive graphics and construction of multiview ISE 230 Introduction to Stochastic Models in Operations representations in two and three dimensional space. Applications in Research 3 Credits industrial engineering. Must have sophomore standing in industrial Formulating, analyzing, and solving mathematical models of real- engineering. world problems in systems exhibiting stochastic (random) behavior. Discrete and continuous Markov chains, queueing theory, inventory ISE 121 Applied Engineering Statistics 3 Credits control, Markov decision process.
  • 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

    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.
  • Major Factors That Influence the Employment Decisions of Generation X Consulting Engineers

    Major Factors That Influence the Employment Decisions of Generation X Consulting Engineers

    Old Dominion University ODU Digital Commons Engineering Management & Systems Engineering Management & Systems Engineering Theses & Dissertations Engineering Spring 2002 Major Factors That Influence the Employment Decisions of Generation X Consulting Engineers Robert William Mayfield Old Dominion University Follow this and additional works at: https://digitalcommons.odu.edu/emse_etds Part of the Engineering Commons, Organizational Behavior and Theory Commons, and the Work, Economy and Organizations Commons Recommended Citation Mayfield, Robert W.. "Major Factors That Influence the Employment Decisions of Generation X Consulting Engineers" (2002). Master of Science (MS), Thesis, Engineering Management & Systems Engineering, Old Dominion University, DOI: 10.25777/t41p-rd52 https://digitalcommons.odu.edu/emse_etds/102 This Thesis is brought to you for free and open access by the Engineering Management & Systems Engineering at ODU Digital Commons. It has been accepted for inclusion in Engineering Management & Systems Engineering Theses & Dissertations by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. MAJOR FACTORS THAT INFLUENCE THE EMPLOYMENT DECISIONS OF GENERATION X CONSULTING ENGINEERS bv Robert William Mayfield B.S. March 1994, The Ohio State University A Thesis Submitted to the Faculty o f Old Dominion University in Partial Fulfillment o f the Requirement for the Degree of MASTER OF SCIENCE ENGINEERING MANAGEMENT OLD DOMINION UNIVERSITY May 2002 Approved by: Charles Keating (Direct Paul Kauffmai ember) Andres Sousa-Poza (Member) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT MAJOR FACTORS THAT INFLUENCE THE EMPLOYMENT DECISIONS OF GENERATION X CONSULTING ENGINEERS Robert William Mayfield Old Dominion University. 2002 Director: Dr. Charles Keating The purpose of this research was to study Generation X consulting engineers (those bom between the years 1964 and 1980) in Lynchburg.
  • Novel Substructural Health Monitoring Method Without Interface Measurements Using State Space Analysis and Extended Kalman Filtering

    Novel Substructural Health Monitoring Method Without Interface Measurements Using State Space Analysis and Extended Kalman Filtering

    Novel Substructural Health Monitoring Method without Interface Measurements using State Space Analysis and Extended Kalman Filtering by Arianne Layard Muelhausen Under the Supervision of Prof. Brock Hedegaard A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE (Civil and Environmental Engineering) at the University of Wisconsin-Madison 2018 Contents 1 Introduction 2 2 Literature Review 4 3 Methodology 8 3.1 State Space Analysis . .8 3.2 Kalman Filter . .9 3.3 Extended Kalman Filter . 11 3.4 Substructural Identification using Extended Kalman Filtering . 12 3.4.1 Global Equation of Motion . 13 3.4.2 Substructural Equation of Motion . 14 3.4.3 State Space Formulation: State Transition Equation . 17 3.4.4 State Space Formulation: Measurement Equation . 18 3.4.5 Implementation of Extended Kalman Filter . 19 3.5 Methodology Step-by-Step Summary . 24 4 Results 25 4.1 Model Description . 25 4.2 Case One: All DOFs Measured . 26 4.3 Case Two: All Interface and Some Interior DOFs Measured . 29 4.4 Case Three: Some Interface and Some Interior DOFs Measured . 31 4.5 Case Four: No Interface and Some Interior DOFs Measured . 38 4.6 Discussion on Limitations of Method . 40 5 Conclusion 41 6 Work Cited 42 1 1 Introduction Structural Health Monitoring (SHM) at its core is a process to identify damage, defined as either material or geometric change, of a system that negatively affects the systems performance[7]. SHM seeks to address four questions: (Level 1) Detection: Is damage present? (Level 2) Localization: What is the probable location of damage? (Level 3) Assessment: What is the severity of the damage? (Level 4) Prognosis: What is the remaining service life of the damaged system? SHM can be used to monitor structures affected by external stimuli, long-term movement, ma- terial degradation, or demolition.
  • Multivariate Statistical Process Monitoring Using Classical

    Multivariate Statistical Process Monitoring Using Classical

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Newcastle University eTheses Multivariate Statistical Process Monitoring Using Classical Multidimensional Scaling Prepared by: Mohd Yusri Mohd Yunus A Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy School of Chemical Engineering and Advanced Materials Newcastle University UK May 2012 ABSTRACT A new Multivariate Statistical Process Monitoring (MSPM) system, which comprises of three main frameworks, is proposed where the system utilizes Classical Multidimensional Scaling (CMDS) as the main multivariate data compression technique instead of using the linear- based Principal Component Analysis (PCA). The conventional method which usually applies variance-covariance or correlation measure in developing the multivariate scores is found to be inappropriately used especially in modelling nonlinear processes, where a high number of principal components will be typically required. Alternatively, the proposed method utilizes the inter-dissimilarity scales in describing the relationships among the monitored variables instead of variance-covariance measure for the multivariate scores development. However, the scores are plotted in terms of variable structure, thus providing different formulation of statistics for monitoring. Nonetheless, the proposed statistics still correspond to the conceptual objective of Hotelling’s T2 and Squared Prediction Errors (SPE). The first framework corresponds to the original
  • Contributions of the Taguchi Method

    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

    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

    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

    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.
  • On Simulation of Cross Correlated Random Fields Using Series Expansion Methods

    On Simulation of Cross Correlated Random Fields Using Series Expansion Methods

    ENGINEERING MECHANICS 2009 National Conference with International Participation pp. 1431–1443 Svratka, Czech Republic, May 11 – 14, 2009 Paper #139 ON SIMULATION OF CROSS CORRELATED RANDOM FIELDS USING SERIES EXPANSION METHODS M. Vorechovskˇ y´ 1 Summary: A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross cor- relation coefficients is presented in the paper. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical au- tocorrelation function and the cross correlation structure between each pair of sim- ulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such a decomposition represents a significant reduction of compu- tational effort. Non-Gaussian components of a multivariate random field are proposed to be sim- ulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations. 1. Introduction The random nature of many features of physical events is widely recognized both in industry and by researchers.