Design of Experiments (DOE) in New Product Design & Development

Transcription

1 Design of Experiments (DOE) in New Product Design & Development 31 st Annual International Test & Evaluation Symposium 7 October 2014 Arlington, VA 14-DFSSLE-10A Air Academy Associates Office: Fax:

2 Purpose of this Presentation: to debunk the myth that Design of Experiments (DOE) cannot or should not be used in New Product Design and Development Page 2

3 Key Points Concept of a Transfer Function Relationship Between DOE and Transfer Functions Examples of DOE-generated Transfer Functions in R&D Design Techniques Using Transfer Functions Expected Value Analysis Parameter (Robust) Design DOE in Modeling and Simulation Page 3

4 Transfer Function: The Bridge to Innovation X 1 Parameters or Factors that Influence the CTC X 2 X 3 Process y (CTC) ŷ = f 1 (x 1, x 2, x 3 ) ŝ = f 2 (x 1, x 2, x 3 ) Where does the transfer function come from? Exact transfer Function Approximations - DOE - Historical Data Analysis - Simulation Page 4

5 Exact Transfer Functions Engineering Relationships - F = ma - V = IR 9V x R 1 R 2 The equation for current (I) through this DC circuit is defined by: The equation for magnetic force at a distance X from the center of a solenoid is: N H 2 V I R1 R2 R R r x V ( R1 R R R 1 (.5 x) ) r 2.5 x (.5 x) 2 r where N: total number of turns of wire in the solenoid : current in the wire, in amperes r : radius of helix (solenoid), in cm : length of the helix (solenoid), in cm x : distance from center of helix (solenoid), in cm H: magnetizing force, in amperes per centimeter Page 5

6 Design of Experiments (DOE) An optimal data collection methodology Interrogates the process Used to identify important relationships between input factors and outputs Identifies important interactions between process variables Can be used to optimize a process Changes I think to I know Page 6

7 What is a Designed Experiment? Purposeful changes of the inputs (factors) in order to observe corresponding changes in the output (response). A = X 1 Inputs B = X 2 C = X 3 D = X 4... PROCESS Y 1 Y 2... Outputs Run X 1 X 2 X 3 X 4 Y 1 Y Y S Y Page 7

8 DOE Helps Determine How Inputs Affect Outputs i) Factor A affects the average of y A 1 A 2 ii) Factor B affects the standard deviation of y y B 1 B 2 iii) Factor C affects the average and the standard deviation of y y C 2 C 1 iv) Factor D has no effect on y y D 1 = D 2 y Page 8

9 What Makes DOE so Powerful? (Orthogonality: both vertical and horizontal balance) A Full Factorial Design for 3 Factors A, B, and C, Each at 2 levels: Run A B C AB AC BC ABC Page 9

10 Famous Quote All experiments (tests) are designed; some are poorly designed, some are well designed. George Box ( ), Professor of Statistics, DOE Guru Page 10

11 Design of Experiments (DOEs): A Subset of All Possible Test Design Methodologies The Set of All Possible Test Design Methodologies (Combinatorial Tests) One Factor At a Time (OFAT) Boundary Value Analysis (BVA) Best Guess (Oracle) Orthogonal or Nearly Orthogonal Test Designs (DOEs) Equivalence Partitioning (EP) Page 11

12 Motivation for DOE from Dr. Gilmore (DOT&E) 1. One of the most important goals of operational testing is to characterize a system s effectiveness over the operational envelope. 2. I advocate the use of DOE to ensure that test programs are able to determine the effect of factors on a comprehensive set of operational mission-focused and quantitative response variables. 3. Future test plans must state clearly that data are being collected to measure a particular response variable (possibly more than one) in order to characterize the system s performance by examining the effects of multiple factors and clearly delineating what statistical model (e.g., main effects and interactions) is motivating the variation of the test. 4. Confounding factors must be avoided. 5. Another pitfall to avoid is relying on binary metrics as the primary response variable. Page 12

13 Value Delivery: Reducing Time to Market for New Technologies INPUT OUTPUT Pitch ) (0, 15, 30) Roll ) (0, 15, 30) Modeling Flight W1F ) (-15, 0, 15) Characteristics Six Aero- W2F ) W3F ) (-15, 0, 15) (-15, 0, 15) of New 3-Wing Aircraft Characteristics Patent Holder: Dr. Bert Silich Total # of Combinations = 3 5 = 243 Central Composite Design: n = 30 Page 13

14 Aircraft Equations C L = (P) (P) +.012(R) -.043(WD1) -.117(WD2) +.185(WD3) +.010(P)(WD3) -.042(R)(WD1) +.035(R)(WD2) +.016(R)(WD3) +.010(P)(R) -.003(WD1)(WD2) -.006(WD1)(WD3) C D = (P) (P) -.004(WD1) -.013(WD2) +.013(WD3) +.002(P)(R) -.004(P)(WD1) -.009(P)(WD2) +.016(P)(WD3) -.004(R)(WD1) +.003(R)(WD2) +.020(WD1) (WD2) (WD3) 2 C Y = -.006(P) -.006(R) +.169(WD1) -.121(WD2) -.063(WD3) -.004(P)(R) +.008(P)(WD1) -.006(P)(WD2) -.008(P)(WD3) -.012(R)(WD1) -.029(R)(WD2) +.048(R)(WD3) -.008(WD1) 2 C M = (P) (P) -.007(R) +.024(WD1) +.066(WD2) -.099(WD3) -.006(P)(R) +.002(P)(WD2) -.005(P)(WD3) +.023(R)(WD1) -.019(R)(WD2) -.007(R)(WD3) +.007(WD1) (WD2) (WD1)(WD2) +.002(WD1)(WD3) C YM =.001(P) +.001(R) -.050(WD1) +.029(WD2) +.012(WD3) +.001(P)(R) -.005(P)(WD1) -.004(P)(WD2) -.004(P)(WD3) +.003(R)(WD1) +.008(R)(WD2) -.013(R)(WD3) +.004(WD1) (WD2) (WD3) 2 C e =.003(P) +.035(WD1) +.048(WD2) +.051(WD3) -.003(R)(WD3) +.003(P)(R) -.005(P)(WD1) +.005(P)(WD2) +.006(P)(WD3) +.002(R)(WD1) Page 14

15 Leak Repair Clamp Process Clamp Size (8,24) Radial Gap (.045,.090,.135) Temperature (90, 180) Repair Clamp Cycles to failure Bolt Tension/Torque (7.5K, 30K) Page 15

16 Repair Clamp Regression Results Transfer Function: y = B-583C+525BC, B=Radial Gap C=Temperature Page 16

17 Response Value Surface Plot of the Transfer Function cycles until failure Y-hat Surface Plot Radial Gap vs Temp Constants: Clamp = 16 Torque = Temp Radial Gap Page 17

18 Contour Plot cycles until failure Y-hat Contour Plot Radial Gap vs Temp Constants: Clamp = 16 Torque = Temp Radial Gap Page 18

19 Fusing Titanium and Cobalt-Chrome Courtesy Rai Chowdhary Page 19

20 Case Study: OnTech Self-Heating Container Identify Key Features (VOC) Self-heating Activated by button on bottom of can Used for hot beverages and soups Disposable Environmentally compatible Air Academy Associates Do Not Reproduce. Page 20

21 Case Study: General Design Concept Beverage Design Convection Energy release Calcium Oxide (CaO) Water for reaction Point of activation Page 21

22 Case Study: Transfer Functions Example: Time to use and Can temp as a function of Wall thickness, CaO mass, and H 2 O volume Design Wall thickness (X1) CaO mass (X2) H 2 0 volume (X3) Y1=f 1 (X1, X2, X3) Y2=f 2 (X1, X2, X3) Time to use (Y1) Can temp (Y2) How do we find the functions f 1 and f 2? First principle equations (Physics / Engineering equations) Analytical Models (Simulation and Regression) FEA, CFD, etc. Empirical models (Design of Experiments) Page 22

23 The Value of Transfer Functions Simple and compact way of understanding relationships between performance measures or response variables (Y s) and the factors (X s) that influence them. Allows us to Predict the response variable (y), with associated risk levels, before any change in the product or process is made. Assess the product/process capability in the presence of uncontrolled variation or noise using Monte Carlo Simulation (DFSS tool: Expected Value Analysis). Understand the impact of the factors (sensitivity analysis) Optimize performance easily using DFSS tools such as parameter design and tolerance allocation. Greatly enhance one s knowledge of a product or process. In general, they are the gateway to systematic innovation. Provide a meaningful metric for the maturity in DFSS for any organization. Page 23

24 Expected Value Analysis (EVA) EVA is the technique used to determine the characteristics of the output distribution (mean, standard deviation, and shape) when we have knowledge of (1) the input variable distributions and (2) the transfer functions. X 1 y 1 = f 1 (X 1, X 2, X 3 ) y 1 X 2 X 3 y 2 = f 2 (X 1, X 2, X 3 ) y 2 Variation in the inputs causes variation in the output. Page 24

25 Expected Value Analysis Example y = f(x) 6 2 x y = x 2? What is the mean or expected value of the y (output) distribution? What is the shape of the y (output) distribution? Page 25

26 Expected Value Analysis Example (Cycle Time) S1 S2 S3 T Step 1 Step 2 Step 3 Total Time = S1 + S2 + S hrs 1 3 hrs hrs Spec/Goal: Complete in <= 16 hrs The simulated results are shown on the next page. What is the expected value (mean) of the total cycle time? What is the shape of the output distribution? Approximately what percent of the time will it take longer than 16 hours to complete all 3 steps? Page 26

27 Expected Value Analysis Example (Cycle Time) (EVA Results) Page 27

28 Parameter Design (Robust Design) Y X 1 1 LSL USL X 2 2 Y Process of finding the optimal mean settings of the input variables to minimize the resulting dpm. X 1 X 2 new init init new LSL USL Page 28

29 Parameter Design (Robust Design) T If you re the designer, which setting for X do you prefer? X 1 X 2 X T Changing the mean of an input may possibly reduce the output variation! X 1 X 2 X Page 29

30 Robust Design Simulation* Example Plug Pressure (20-50) Bellow Pressure (10-20) Ball Valve Pressure ( ) Nuclear Reservoir Level Control Process Reservoir Level ( ) Water Temp (70-100) * From SimWare Pro by Philip Mayfield and Digital Computations Page 30

31 Prior to Robust Design (defect rate is 61%) Page 31

32 After Robust Design (defect rate is %) Page 32

33 Applications of Modeling and Simulation Automotive Simulation of stress and vibrations of turbine assembly for use in nuclear power generation Power Simulation of underhood thermal cooling for decrease in engine space and increase in cabin space and comfort Evaluation of dual bird-strike on aircraft engine nacelle for turbine blade containment studies Electronics Aerospace Evaluation of cooling air flow behavior inside a computer system chassis Page 33

34 Multidisciplinary Design Optimization (MDO): A Design Process Application Page 34

35 Summary of "Modeling the Simulator" Perform Screening Design Using the Simulator if necessary Perform Modeling Design Using the Simulator to Build Low Fidelity Model Perform Expected Value Analysis, Robust Design, and Tolerance Allocation Using Transfer Function Validate Design Using the Simulator Critical Parameters ID'd Transfer Function on Critical Parameters Optimized Design Optimized Simulator Build Prototype to Validate Design in Real World Page 35

36 Thank You Questions Colorado Springs, Colorado 2104 Air Academy Associates, LLC. Do Not Reproduce. Page 36

37 Examples of Computer Aided Engineering (CAE) and Simulation Software Mechanical motion: Multibody kinetics and dynamics ADAMS DADS Implicit Finite Element Analysis: Linear and nonlinear statics, dynamic response MSC.Nastran, MSC.Marc ANSYS Pro MECHANICA ABAQUS Standard and Explicit ADINA Explicit Finite Element Analysis : Impact simulation, metal forming LS-DYNA RADIOSS PAM-CRASH, PAM-STAMP General Computational Fluid Dynamics: Internal and external flow simulation STAR-CD CFX-4, CFX-5 FLUENT, FIDAP PowerFLOW Page 37

38 Examples of High Fidelity Simulation Models Preprocessing: Finite Element Analysis and Computational Fluid Dynamics mesh generation ICEM-CFD Gridgen Altair HyperMesh I-deas MSC.Patran TrueGrid GridPro FEMB ANSA Postprocessing: Finite Element Analysis and Computational Fluid Dynamics results visualization Altair HyperMesh I-deas MSC.Patran FEMB EnSight FIELDVIEW ICEM CFD Visual3 2.0 (PVS) COVISE Page 38

39 Applying Modeling and Simulation to Automotive Vehicle Design IDENTIFY CTCs, CDPs Many, Many x s SCREENING DESIGN (DOE PRO) The critical few CDP s Examples of CTCs: NASTRAN RADIOSS MADYMO Safety CTCs with constraints specified by FMVSS (Federal Motor Vehicle Safety Standards) no federal requirements on these CTCs y 1 = weight of vehicle y 2 = cost of vehicle y 3 = frontal head impact y 4 = frontal chest impact y 5 = toe board intrusion y 6 = hip deflection y 7 = rollover impact y 8 = side impact y 9 = internal aerodynamics (airflow) y 10 = external aerodynamics (airflow) y 11 = noise y 12 = vibration (e.g., steering wheel) RADIOSS DYNA MADYMO CFD y 13 = harshness (e.g., over bumps, shocks) Integrated processes with high fidelity CAE analyses on HPC servers Examples of Critical Design Parameters (CDPs or Xs): NASTRAN x 1 = roof panel material x 2 = roof panel thickness x 3 = door pillar dimensions i beam x 4 = shape/geometry x 5 = windshield glass x 6 = hood material, sizing and thickness x 7 = under hood panel material, sizing and thickness t 2 t 1 y 14 = durability (at 100K miles) Page 39

40 Applying Modeling and Simulation to Automotive Vehicle Design (cont.) MODELING DESIGN (DOE PRO) CDPs MONTE CARLO SIMULATION (DFSS MASTER) CDPs, CTCs Robust Designs VALIDATION NASTRAN RADIOSS MADYMO High Fidelity Models Response Surface Models Low Fidelity Models NASTRAN RADIOSS MADYMO High Fidelity Models Page 40

41 GEMS LightSpeed TM CT Scanner GE's First DFSS System ('98): Full Use of Six Sigma/DFSS Tools Key customer CTQs identified - Image quality - Speed - Software reliability - Patient comfort Disciplined systems approach: 90 system CTQs 33 Six Sigma (DMAIC) or DFSS projects/studies Scorecard-driven Part CTQs verified before systems integration Leading-Edge Technology World's first 16-row CT detector Multi-slice data acquisition 64-bit RISC computer architecture Long-life Performix TM tube Head Abdomen Results Better image quality - Earlier, more reliable diagnoses - New applications; vascular imaging, pulmonary embolism, multi-phase liver studies, Much faster scanning: - Head: from 1 min to 19 sec (9 million/yr) - Chest/abdomen: from 3 min to 17 sec (4 million/yr) Clinical productivity up 50% 10x improvement in software reliability Patient comfort improved shorter exam time Development time shortened by 2 years High market share; significant margin increase "Biggest breakthrough in CT in a decade," Gary Glazer, Stanford Page 41

42 Sample of Who Has Used Our DFSS Methods and Tools Page 42