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Robust Design & Prototyping

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PlanningPlanning

Robust Design and Quality in the Product Development Process

ConceptDevelopment

ConceptDevelopment

System-LevelDesign

System-LevelDesign

DetailDesignDetail

DesignTesting andRefinement

Testing andRefinement

ProductionRamp-Up

ProductionRamp-Up

Quality efforts aretypically made here,when it is too late.

Robust Conceptand System

Design

Robust Parameter

Design

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Definition of Robust Design

A robust product (process) performs as intended even under non-ideal conditions such as manufacturing process variations or a range of operating situations.

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Goals for Designed Experiments

ModelingUnderstanding relationships between

design parameters and product performance

Understanding effects of noise factors Optimizing

Reducing product or process variationsOptimizing nominal performance

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Robust DesignsA robust product or process performs correctly, even in the presence of noise factors.

Noise factors may include: parameter variations environmental changes operating conditions manufacturing variations

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Robust Design Example: Seat Belt Experiment- Submarining Problem

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Who is the better target shooter?

Sam John

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Who is the better target shooter?

Sam John

Sam can simply adjust his sights.

John requires lengthy training.

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Exploiting Non-Linearity to Achieve Robust Performance

Response = fA (A) + fB (B)What level of factor B gives the robust response?How do we use factor A?

Response toFactor AfA

A1 B2B1

fBResponse to

Factor B

A2

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Five Steps of DOE based Robust design process

To develop a robust design through DOE, seven steps are suggested:1- Identify control factors, noise factors, and performance metrics2- Formulate an objective function3- Develop the experimental plan4- Run the experiment5- Conduct the analysis6- Select and confirm factor set-points7- Reflect and repeat

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Robust Design Procedure Step 1: Parameter Diagram

Step 1: Select appropriate controls, response, and noise factors to explore experimentally.

Control factors (input parameters) Noise factors (uncontrollable) Performance metrics (response)

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The P Diagram

Productor

Process

Noise Factors

Control Factors Performance Metrics

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Parameter Diagram

PassengerRestraint Process

Control Factors Performance Metrics

Noise Factors

Belt webbing stiffnessBelt webbing frictionLap belt force limiterUpper anchorage stiffnessBuckle cable stiffnessFront seatback bolsterTongue frictionAttachment geometry

Shape of rear seatType of seat fabricSeverity of collisionWear of componentsPositioning of passengerPositioning of belts on bodySize of passengerType of clothing fabricWeb manufacturing variationsLatch manufacturing variations

Back angleSlip of buttocksHip rotationForward knee motion

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Example: Brownie Mix Control Factors

Recipe Ingredients (quantity of eggs, flour, chocolate)

Recipe Directions (mixing, baking, cooling) Equipment (bowls, pans, oven)

Noise Factors Quality of Ingredients (size of eggs, type of oil) Following Directions (stirring time, measuring) Equipment Variations (pan shape, oven temp)

Performance Metrics Taste Testing by Customers Sweetness, Moisture, Density

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Robust Design Procedure Step 2: Objective Function

Step 2: Define an objective function (of the response) to optimize.

maximize desired performance minimize variations target value signal-to-noise ratio ->measure robustnessTaguchi formula for signal-to-noise:A ratio with desired response in the numerator and

the variance of the response as denominator

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Types of Objective Functions

Smaller-the-Bettere.g. variance

= 1/2

Larger-the-Bettere.g. performance

= 2

Nominal-the-Beste.g. target= 1/(t)2

Signal-to-Noisee.g. trade-off

= 10log[2/2]

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Robust Design Procedure Step 3: Plan the Experiment

Step 3: Plan experimental runs to elicit desired effects.

Use full or fractional factorial designs to identify interactions.

Use an orthogonal array to identify main effects with minimum of trials.

Use inner and outer arrays to see the effects of noise factors.

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Experiment Design: Full Factorial Consider k factors, n levels each. Test all combinations of the factors. The number of experiments is nk . Generally this is too many experiments, but

we are able to reveal all of the interactions.Expt # Param A Param B

1 A1 B12 A1 B23 A1 B34 A2 B15 A2 B26 A2 B37 A3 B18 A3 B29 A3 B3

2 factors, 3 levels each:

nk = 32 = 9 trials

4 factors, 3 levels each:

nk = 34 = 81 trials

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Experiment Design: Fractional Factorial A small fraction of the full factorial. It is still balance. This means that for the several

trials at any given factor level, each of the other factors is tested at every level the same number of times.

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Experiment Design:

Fractional Factorial

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Experiment Design: Orthogonal Array Smallest fractional factorial plan. Taguchi popularized it. Consider k factors, n levels each. Test all levels of each factor in a balanced way. The number of experiments is order of 1+k(n-1). This is the smallest balanced experiment design. BUT main effects and interactions are confounded. Named according the number of rows, L4,L8,L9,L27 and so on.

4 factors, 3 levels each:

1+k(n-1) =

1+4(3-1) = 9 trials

Expt # Param A Param B Param C Param D1 A1 B1 C1 D12 A1 B2 C2 D23 A1 B3 C3 D34 A2 B1 C2 D35 A2 B2 C3 D16 A2 B3 C1 D27 A3 B1 C3 D28 A3 B2 C1 D39 A3 B3 C2 D1

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Experiment Design: One Factor at a Time Consider k factors, n levels each. Test all levels of each factor while freezing the

others at nominal level. (And the first trial having all the factors at the nominal level)

The number of experiments is nk+1. BUT this is an unbalanced experiment design.

4 factors, 2 levels each:

nk+1 =

2x4+1 = 9 trials

Expt # Param A Param B Param C Param D1 A2 B2 C2 D22 A1 B2 C2 D23 A3 B2 C2 D24 A2 B1 C2 D25 A2 B3 C2 D26 A2 B2 C1 D27 A2 B2 C3 D28 A2 B2 C2 D19 A2 B2 C2 D3

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Using Inner and Outer Arrays Induce the same noise factor levels for each

combination of controls in a balanced manner

E1 E1 E2 E2F1 F2 F1 F2G2 G1 G2 G1

A1 B1 C1 D1A1 B2 C2 D2A1 B3 C3 D3A2 B1 C2 D3A2 B2 C3 D1A2 B3 C1 D2A3 B1 C3 D2A3 B2 C1 D3A3 B3 C2 D1

inner x outer =L9 x L4 =36 trials

4 factors, 3 levels each:L9 inner array for controls

3 factors, 2 levels each:L4 outer array for noise

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Robust Design Procedure Step 4: Run the Experiment

Step 4: Conduct the experiment. Vary the control and noise factors Record the performance metrics Compute the objective function

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Robust Design Procedure Step 5: Conduct Analysis

Step 5: Perform analysis of means. Compute the mean value of the objective

function for each factor setting. Identify which control factors reduce the

effects of noise and which ones can be used to scale the response. (2-Step Optimization)

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Analysis of Means (ANOM) Plot the average effect of each factor level.

Factor Effects on S/N Ratio

A1

A2

A3

B1

B2

B3C1

C2

C3

D1

D2 D3

10.0

11.0

12.0

13.0

14.0

15.0

Choose the best levels of these factors

Scaling factor?

Prediction of response:E[(Ai, Bj, Ck, Dl)] =

+ ai + bj + ck +dl

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Case Study: Factors and the selected L8 array

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Case Study: Obtained data

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Factor Effects by Analysis of MeanCase Study: Factor effects charts

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Robust Design Procedure Step 6: Select Setpoints

Step 6: Select control factor setpoints. Choose settings to maximize or minimize

objective function. Consider variations carefully. Advanced use: Conduct confirming experiments. Set scaling factors to tune response. Iterate to find optimal point. Use higher fractions to find interaction effects. Test additional control and noise factors.

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Confounding Interactions Generally the main effects dominate the response.

BUT sometimes interactions are important. This is generally the case when the confirming trial fails.

To explore interactions, use a fractional factorial experiment design.

S/N

B1 B2 B3

A1A2A3

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Product Design and Development Karl T. Ulrich and Steven D. Eppinger 2nd edition, Irwin McGraw-Hill, 2000.

Chapter Table of Contents1. Introduction2. Development Processes and Organizations3. Product Planning4. Identifying Customer Needs5. Product Specifications6. Concept Generation7. Concept Selection8. Concept Testing9. Product Architecture10. Industrial Design11. Design for Manufacturing12. Prototyping13. Product Development Economics 14. Managing Projects

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PlanningPlanning

Product Development Process

ConceptDevelopment

ConceptDevelopment

System-LevelDesign

System-LevelDesign

DetailDesignDetail

DesignTesting andRefinement

Testing andRefinement

ProductionRamp-Up

ProductionRamp-Up

Prototyping is done throughout the development process.

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Concept Development Process

Perform Economic Analysis

Benchmark Competitive Products

Build and Test Models and Prototypes

IdentifyCustomer

Needs

EstablishTarget

Specifications

GenerateProduct

Concepts

SelectProduct

Concept(s)

Set Final

Specifications

PlanDownstreamDevelopment

MissionStatement Test

ProductConcept(s)

DevelopmentPlan

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Prototyping Example: Apple PowerBook Duo Trackball

Trackball

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Four Uses of Prototypes Learning

answering questions about performance or feasibility

e.g., proof-of-concept model Communication

demonstration of product for feedback e.g., 3D physical models of style or function

Integration combination of sub-systems into system model e.g., alpha or beta test models

Milestones goal for development teams schedule e.g., first testable hardware

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Physical vs. Analytical PrototypesPhysical Prototypes

Touchable approximation of the product.

May exhibit unmodeled behavior.

Some behavior may be an artifact of the approximation.

Often best for communication.

Analytical Prototypes Mathematical model of the

product. Can only exhibit behavior

arising from explicitly modeled phenomena. (However, behavior is not always anticipated.

Some behavior may be an artifact of the analytical method.

Often allow more experimental freedom than physical models.

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Focused vs. Comprehensive Prototypes

Focused Prototypes Implement one or a few

attributes of the product.

Answer specific questions about the product design.

Generally several are required.

Comprehensive Prototypes Implement many or all

attributes of the product. Offer opportunities for

complex testing. Often best for milestones

and integration.

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Alpha and Beta Prototypes

Alpha Prototypes Early Prototypes are usually built

with production-intent parts- parts with the same geometry and material properties as intended for the production version but not necessary with the actual processes to be used in the production.

To test if the product will work as designed.

Beta Prototypes Later Prototypes are usually built with

parts supplied by the intended production but not necessary with the intended final assembly process.

Are usually tested by the customers in their own environments.

To answer questions about the performance and reliability.

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Types of Prototypes

ComprehensiveFocused

Physical

Analytical

finalproduct

betaprototype

alphaprototypeballsupport

prototype

simulationof trackball

circuits

equationsmodeling ball

supports

trackball mechanismlinked to circuit

simulation

notgenerallyfeasible

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Boeing 777 TestingBrakes Test Minimum rotor thickness Maximum takeoff weight Maximum runway speed Will the brakes ignite?Wing Test Maximum loading When will it break? Where will it break?

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Comprehensive Prototypes Anticipated benefits of prototype in reducing risk must

be weighted against the prototyping cost

Cost of Comprehensive PrototypeHighLow

Tech

nica

l or M

arke

t Ris

kH

igh

Low

One prototype may be used for verification.

Few or no comprehensiveprototypes are built.

Many comprehensiveprototypes are built.

Some comprehensiveprototypes build (and sold?).

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Four Steps of Planning for Prototyping

In order to plane for prototyping, four steps are suggested:1- Define the purpose of the prototype2- Establish the level of approximation of the prototype3- Outline an experimental plan4- Create and schedule for procurement, construction and testing

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Rapid Prototyping Methods Most of these methods are additive,

rather than subtractive, processes. Build parts in layers based on CAD

model. SLA=Stereolithogrpahy Apparatus SLS=Selective Laser Sintering 3D Printing LOM=Laminated Object Manufacturing Others every year...

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Virtual Prototyping

3D CAD models enable many kinds of analysis: Fit and assembly Manufacturability Form and style Kinematics Finite element analysis (stress, thermal) Crash testing more every year...

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BMW Virtual Crash Test

From: Scientific American, March 1999

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Traditional Prototyping Methods

CNC machining Rubber molding + urethane casting

Materials: wood, foam, plastics, etc. Model making requires special skills.

Slide Number 1Robust Design and Quality in the Product Development ProcessSlide Number 3Goals for Designed ExperimentsRobust DesignsRobust Design Example:Seat Belt Experiment- Submarining ProblemWho is the better target shooter?Who is the better target shooter?Exploiting Non-Linearity to Achieve Robust PerformanceSlide Number 10Robust Design ProcedureStep 1: Parameter DiagramThe P DiagramParameter DiagramExample: Brownie MixRobust Design ProcedureStep 2: Objective FunctionTypes of Objective FunctionsRobust Design ProcedureStep 3: Plan the ExperimentExperiment Design: Full FactorialExperiment Design: Fractional FactorialExperiment Design: Fractional FactorialExperiment Design: Orthogonal ArrayExperiment Design: One Factor at a TimeUsing Inner and Outer ArraysRobust Design ProcedureStep 4: Run the ExperimentRobust Design ProcedureStep 5: Conduct AnalysisAnalysis of Means (ANOM)Slide Number 27Slide Number 28Slide Number 29Robust Design ProcedureStep 6: Select SetpointsConfounding InteractionsProduct Design and DevelopmentKarl T. Ulrich and Steven D. Eppinger2nd edition, Irwin McGraw-Hill, 2000.Product Development ProcessConcept Development ProcessPrototyping Example:Apple PowerBook Duo TrackballFour Uses of PrototypesPhysical vs. Analytical PrototypesFocused vs. Comprehensive PrototypesAlpha and Beta PrototypesTypes of PrototypesBoeing 777 TestingComprehensive PrototypesAnticipated benefits of prototype in reducing risk must be weighted against the prototyping costSlide Number 43Rapid Prototyping MethodsVirtual PrototypingBMW Virtual Crash TestTraditional Prototyping Methods