Robust Design Integrated Product and Process Development MeEn 475/476 “Great Product, Solid, and just always works.” - CNET user review of MacBook Pro

Objectives 1.Define Robust Design 2.Explore how it fits in the context of product and process development 3.Identify why people do robust design 4.Learn how to do robust design 2

Main Conceptual Message 3 Noise – Uncontrolled variations that may affect performance; such as manufacturing variations or operating conditions. Robust Product (or process) – performs as intended even in the presence of noise. Robust Design – product development activity of improving desired performance while minimizing the effect of noise.

Motorola Razr 4

Class Challenge 5 Your Design Output (Functionality, Performance) Noise Factors Control Factors

Team 31, for example 6 Your Design Drilling Rate (in/min) Speed of Turn Soil Type Down Pressure Pump Flow Pump Pressure

Main Conceptual Message 7 Objective Function = F(x) + G(y) Design Option 1 = F(X1) + G(Y2) Design Option 2 = F(X2) + G(Y1)

Main Conceptual Message 8 Robust Design Methodology 1. Identify control factors, noise factors, performance metrics 2. Formulate an objective function 3. Develop an experimental plan 4. Run the experiment 5. Conduct the analysis 6. Select and confirm designs 7. Reflect and repeat

An I/O look at design… 9 ? F(x), G(y)

Simple Example 1.Geometry 2.Material 3.Loading ? Known or derived from Functional Specification

Simple Example 1.Geometry 2.Material 3.Loading ? Vertical Deflection at Tip, Safety Factor on Yield due to Bending,

Vertical Deflection at Tip, Safety Factor on Yield due to Bending, Simple Example 1.Geometry 2.Material 3.Loading

Simple Example Fixed Factors Control Factors Vertical Deflection at Tip, Safety Factor on Yield due to Bending,

Important Observation #1 Observation: More than one combination of b and h satisfy the performance metrics

Terminology Setpoint – a particular set of values for input parameters Any guesses on which setpoint is most robust ?

Important Observation #2 Observation: Transmission of noise to the performance model may vary with different setpoints

Comparing two Setpoints 17

Terminology Review Noise – Uncontrolled variations that may affect performance; such as manufacturing variations or operating conditions. Robust Product (or process) – performs as intended even in the presence of noise.

Terminology Review Robust Design – product development activity of improving desired performance while minimizing the effect of noise. 1.Where does Robust Design fit in the product development process? 2.What benefits could come from Robust Design?

How to do Robust Design Geometry Material Loading Noise ? Known or derived from Functional Specification What factors are needed to evaluate the performance metrics? What are the things we want to measure regarding the design’s performance? Do we want to maximize, minimize, hit a target, or some combination thereof?

More on Performance Metrics We have known differentiable equations Single variable cases Multiple variable cases We have known non-differentiable equations We have time-consuming equations or experiments

Single Variable Case Transmission of Noise

Single Variable Case Transmission of Noise

Single Variable Case Form an Objective Function Problem Objective Hit the Target Deflection While keeping the Safety Factor at or above 1 Subject to Traditional Optimization Robust Design Optimization

Would result in…

Multiple Variable Cases Transmission of Noise Assumptions Independent variables Variation in x is small Objectives and constraints are differentiable

Non-differentiable Equations Monte Carlo Simulation 1.Generate a large number slightly differing setpoints 2.Execute performance metrics for each generated setpoint 3.Characterize the mean and standard deviation of the execution data

Monte Carlo Simulation Results 28

Time Consuming Eqs or Experiments

Response Surface Methodology Select a starting design Run a screening experiment Build a response surface model Optimize Refine response surface

Screening Design Number of runs Full Factorial: R = 3 F Box Behnken: R = 2*F Example: 12 factors 531,441 runs for Full Factorial 289 runs for Box Behnken

Screening Model

C = 73.20% C = 71.89% Theoretical Experimental Does RD really work? C = 73.20% C = 71.89% Theoretical Experimental Weight, B. L., Mattson, C. A., Magleby, S. P., and Howell, L. L., “Configuration Selection, Modeling, and Preliminary Testing in Support of Constant Force Electrical Connectors,” ASME Journal of Electronic Packaging. Only a small percentage of contacts were tested due to manufacturing variations

Does RD really work? C = 98.02% F avg = 0.83 N C = 73.20%

Does RD really work? Optimized Percentage Monte Carlo Average Percentage Monte Carlo Standard Deviation Previous Work Case 1 Case %91.94%1.66% 98.02%94.84%2.57% 73.20%66.98%2.04%

Class Objectives and Summary 1.What is Robust Design? 2.How it fits in the context of product and process development? 3.What benefits could come from robust design? 4.How do we do robust design? 36

Class Objectives and Summary 1.What is Robust Design? 2.How it fits in the context of product and process development? 3.What benefits could come from robust design? 4.How do we do robust design? 37

Class Objectives and Summary 1.What is Robust Design? 2.How it fits in the context of product and process development? 3.What benefits could come from robust design? 4.How do we do robust design? 38

Class Objectives and Summary 1.What is Robust Design? 2.How it fits in the context of product and process development? 3.What benefits could come from robust design? 4.How do we do robust design? 39