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1 C. F. Jeff Wu School of Industrial and Systems Engineering Georgia Institute of Technology Quality Improvement: from Autos and Chips to Nano and Bio Legacies of Shewhart and Deming. Quality improvement via robust parameter design: Taguchi’s origin in manufacturing. Extensions of RPD: operating windows and feedback control. Incorporation of physical knowledge/data. Advanced manufacturing: new concept/paradigm?

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Developed statistical process control (SPC) to quickly detect if a process is out of control. Classify process variability into two types. Common (chance) causes: natural variation, in control. Shewhart’s Paradigm 2

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Developed statistical process control (SPC) to quickly detect if a process is out of control. Classify process variability into two types. Common (chance) causes: natural variation, in control. Special (assignable) causes: suggests process out of control. Shewhart’s Paradigm 3

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Walter Shewhart American physicist, mathematician, statistician. Developed SPC while working for Western Electric (Bell Telephone). Original 1924 work in one page memo, 1/3 of which contains a control chart. Background: to tackle manufacturing variation. SPC should be viewed more as a scientific methodology, than a charting technique. Deming was introduced to Shewhart in 1927; was tremendously influenced by the SPC methodology; Deming’s key insight: Shewhart’s SPC can also be applied to enterprises; this led to his later work and big impact in quality management. 4

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Deming’s Statistical Legacies As Shewhart, Deming was a physicist, mathematician, statistician. He studied statistics with Fisher and Neyman in 1936. He edited the book “Statistical Method from the Viewpoint of Quality Control” in 1939. He devised sampling techniques used in the 1940 Census, developed the Deming-Stephan algorithm, an early work on iterative proportional fitting in categorical data. His bigger impact in quality management started with his visits and lectures in Japan in 1950’s. 5

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Design of Experiments (DOE) If a process is in control but with low process capability, use DOE to further reduce process variation. Pioneering work by Fisher, Yates, Finney, etc. before WWII. DOE in industries was widely used after the war; George Box’s work on Response Surface Methodology. Genichi Taguchi’s ( ) pioneering work on robust parameter design. Paradigm shift: use DOE for variation reduction, which is the major focus of my talk. 6

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Robust Parameter Design Statistical/engineering method for product/process improvement (G. Taguchi), introduced to the US in mid-80s. Has made considerable impacts in manufacturing (autos and chips); later work in other industries. Two types of factors in a system: – control factors: once chosen, values remain fixed; – noise factors: hard-to-control during normal process or usage. Parameter design: choose control factor settings to make response less sensitive (i.e. more robust) to noise variation; exploiting control-by-noise interactions. 7

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Y=f(X,Z) Noise Variation (Z)Response Variation (Y) Control X=X 1 Y=f(X,Z) Noise Variation (Z) Control X=X 1 Response Variation (Y) Traditional Variation Reduction Variation Reduction through Robust Parameter Design 8

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Shift from Traditional Strategy Emphasis shifts from location effect estimation to dispersion effect estimation and variation reduction. Control and noise factors treated differently: C×N interaction treated equally important as main effects C and N, which violates the effect hierarchy principle. This has led to a different/new design theory. Another emphasis: use of performance measure, including log variance or Taguchi’s idiosyncratic signal-to-noise ratios, for system optimization. Has an impact on data analysis strategy. 9

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20 (b) 0 mV -42 -21 -14 -28 -35 -7 0 20 µm -42mV x y z 2 µm (a) RLRL (c) Robust optimization of the output voltage of nanogenerators Nano Research 2010 (Stat-Material work at GT) 10

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Experimental Design 11 Control factors Noise factor

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New setting is more robust µ µ 12

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Further Work Inspired by Robust Parameter Design Two examples: The method of operating windows to widen the designer’s capability. RPD combined with feedback control, both offline and online adjustments. 13

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14 Method of Operating Window (OW) Operating window is defined as the boundaries of a critical parameter at which certain failure modes are excited. Originally developed by D. Clausing (1994 and earlier) at Xerox, Taguchi (1993). Approach: ̵Identify a critical parameter: low values of which lead to one failure mode and high values lead to the other failure mode. ̵Measure the operating window at different design settings. ̵Choose a design to maximize the operating window.

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15 Paper Feeder Example Two failure modes Misfeed : fails to feed a sheet Multifeed: Feeds more than one sheet

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Standard Approach Feed, say, 1000 sheets at a design setting; observe # of misfeeds and # of multifeeds; repeat for other settings; choose a design setting to minimize both. Problems: require large number of tests to achieve good statistical power; difficult to distinguish between different design settings; conflicting choice of levels (settings that minimize misfeeds tend to increase multifeeds). 16

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17 OW Approach in Paper Feeder Example Stack force is a critical parameter and is easy to measure. A small force leads to misfeed and a large force leads to multifeed. misfeedoperating window multifeed 0 l u stack force (l, u): operating window Stack force: operating window factor No clear boundaries separating the failure modes Can be defined with respect to a threshold failure rate: l = force at which 50% misfeed occurs, u = force at which 50% multifeed occurs.

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N1: 0 0 0 N2: N3: Operating window Taguchi’s Two-Step Procedure 18

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A Rigorous Statistical Approach to OW Under some probability models for the failure modes and a specific loss function, Joseph-Wu (2002) showed that a rigorous two-step optimization leads to a performance measure similar to Taguchi’s SN ratio. The procedure also allows modeling and estimation, in addition to design optimization. See the illustration with paper feeder experiment. 19

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Factors and Levels Joseph-Wu, 2004, Technometrics Data, courtesy of Dr. K. Tatebayashi of Fuji-Xerox. 20

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Optimization old new misfeedmultifeed Analysis led to new design with wider operating window. 22

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23 Examples of Operating Window Factors Process/ Product Failure or defect type 1 2 Operating window factor Wave soldering VoidsBridgesTemperature Resistance welding Under weld ExpulsionTime Image transferOpensShortsExposure energy ThreadingLooseTightDepth of cut Picture printing BlackBlurWater quantity

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24 Robust Parameter Design With Feedback Control Dasgupta and Wu, 2006, Technometrics To develop a unified and integrated approach to obtain the best control strategy using parameter design. RPD with feedfoward control, Joseph (2003, Technometrics).

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25 Strategies for minimizing effect of noise on output Robust parameter designProcess Adjustment Feedforward ControlFeedback Control (One-time activity; Limited applicability) (Continuous activity; Wider applicability) Offline and Online Reduction of Variation Measure the noise Change adjustment factor Measure the output Change adjustment factor

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26 Control factors: Noise factors: X 1, X 2,.., X p Adjustment Factor: N 1, N 2,.., N q CtCt CONTROL EQUATION : C t = f(e t, e t-1, …) OUTPUT: Y t = (X,N,C t-1,C t-2, …) + z t Process dynamics Process disturbance Output error: e t = Y t - target Feedback Control with Control and Noise Factors Functional form FIND OPTIMAL SETTINGS OF : X 1, X 2,.., X p PARAMATERS OF f

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27 An Example: the Packing Experiment Target weight = 50 lb Main (course) feed = 38 lb Dribble (fine) feed = 12 lb C = 0 X (14 control factors) N (material composition) Sampled bag weight (Y) = 49.5 lb error = 49.5-50 = -0.5 lb -C = k I (-0.5) = (0.1 ) (-0.5) = -0.05 lb C = 0.05 38.05 lb 11.95 lb

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28 Results and Benefits Optimum combination selected using plots and fitted model. Prior to experimentation s = 0.121 What was achieved s = 0.031 (Dasgupta et al. 2002) What could have been achieved s = 0.0159

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In-Process Quality Improvement (IPQI) Manufacturing Design Measurement End Product Shipping Concept Evaluation Quality Management (Designed Experiments) (SPC Techniques) (Deming’s QC Philosophy) IPQI Approach developed by Jan Shi (GT), IPQI slides courtesy of Shi 29

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Example of IPQI: Knowledge-based Diagnosis for Auto Body Assembly 1. Engineering: Hierarchical Structure Model of Assembly Product/Process 2. Statistical: Correlation, clustering, hypothesis testing 30

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Manifestation of a single fault P: Pin C: Clamp M: Measurement point 31 Engineering analysis by rigid body motion

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Fusion of Knowledge and Data Principal Component Analysis (PCA) Relationship between PCA and Fixture Fault Pattern 32

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Other Engineering Examples of IPQI Manufacturing ProcessStatistical methodsEngineering knowledge Tonnage signature analysis in forming Wavelet analysisTime and frequency information due to press and die design Wafer profile modeling and analysis in wire slicing Gaussian Process modelDynamics model of wire slicing operations On-line bleeds detection in continuous casting Imaging feature extraction and design of experiments Mechanism of bleeds formation in casting Variation modeling and analysis for multistage wafer manufacturing Data mining and probability network modeling System layout and system design information 33

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From Knowledge to Data: Physical-Statistical Modeling Simulation experiments have been widely used in lieu of physical experiments. The latter are more expensive, time-consuming or only observed when events like flooding suddenly happen. SE can be an indispensible tool in quality improvement, especially for paucity of physical data or low failure rates. Example: validation of finite element experiment with limited physical data in fatigue life prediction of solder bumps in electronic packaging of chips. 34

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35 Convex Up (+) Concave Up (-) Effects of Warpage on Solder Bump Fatigue Tan-Ume-Hung-Wu, 2010, IEEE Tran. Advanced Packaging PWB samples can have different initial warpage or can be flat. ─ PWBA warpage can be either convex or concave as shown below: Two packages (27x27-mm, 35x35-mm) ─ Each package placed at three different locations: Location 1 Location 2Location 3

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36 Factors studied in Finite Element Method (FEM) Factors: = fatigue life estimation of solder bumps (cycles) maximum initial PWB warpage at 25 C (mm) 2105.3, 3076.6, 3824.0 warpage shape+1: Convex up; -1 Concave up package dimension (mm) 27 by 27, 35 by 35 location of package (mm)Center, 60-30, Outmost solder bump materialSn-Pb, Lead-free 84 FEM runs were conducted.

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37 Objective: To verify and correlate 3-D finite element simulation results. PWB with 35 35 mm PBGA at Location 2 PWB with 35 35 mm PBGA at Location 4 Standard Thermal Cycling Profile Accelerated Thermal Cycling Test Experimental Study of Solder Bump Fatigue Reliability Affected by Initial PWB Warpage

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38 FEM Simulation vs Experimental Study maximum PWB warpage Fatigue life (Cycle) FEM Simulations Experimental Data

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39 Integration of FEM and Physical Data

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40 Validation of Kriging Model Case Max. Initial Warpage across PWB at Room Temp. (mm) PBGA Dimensio n (mm) Distance from PBGA Center to Board Center (mm) Fatigue Life from Predictio n Model (Cycles) Experimenta l Fatigue Life (Cycles) Difference 1-1.833 27 27 6726332750-4.3 % 2-2.013 27 27 3024652625-6.1 % 3-2.171 35 35 67250724004.4 % 4-2.425 35 35 30227722501.2 % Compare experimental fatigue life with kriging model prediction under four untried settings. Outperforms FEM prediction.

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Challenges in Advanced Manufacturing Typical features: small volume, many varieties, high values. Recent example: additive manufacturing (3D printing). Parts made-on-demand as in battle fields. Situation more extreme than run-to-run control in semi-conductor industries. Scalable manufacturing process: from lab, to pilot, to mass scale production; bio-inspired materials (next slides). What new concepts and techniques are needed to tackle these problems? More use of comp/stat modeling and simulations. What else? 41

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Nanopowder Manufacturing Scale-up Atomizer Control cost Engineering knowledge Data Statistical Model Calibration Control & Evaluation Quality Indices Predictive Model Development Jan Shi Lab Challenges: Nano-metrology analysis for process control Variation propagation in multi- stage manufacturing process Process control capability Goal: 1kg/day to 1000kg/day 42

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http://stemcelligert.gatech.edu ApplicationsStem Cell Biology Efficient, scalable & robust technologies Reprogramming Isolation Manufacturing of diagnostic platforms & regenerative therapies from stem cells Pluripotent Multipotent Unipotent Stem Cell Biomanufacturing 43

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Summary Remarks Quality management has made major economical and societal impacts. Quality engineering is the lesser known cousin. It has helped improve quality and reduce cost; witness the revival of US auto industries. Statistical design of experiments has a glorious history: agriculture, chemical, manufacturing, etc. Wider use of product/system simulations is expected in hi-tech applications. Further development requires new concepts and paradigm not found in traditional work. 44

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Geometrical interpretation of the failing P 2 The relationships of variations among sensing data due to locator P 2 failure: 45

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