Lecture 09 Multiattribute Utility Theory: Example Application … · Lecture Outline 1 3D Printing...

3D Printing ApplicationExample: Light Switch Cover Plate

Project 1

Lecture 09Multiattribute Utility Theory:

Example Application Design and Manufacturing

Jitesh H. Panchal

ME 597: Decision Making for Engineering Systems Design

Design Engineering Lab @ Purdue (DELP)School of Mechanical Engineering

Purdue University, West Lafayette, INhttp://engineering.purdue.edu/delp

September 19, 2019ME 597: Fall 2019 Lecture 09 1 / 27

http://engineering.purdue.edu/delp


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Lecture Outline

1 3D Printing Application

2 Example: Light Switch Cover Plate1. Assessing the Multi-attribute Utility Function2. Choosing Alternative based on the Utility Function

3 Project 1

Fernandez, M.G., Seepersad, C.C., Rosen, D.W., Allen, J.K., and Mistree, F., 2005, “DecisionSupport in Concurrent Engineering – The Utility-Based Selection Decision Support Problem,”,Concurrent Engineering, Vol. 13, No. 1, 13-27.

ME 597: Fall 2019 Lecture 09 2 / 27


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3D Printing Processes

FDM: Fused Deposition Modeling

Polyjet

SLA: Stereolithography

SLS: Selective Laser Sintering

DMLS: Direct Metal Laser Sintering

ME 597: Fall 2019 Lecture 09 3 / 27


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Fused Deposition Modeling (FDM)

Fused Deposition Modeling is an additive manufacturing process which isused to build concept models, functional prototypes and end-use parts withengineering-grade and high accuracy thermoplastics. The FDM technology isdesigned to create with production-grade thermoplastic materials thatpossess the most mechanical, thermal and chemical strength.

Source: http://proto3000.com/fdm-thermoplastic-materials.phpME 597: Fall 2019 Lecture 09 4 / 27


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Stereolithography (SLA)

Stereolithography is one of the most advanced and accurate rapidprototyping technologies, which is most ideal for concept modeling,fit-form-function testing and a variety of molding techniques. In an SLAprocess, the laser is capable of fusing metal, plastic, glass and ceramicparticles into a 3D Printed model. Offering a variety of different colouredmaterials, SLA is an ideal technology for economical and rapid 3D printing.

Source: http://proto3000.com/sla-photopolymer-materials.phpME 597: Fall 2019 Lecture 09 5 / 27


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Diverse Applications of 3D Printing

Concept Modeling

Display Parts Finishing

Fastening and Gluing

Fit and Form Testing

Functional Testing

Heat Resistance Testing

Manufacturing-Tooling

Medical and Dental Tooling

Rubber Part Testing

Shape Changing

Surface Improvement

ME 597: Fall 2019 Lecture 09 6 / 27


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1. Assessing the Multi-attribute Utility Function2. Choosing Alternative based on the Utility Function

Example: Light Switch Cover Plate Assembly

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Systems Realization Laboratory

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11Motivation«

Testing Snap-Fits on a Light Switch Cover Plate Assembly

Primary Goals for Rapid Prototyping in this

example«

¸ Functional Product Validation

¸ Determining closeness of fit/tolerance of the

two interfacing components

¸ Obtaining a basic feel for the product

¸ Visual and physical confirmation of 3D

interface integrity

Challenge:

Resource Selection

¸ Choosing a suitable RP Material and

Process Combination

Producing a Rapid Prototype that closely

resembles the final production part

¸ Functional behavior

¸ Geometry

ß Detail

ß Accuracy

Objectives of the Prototype:

functional product validation, particularly with respect tothe snap-fitting of components,

determining closeness of fit or tolerance of the twointerfacing components,

obtaining a feel for the product, and

visual and physical confirmation of 3D interface integrity

ME 597: Fall 2019 Lecture 09 7 / 27


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Identifying Attributes

1 Tensile strength: The strength of the material under tension2 Young’s modulus: The modulus of elasticity of the material3 Flexural strength: The strength of the material under bending4 Flexural modulus: The modulus of flexural stiffness of the material5 Detail capability: The ability to reproduce the part in sufficient detail.6 Accuracy: The ability to reproduce the part with sufficient accuracy

(maintaining dimensional requirements)7 Elongation at break8 Hardness9 Density

10 Heat Deflection11 Durability12 Build Time13 Cost

ME 597: Fall 2019 Lecture 09 8 / 27


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Assessment Procedure for Multiattribute Utility Functions

1 Introducing the terminology and ideas.2 Identifying relevant independence assumptions.3 Assessing conditional utility functions or isopreference curves.4 Assessing the scaling constants.5 Checking for consistency and reiterating.

Refer to Lecture 8.

ME 597: Fall 2019 Lecture 09 9 / 27


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Step 2: Identifying Relevant Independence Assumptions

Goal: To simplify utility assessment.

Determine whether one (or more) of these conditions is (are) satisfied.1 Preferential Independence2 Conditional Utility Independence3 Mutual Utility Independence4 Additive Independence

Rest of the slides are based on the assumption that Additive Independencecondition is satisfied, i.e.,

U(x1, x2, . . . , xN) =N∑

i=1

kiui(xi)

Refer to Lectures 7 and 8.

ME 597: Fall 2019 Lecture 09 10 / 27


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Step 3: Assessing Conditional Utility Functions, ui(xi)

Procedure:1 Preparing for assessment2 Identifying the relevant qualitative characteristics3 Specifying quantitative restrictions4 Choosing a utility function5 Checking for consistency

Refer to Lecture 6.

ME 597: Fall 2019 Lecture 09 11 / 27


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Step 3: Assessing Conditional Utility FunctionsQualitative Characteristics

Attribute: Tensile Strength

Monotonicity: Non-monotonic. Utility is maximum at the target value.

Lower Unacceptable: 50 MPa

Ideal: 65 MPa

Upper Unacceptable: 75 MPa

Risk attitude: Risk averse

ME 597: Fall 2019 Lecture 09 12 / 27


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Step 3: Assessing Conditional Utility FunctionsQuantitative Characteristics

The chosen functional form: u(x) = a + bx + cedx

For this function, the risk measure,

r(x) = −u′′(x)u′(x)

= − d2edx(bc+ dedx

)

Question

Under which conditions does this function model risk aversion?

ME 597: Fall 2019 Lecture 09 13 / 27


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Tensile Strength:

Lower Unacceptable: 50 MPa

Ideal: 65 MPa

Upper Unacceptable: 75 MPa

Split the utility function into two partsand set scale:

Left Side Utility Function:

uL(50) = 0, uL(65) = 1

Right Side Utility Function:

uR(65) = 1, uR(75) = 0

50 60 70 80

0

0.2

0.4

0.6

0.8

1

Left Hand Side

Right Hand Side

x : Tensile Strength

u(x)

ME 597: Fall 2019 Lecture 09 14 / 27


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Lottery question 1:

〈50, 0.5, 65〉 ∼ x0.5

Say answer is: x0.5 = 54.43

45 50 55 60 65 70

0

0.2

0.4

0.6

0.8

1


u(x)

Lottery question 2:

〈50, 0.5, 54.43〉 ∼ x0.25


45 50 55 60 65 70

0

0.2

0.4

0.6

0.8

1


u(x)

ME 597: Fall 2019 Lecture 09 15 / 27


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Lottery question 3:

〈54.43, 0.5, 65〉 ∼ x0.75


45 50 55 60 65 70

0

0.2

0.4

0.6

0.8

1


u(x)

Curve Fit: u(x) = a + bx + cedx

uL(x) = 1.022− 2981e−0.16x

45 50 55 60 65 70

0

0.2

0.4

0.6

0.8

1


u(x)

ME 597: Fall 2019 Lecture 09 16 / 27


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uL(x) = 1.022− 2981e−0.16x

uR(x) = 2.018− 0.01103e0.06934x

50 60 70 80

0

0.2

0.4

0.6

0.8

1

uL(x) uR(x)


u(x)

ME 597: Fall 2019 Lecture 09 17 / 27


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Step 4: Assessing the Scaling Constants

Additive Multi-attribute Utility Function,

U(x1, x2, . . . , xN) =N∑

i=1

kiui(xi)

Approach: To find ki , use indifference questions such as:

(TS0,YM0.55,FS0.55,FM0.55,DC0.55,A0.55)

∼

( TS? ,YM0.45,FS0.45,FM0.45,DC0.45,A0.45)

Need (N − 1) such questions to estimate ki .

Note: This is not a lottery question.ME 597: Fall 2019 Lecture 09 18 / 27


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Step 4: Assessing the Scaling ConstantsOutcome

Attribute k -valueTensile Strength k1 = 0.193741Young’s Modulus k2 = 0.1864461Flexural Strength k3 = 0.189041Flexural Modulus k4 = 0.1922651Detail Capability k5 = 0.1563661Accuracy k6 = 0.0821421

ME 597: Fall 2019 Lecture 09 19 / 27


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Identify Alternatives

Process-Material Combinations:1 SLA250 with DSM7110 (by DSM Somos R©)2 SLA3500 with SL7510 (by Vantico AG)3 SLA3500 with DSM8120 (by DSM Somos R©)4 FDM1650 with P400 (by Stratasys Inc.)5 MJM2100 with TJ75 (by 3D Systems)

ME 597: Fall 2019 Lecture 09 20 / 27


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Probability Distributions of Attributes for an AlternativeExample: SLA250-DSM7110

Tensile Strength

40 50 60 70 80

0

1

2

3

4

·10−2

x : Tensile Strength (MPa)

p(x)

:P

DF

Young’s Modulus

1,600 1,800 2,000 2,200 2,400 2,600

0

0.5

1

1.5

·10−3

x : Young’s Modulus (MPa)p(

x):

PD

F

Determine these for each attribute for each alternative!

ME 597: Fall 2019 Lecture 09 21 / 27


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Evaluate the Expected Utility for Each Alternative

For the additive multi-attribute utility function,

U(x1, x2, . . . , xN) =N∑

i=1

kiui(xi)

The expected utility,

E [U(x1, x2, . . . , xN)] =N∑

i=1

kiE [ui(xi)]

Therefore, first calculate the expectation of the single-attribute utilityfunctions, and then scale them.

ME 597: Fall 2019 Lecture 09 22 / 27


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Tensile Strength for SLA250-DSM7110

40 50 60 70 80

0

1

2

3

4

·10−2

x : Tensile Strength (MPa)

p(x)

:P

DF

50 60 70 80

0

0.2

0.4

0.6

0.8

1

uL(x) uR(x)


u(x)

E [u(x)] =∫

p(x)u(x)dx

Denote this as: E [u1(TS)]

ME 597: Fall 2019 Lecture 09 23 / 27


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Expected Utility for an Alternative:

E [U(x1, x2, . . . , xN)] =N∑

i=1

kiE [ui(xi)]

=k1E [u1(TS)] + k2E [u2(YM)]

+ k3E [u3(FS)] + k4E [u4(FM)]

+ k5E [u5(DC)] + k6E [u6(A)]

ME 597: Fall 2019 Lecture 09 24 / 27


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Results: Expected Utility

Alternative Expected UtilitySLA250-DSM7110 0.62214SLA3500-SL7510 0.44195SLA3500-DSM8120 0FDM1650-P400 0MJM2100-TJ75 0

Choose the alternative with the maximum expected utility!

ME 597: Fall 2019 Lecture 09 25 / 27


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Project 1: Decision Making Using Expected Utility Theory

Learning Objective: To improve understanding of multi-attribute utility theorythrough application in a engineering design/manufacturing context.

Tasks:1 Identify a decision situation related to your area of expertise/interest.2 Frame one decision by identifying objectives, attributes, and alternatives.3 Assess multi-attribute utility function by following the steps listed in

Slide 9.4 For each alternative, quantify the uncertainty (probability distributions)

associated with achieving each attribute.5 Evaluate the expected utility of each alternative, and identify the most

preferred alternative.

Submit your report by October 20th, 2019.

ME 597: Fall 2019 Lecture 09 26 / 27


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Summary

1 3D Printing Application

2 Example: Light Switch Cover Plate1. Assessing the Multi-attribute Utility Function2. Choosing Alternative based on the Utility Function

3 Project 1

Reading material: Fernandez, M.G., Seepersad, C.C., Rosen, D.W., Allen,J.K., and Mistree, F., 2005, “Decision Support in Concurrent Engineering –The Utility-Based Selection Decision Support Problem,”, ConcurrentEngineering, Vol. 13, No. 1, 13-27.

ME 597: Fall 2019 Lecture 09 27 / 27

Lecture 09 Multiattribute Utility Theory: Example Application … · Lecture Outline 1 3D Printing...

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