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Nov 27, 2014

Copyright Tapan Bagchi 1Quality Engineering and Taguchi MethodsCopyright Tapan Bagchi 2Robust Chocolate Bars are better!Ambient TemperaturePlasticityRobust performancePoor performanceCopyright Tapan Bagchi 3Taguchi Methods (or Quality Engineeringor Robust Design) Focus is on reducing variability of responseto maximize robustness, generally achieved through Orthogonal Array ExperimentsCopyright Tapan Bagchi 4The Genesis of DOESir Ronald Alymer Fisher (1890-1962) was the pioneer of DOE. He was responsible for statistics and data analysis at the Rothamsted Agricultural Experiment Station in London, England. Fisher developed and was the first to use ANOVA in the statistical analysis of experimental data. Copyright Tapan Bagchi 5Historical PerspectiveGeorge E. P. Box (born 1919) was a student of R A Fisher. He made several advances to Fishers work in DOE theory and statistics. The founding chair of the University of Wisconsins Department of Statistics, Box was appointed the R. A. Fisher Professor of Statistics at UW in 1971.Copyright Tapan Bagchi 6Objective of this Lecture: To explore the basic ideas of two-level factorial design of experiments (DOE) and the connection of QE to statistical process control (SPC)Key Points:QE Overview DOE can help uncover significant variables and interactions among variables SPC can help uncover process shifts Quality engineering tools help the investigator to discover a path for process improvementCopyright Tapan Bagchi 7Typical QE Applications In manufacturing - improve performance of a manufacturing process In process development - improve yields, reduce variability and cost. In design - evaluation and comparison of basic configurations, materials, and parameters The method is called Taguchi Methods. The key tool is DOE.Copyright Tapan Bagchi 8Copyright Tapan Bagchi 9C R RaoYoud know Rao from his Cramer-Rao Inequality. Rao is recognized worldwide as a pioneer of modern multivariate theory and as one of the world's top statisticians, with distinctions as a mathematician, researcher, scientist, and teacher. Taught Taguchi.Author of 14 books and over 300 papers.Copyright Tapan Bagchi 10Genichi TaguchiAn engineer who developed an approach (now called Taguchi Methods) involving statistically planned experiments to reduce variation in quality. Learned DOE from Professor Rao. In 1960s he applied his learning in Japan. In 1980s he introduced his ideas to US at AT&T.Copyright Tapan Bagchi 11What are Taguchis Contributions? Quality Engineering PhilosophyTargets and Loss functions MethodologySystem, Parameter, Tolerance design steps Experiment Designuse of Orthogonal arrays Analysisuse Signal-to-Noise (S/N ratios)Copyright Tapan Bagchi 12616587 7779756760DOBstandard orderD B O Avg Response1 672 + 793 + 614 + + 755 +656 + +607 + +778 + + +87FACTOR LOW(-) HIGH (+)D (Driver) regular oversizedB (Beverage) beer waterO (Ball) 3-piece balata- - - + - -1 2358 746+ - ++ + ++ + -- + +- + -- - +DBOConventional DOE focuses only onAverage ResponseQE focuses on Variability ofResponseCopyright Tapan Bagchi 13Taguchis Key Contributions Quality Engineering Philosophy Methodology Experiment Design AnalysisCopyright Tapan Bagchi 14The Taguchi Loss Functionand the typically assumed Loss to the CustomerTargetLo SpecHi SpecLossCopyright Tapan Bagchi 15Taguchis Quality PhilosophyLoss = k(P - T)2not 0 if within specsand 1 if outsideOn Target Productionis more important than producing within SpecsLS T USLS T US Conventional viewTaguchis viewCopyright Tapan Bagchi 16Taguchi focused on Off-Line Quality ControlOff-Line Quality Control = Improving quality and reducing total cost in the product or process design stageTotal Cost means cost to society so it includes the cost of problems in manufacturing and the cost of problems in the field.Copyright Tapan Bagchi 17Definition:Robust DesignA Design that results in products or services that can function over a broad range of usage and environmental conditionsTaguchis key contribution is Robust DesignCopyright Tapan Bagchi 18Taguchis Contributions Contd. Quality Engineering Philosophy Methodology Experiment Design AnalysisCopyright Tapan Bagchi 19Taguchis Product Design Approach has 3 Steps1. System DesignChoose the sub-systems, mechanisms, form of the prototypedevelop the basic design. This is similar to conventional engineering design2. Parameter DesignOptimize the system design so that it improves quality (robustness) and reduces cost3. Tolerance DesignStudy the tradeoffs that must be made and determine what tolerances and grades of materials are acceptableCopyright Tapan Bagchi 20Parameter Design (the Robust Design step) Optimize the settings of the design parameters to minimize its sensitivity to noiseROBUSTNESS. By highlighting robustness as a key quality requirement, Taguchi really opened a whole area that previously had been talked about only by a few very applied people. His methodology is heavily dependent on design of experiments like Fishers and Boxs methods, but the difference he made was that for response he looked at not only the mean but also the variance of performanceCopyright Tapan Bagchi 21Robust Designhow it is done Identify Product/Process Design Parameters that Have significant / little influence on Performance Minimize performance variation due to Noise factors Minimize the processing cost Methodology: Design of Experiments (DOE) Examples - Chocolate mix, Ina Tile Co., Sony TVTarget Performance (t)Actual Performance (P)Design Parameters (D)Noise Factors (N): Internal & ExternalProduct / ProcessCopyright Tapan Bagchi 22Taguchis Experimental FactorsParameter design step identifies and optimizes the Design Factors Control Factors Design factors that are to be set at optimal levels to improve quality and reduce sensitivity to noise Size of parts, type of material, Value of resistors, etc Noise Factors Factors that represent the noise that is expected in production or in actual use of the product Dimensional variation Operating Temperature Adjustment Factor Affects the mean but not the variance of a response Deposition time in silicon wafer fabrication Signal Factors Set by the user to communicate desires of the user Position of the gas pedalCopyright Tapan Bagchi 23Taguchis Contributions Contd. Quality Engineering Philosophy Methodology Experiment Design use orthogonal arrays AnalysisCopyright Tapan Bagchi 24Several different types of Experimental plans (designs) are available to the design engineerFactorial, Fractional, Central Cuboid, etc. Taguchi used Orthogonal DesignsCCenterSScreeningFFactorialOOrthogonalFFFractional factorialFocus: Handle many factorsOutput: List of Important Factors, Best Settings, Good designCopyright Tapan Bagchi 25Full Factorial Array Example: The 23(8-trial) array1 2 3 4 5 6 71 1 1 1 1 1 11 1 1 2 2 2 21 2 2 1 1 2 21 2 2 2 2 1 12 1 2 1 2 1 22 1 2 2 1 2 12 2 1 1 2 2 12 2 1 2 1 1 2C B -BC A -AC -AB -ABCFull Factorial Factor Assignments to Experimental Array ColumnsSuch experiments can find all Main & two- and three-factor InteractionsArray Columns ResponseACBCopyright Tapan Bagchi 26The L8Orthogonal Array Example: Taguchi used these1 2 3 4 5 6 71 1 1 1 1 1 11 1 1 2 2 2 21 2 2 1 1 2 21 2 2 2 2 1 12 1 2 1 2 1 22 1 2 2 1 2 12 2 1 1 2 2 12 2 1 2 1 1 2C B D A E F GOrthogonal Array Factor Assignments to Experimental ColumnsSuch experiments can find all 7 Main effects.Array Columns ResponseAFD B EC GCopyright Tapan Bagchi 27Taguchis Orthogonal Experimental Plan7 Factors (A, B, C, D, E, F and G) may potentially influence the production of defective tilesCopyright Tapan Bagchi 28Calculation of Factor EffectsCopyright Tapan Bagchi 29Main Effects of Process Factors on %Defects in TilesCopyright Tapan Bagchi 30Alternative Design Notations for Orthogonal ArraysStd. Fisher's Original Yates Group Theory TaguchiOrder A B C A B C A B C1 1 0 0 0 1 1 12 + a 1 0 0 2 1 13 + b 0 1 0 1 2 14 + + ab 1 1 0 2 2 15 + c 0 0 1 1 1 26 + + ac 1 0 1 2 1 27 + + bc 0 1 1 1 2 28 + + + abc 1 1 1 2 2 2X1X2 X3X1X2 X3Copyright Tapan Bagchi 31Taguchis OA-based Experimental Design Matrix NotationTotal Number of Runs( )kNL 2Number of Levels per FactorNumber of FactorsCopyright Tapan Bagchi 32Linear Graphs for the L8ArrayLinear graphs guide assignment of factors to L8columns12345671234567 Main effects are assigned to columns at nodes in the graph. Interactions are assigned to the columns on the lines.Copyright Tapan Bagchi 33Some Orthogonal Array DesignsClassical(2-level Factorials)Taguchi23242526-327-123-1=L427-4=L8215-11=L16L12L18L27See Montgomery (1997), Design and Analysis of Experiments, P. 631Copyright Tapan Bagchi 34Taguchi Orthogonal Array Tables 2-level (fractional factorial) arrays L4(23). L8(27), L16(215). L32(231), L64(263) 2-level array L12(211) (Plackett-Burman Design) 3-level arrays L9(34). L27(313), L81(340) 4-level arrays L16(45). L64(421) 5-level array L25(56) Mixed-level arrays L18(21x37), L32(21x49), L50(21x511) L36(211x312), L36(23x313), L54(21x325)Copyright Tapan Bagchi 35Comments on Taguchi Arrays Taguchi designs are large screening designs Assumes most interactions are small and those that arent are known ahead of time. Taguchi claims that it is possible to eliminate interactions either by correctly specifying the response and design factors or by using a sliding setting approach to those factor levels. Doesnt guarantee that we get highest resolution design. Instead of designing the experiment to investigate potential interactions, Taguchi prefers to use three-level factors to estimate curvatureCopyright Tapan Bagchi 36Taguchis Robust Design Experiments Taguchi advocated usinginner and outer arraydesigns to take into account noise factors (outer)

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