Report

Quality Improvement: from Autos and Chips to Nano and Bio C. F. Jeff Wu School of Industrial and Systems Engineering Georgia Institute of Technology • 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? 1 Shewhart’s Paradigm • 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. Toyota GM UC L Sample Mean 25.0 22.5 UC L _ _ _ X X 20.0 LC L 17.5 15.0 LC L 1 2 3 4 5 6 7 8 Sample 9 10 11 12 13 14 15 2 Shewhart’s Paradigm • 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. 1 22 1 UC L Sample Mean 21 20 _ _ X 19 LC L 18 1 3 5 7 9 11 13 15 17 19 21 23 Sample 3 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 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 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 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 Variation Reduction through Robust Parameter Design Robust Parameter Design Traditional Variation Reduction Control X=X1→ X=X X=X21 Noise Variation (Z) Response Variation (Y) Y=f(X,Z) 8 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 Robust optimization of the output voltage of nanogenerators (b) (a) 2 µm (c) RL 0 z -42 mV 0 mV -7 -14 -21 -28 -35 -42 Nano Research 2010 (Stat-Material work at GT) 10 Experimental Design Control factors Noise factor 11 New setting is more robust Mean Value of Electrical Pulses (mV) 40 120nN,30 137nN,40 µm/s µm/s 30 20 10 0 0 10 20 30 Number of Scans 40 50 12 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 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. 14 Paper Feeder Example Two failure modes • Misfeed : fails to feed a sheet • Multifeed: Feeds more than one sheet 15 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 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. misfeed 0 operating window l multifeed 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. 17 Taguchi’s Two-Step Procedure N1: 1 0 N2: 0 1 2 2 N3: 0 3 3 Operating window • 1. Find a control factor setting to maximize the signal-to-noise ratio = −log 1 21 =1 1 =1 2 , where N1, N2,… represent noise factor conditions. 2. Adjust OW factor to the middle of the operating window. • But the method lacks a sound justification. 18 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 Factors and Levels Control factors Feed belt material Speed Drop height Center roll Width Guidance angle Tip angle Turf Noise factors Stack quantity Notation A B C D E F G H 1 Type A 288 3 Absent 10 0 0 0 Levels 2 Type B 240 2 Present 20 14 3.5 1 3 192 1 30 28 7 2 N Full Low - Joseph-Wu, 2004, Technometrics Data, courtesy of Dr. K. Tatebayashi of Fuji-Xerox. 20 21 Optimization Analysis led to new design with wider operating window. misfeed new multifeed old 22 Examples of Operating Window Factors Process/ Product Failure or defect type 1 2 Operating window factor Wave soldering Voids Bridges Temperature Resistance welding Under weld Expulsion Time Image transfer Opens Shorts Exposure energy Threading Loose Tight Depth of cut Picture printing Black Blur Water quantity 23 Robust Parameter Design With Feedback Control • To develop a unified and integrated approach to obtain the best control strategy using parameter design. RPD with feedfoward control, Joseph (2003, Technometrics). Dasgupta and Wu, 2006, Technometrics 24 Offline and Online Reduction of Variation Strategies for minimizing effect of noise on output Robust parameter design (One-time activity; Limited applicability) Process Adjustment (Continuous activity; Wider applicability) Feedforward Control Measure the noise Change adjustment factor Feedback Control Measure the output Change adjustment factor 25 Feedback Control with Control and Noise Factors Process dynamics Control factors: X1, X2, .., Xp Noise factors: N1, N2, .., Nq FIND OPTIMAL SETTINGS OF : Process disturbance OUTPUT: Yt = b(X,N,Ct-1 ,Ct-2 , …) + zt X1, X2, .., Xp PARAMATERS OF f Output error: et = Yt - target Adjustment Factor: Ct CONTROL EQUATION : Ct = f(et, et-1, …) Functional form 26 An Example: the Packing Experiment 50.4 50.3 50.2 50.1 X (14 control factors) N (material composition) 50 49.9 49.8 49.7 49 46 43 40 37 34 31 28 25 22 19 16 13 7 10 4 1 49.6 Sampled bag weight (Y) = 49.5 lb Target weight = 50 lb 38.05 lb Main (course) feed = 38 lb Dribble (fine) feed = 12 lb 11.95 lb error = 49.5-50 = -0.5 lb C=0 C = 0.05 -C = kI (-0.5) = (0.1 ) (-0.5) = -0.05 lb 27 Results and Benefits • Optimum combination selected using plots and fitted model. AFTER ... BEFORE ... 50 45 40 35 30 25 20 15 10 5 0 20 10 0 49.70 49.78 49.86 49.94 50.02 50.10 50.18 50.26 50.34 50.42 Prior to experimentation s = 0.121 30 Frequency Frequency 30 20 10 0 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 What was achieved s = 0.031 (Dasgupta et al. 2002) 49.6 49.7 49.8 49.9 50.0 50.1 50.2 50.3 50.4 50.5 What could have been achieved s = 0.0159 28 In-Process Quality Improvement (IPQI) (Deming’s QC Philosophy) Quality Management Concept Evaluation Design Manufacturing Measurement End Product Shipping (SPC Techniques) (Designed Experiments) IPQI Approach developed by Jan Shi (GT), IPQI slides courtesy of Shi 29 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 Manifestation of a single fault M3 Z Y C3 Fault Pattern Fault P1 X C1 C2 P2 M1 P1 P2 P: Pin C: Clamp M: Measurement point M2 O C1 O O C2 O C3 O O Engineering analysis by rigid body motion 31 Fusion of Knowledge and Data Principal Component Analysis (PCA) Relationship between PCA and Fixture Fault Pattern 32 Other Engineering Examples of IPQI Manufacturing Process Statistical methods Engineering knowledge Tonnage signature analysis in forming Wavelet analysis Time and frequency information due to press and die design Wafer profile modeling and Gaussian Process model analysis in wire slicing Dynamics 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 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 Effects of Warpage on Solder Bump Fatigue • PWB samples can have different initial warpage or can be flat. ─ PWBA warpage can be either convex or concave as shown below: Convex Up (+) Concave Up (-) • Two packages (27x27-mm, 35x35-mm) ─ Each package placed at three different locations: Location 1 Location 2 Location 3 Tan-Ume-Hung-Wu, 2010, IEEE Tran. Advanced Packaging 35 Factors studied in Finite Element Method (FEM) • Factors: wmax maximum initial PWB 2105.3, 3076.6, 3824.0 warpage at 25C (mm) wshape warpage shape +1: Convex up; -1 Concave up dp package dimension (mm) 27 by 27, 35 by 35 lp ms location of package (mm) solder bump material Center, 60-30, Outmost Sn-Pb, Lead-free N f = fatigue life estimation of solder bumps (cycles) 84 FEM runs were conducted. 36 Experimental Study of Solder Bump Fatigue Reliability Affected by Initial PWB Warpage Objective: To verify and correlate 3-D finite element simulation results. PWB with 3535 mm PBGA at Location 2 Accelerated Thermal Cycling Test PWB with 3535 mm PBGA at Location 4 Standard Thermal Cycling Profile 37 2600 2400 1600 1800 2000 2200 FEM Simulations 1400 (Cycle) Fatigue life y Experimental Data 2800 FEM Simulation vs Experimental Study -4000 -2000 0 2000 maximum angle PWB warpage 4000 38 Integration of FEM and Physical Data • Use kriging to model the FEM data: Nˆ k ( x) 1101.6 ( x)T 1 ( Nout 1101.6I ), where = FEM output data. • Calibrate the fitted model with experimental data, leading to = 1830.3 − 540max + = 2931.9 − 540max + Ψ −1 − 1101.6 where = fatigue life prediction, max = maximum initial PWB warpage at 25C. 39 Validation of Kriging Model • Compare experimental fatigue life with kriging model prediction under four untried settings. Outperforms FEM prediction. Max. Initial Warpage Case across PWB at Room Temp. (mm) PBGA Dimensio n (mm) Distance from PBGA Center to Board Center (mm) Fatigue Experimenta Life from l Fatigue Predictio Difference Life n Model (Cycles) (Cycles) 1 -1.833 27 27 67 2633 2750 -4.3 % 2 -2.013 27 27 30 2465 2625 -6.1 % 3 -2.171 35 35 67 2507 2400 4.4 % 4 -2.425 35 35 30 2277 2250 1.2 % 40 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 Nanopowder Manufacturing Scale-up Flow Controller Nanomiser Atomizer ® Flame Filter Pump Goal: 1kg/day to 1000kg/day Challenges: • Nano-metrology analysis for process control • Variation propagation in multistage manufacturing process • Process control capability Solution Powder Collection & Dispersion System Atomizing Engineering Gas knowledge Data Control cost Predictive Model Development Statistical Model Calibration Quality Indices Control & Evaluation Jan Shi Lab 42 Stem Cell Biomanufacturing Stem Cell Biology Applications Manufacturing of diagnostic platforms & regenerative therapies from stem cells Isolation Pluripotent Multipotent Unipotent Reprogramming Efficient, scalable & robust technologies 43 http://stemcelligert.gatech.edu 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 Geometrical interpretation of the failing P2 M3 Z C3 Y X C1 C2 M1 P1 M2 P2 The relationships of variations among sensing data due to locator P2 failure: FP2 d(P2 , P1 ) Where 1 d(P1 ,M1 ) 2 d(P1 , M2 ) 3 d(P1 , M3 ) - STD at Mi 2 - STD of faults d(a,b) - distance 45