Variation Management Framework (VMF)Thomas J. Howard on behalf of theDTU Robust Design Group

How much force to press on a lid?

Robust Design: The Transfer FunctionFunction Parameter (FP)

Design Parameter (DP)

8.0 8.17.9Lid Ø (mm)

Press on Force (N)

10.0

3.8

19.1

10.0

9.8

10.1

Robust Design: The Transfer FunctionFP

DP

10.0

9.8

10.1

Robust Design: The Transfer FunctionFP

DP

θ Sensitivity Metric

VMF Q2: Engineering DesignFP

DP

VMF Q2: Engineering DesignFP

DP

The basis of this target and the limits needs to be transparent

VMF Q1: Product SpecificationFP

DPCustomer

satisfaction (CS)

VMF Q1: Product SpecificationFP

DPCS95% 89% 55%

VMF Q3: Production EngineeringFP

DP

Process Parameter (PP)

CS

MouldTemperature

(°C)

8.2

8.28

8.12

VMF Q3: Production EngineeringFP

DP

PP

CS

The Variation Management Framework (VMF)- as a theoretical framework

FP

DP

PP

CS95% 89% 55%

8.0 8.17.9Lid Ø (mm)

Press on Force (N)

MouldCore Ø (mm)

Perceived Quality (%)

10.0

9.8

10.1

8.2

8.28

8.12Howard, Eifler, Pedersen, Göhler, Murthy & Ebro - "The Variation Management Framework (VMF) for Robust Design”, Journal of Quality Engineering (In Review)

An early representation of the basic VMF framework can befound in Whitney (2004) ”Mechanical Assemblies” describingCost/Risk management.

Using the VMF to position research contributions

FP

DP

PP

CS95% 89% 55%

8.0 8.17.9Lid Ø (mm)

Press on Force (N)

MouldCore Ø (mm)

Perceived Quality (%)

10.0

9.8

10.1

8.2

8.28

8.12

Using the VMF to define the 7 levers and 15 RD principle for variation reduction

3

4

2

FP

PP

CS

Using the VMF to organise Work Packages of our research programme

FP

DP

PP

CS95% 89% 55%

8.0 8.17.9Lid Ø (mm)

Press on Force (N)

MouldCore Ø (mm)

Perceived Quality (%)

10.0

9.8

10.1

8.2

8.28

8.12

The relationship between variation in multiple DPs and multiple functional

performance (FP) parameters

WP2 (PhD 2)WP1 (PhD 1)

The relationship between variation in the FRs and the perceived quality of

the product (Q)

Robust Production and Process Capabilities Data Bases and Design Guide

WP3 (PhD 3)

Product Specification

Assy. Process validation. SOP readiness

Customer

Engineering Design

Production Engineering

Objective Market Requirements

Concept selection

Eng. SpecificationGeometry and assembly process design

Tolerance Optimization

Design Freeze

Tools and equipment design

Tools and equipment ready

Using the VMF to describe the product design and development process

Using the VMF to visualise the role of each department for Design & Production

FP

DP

PP

CS

FP

DP

PP

CSRobustDesign

RobustnessAchievement

No doubt the VMF has been great for educational purposes, but does it have

potential for more?

Can it fit the needs of industry?

Gaining a functional overview

Niels HansenChief Engineer, Device R&D

“We now have a good grasp of kinematics and constraints in our part-part interfaces, but these are not linked to function and it can be difficult to get a good functional overview”

Paraphrased from discussions

Perceived quality loss due to variation

Kevin McCauleyGroup Leader, Dimensional Control

“The biggest unknown in dimensional management is knowing how much quality loss is perceived by the customer”

Paraphrased from discussions

Organising and linking transfer functions

Jesper Kenneth OlsenR & D Engineer

“We model many transfer functions, however we currently have no framework for managing them and the links that occur between transfer functions”

Paraphrased from discussions

Quality across departments

Rikke AndersenSix Sigma Engineer

“Quality needs to be managed through a collaboration between engineering and production, requiring tools, methods and shared KPIs”

Paraphrased from discussions

What you said…https://docs.google.com/forms/d/1ooVveQPQrTaA-NVya0M4fzINtsHWgxU8vNIevN_fwYY/edit#responses

We asked you how much you agreed with the following:1. Silo thinking hinders the ability of our organization to deliver product quality

2. The following is a major cost / opportunity-cost for our organizationa. Uncertainty of customer quality expectationsb. Non-optimal designs and trade-offsc. High product performance variabilityd. Inefficient tolerance allocatione. Scrap of components/assemblies/productsf. Uncertainty of impact of design/production changeg. Unquantified decision making

Can we turn the VMF into an operational tool for increasing robustness in new

product development?

Need to add dimensions!

Θ13 FP3 Θ23-3

Θ12 FP2 Θ22-2 Θ22-3

Θ11 FP1 Θ21-1

CS DP1 DP2 DP3

PP1 Θ31-3

PP2 Θ31-1

PP3 Θ32-2

Seems possible.

Can it map reality?

Case Study – The PenMate

MR3 MR2 MR19,84 6,60 7,10 Nominal

9 6 6 Var

Load

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Forc

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Var Nominal

0,38 3,22 FR7

121,33 200,06 FR4

200,06 FR3121,33

FR269,61 818,36

DP5 DP6 DP7 DP8-a DP8-b DP8-c DP9 DP10-a DP10-b DP11 DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20 DP21 DP22 DP23 DP24 DP25 DP26 DP27 DP37 DP66 DP67Nominal 3,00 0,07 0,07 4,70 14,60 1,55 1,00 38,62 28,83 34,95 11,07 11,06 8,35 12,05 14,80 43,60 43,60 43,60 43,60 0,90 0,90 6,50 6,50 5,60 5,60 2703,00 15,65 0,02 0,00

Tol 0,08 0,01 0,01 0,09 0,14 0,07 0,06 0,19 0,17 0,19 0,13 0,13 0,30 0,26 0,14 0,50 0,50 0,50 0,50 0,05 0,05 0,11 0,11 0,10 0,10 3,00 0,14 0,00 0,00

Nominal

0,003 m2 / DP 6

0,025 m1 / DP66

0,07 Sk2 / DP7

0,07 Sk1 / DP6

0 Tc

0,8 Humidity

21 Temp

10 CT3

100 HP3

90 MT3

6 CT2

95 HP2

70 MT2

5 CT1

120 HP1

60 MT1

0,00-0,02

0,3643,680,000,00

1,190,46

20,20 2772,35 2772,35 10,10 -10,10 -10,10 10,10 -10,10 10,10 -10,10 10,10 10,10 -15321,44 -15321,441,66 22,18 22,18 0,96 -1,40 -0,66 0,57 -1,95 1,77 -1,89 1,28 1,28 -15,32 -15,32

-221,85 4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,37-30,97 2,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,372,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

19,36 12,01 0,07 0,07 0,07 -0,07 -0,07 -0,07 -0,070,15 0,10 0,01 0,01 0,01 -0,01 -0,01 -0,02 -0,02

#DIV/0! -0,068 -0,172 -0,028 -0,018-0,272 -0,341 -0,860 -0,141 -0,0910,021 0,027 0,067 0,011 0,0070,213 0,267 0,674 0,110 0,0710,024 0,030 0,076 0,012 0,0080,024 0,030 0,076 0,012 0,008

-0,051 -0,103 -0,017 -0,011 -0,073 -0,085 -0,105 -0,004 -0,004 -0,004 -0,004 -0,011 -0,011 -0,071 -0,071 -0,061 -0,061 -3,784-0,256 -0,517 -0,084 -0,054 -0,364 -0,427 -0,524 -0,022 -0,022 -0,022 -0,022 -0,054 -0,054 -0,354 -0,354 -0,305 -0,305 -18,921

0,023 0,045 0,007 0,005 0,032 0,037 0,046 0,002 0,002 0,002 0,002 0,005 0,005 0,031 0,031 0,027 0,027 0,946

0,225 0,454 0,074 0,048 0,320 0,375 0,461 0,015 0,015 0,015 -0,004 0,048 0,048 0,311 0,311 0,268 0,268 9,461

0,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 -0,022 0,007 0,007 0,043 0,043 0,037 0,037 0,0810,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 0,005 0,007 0,007 0,043 0,043 0,037 0,037 0,081

-0,056 -0,042 -0,051 -0,016 -0,016 -0,027-0,281 -0,210 -0,254 -0,081 -0,081 -0,1370,036 0,002 0,029 0,010 0,010 0,0120,357 0,024 0,286 0,102 0,102 0,1230,069 0,023 0,027 0,020 0,020 0,0240,069 0,023 0,027 0,020 0,020 0,024

0,001 0,001 0,004 0,000 0,000 0,010 0,007 0,009 0,003 0,003 0,002 0,003 0,004 0,001 0,001 0,001 0,001 0,000 0,000 0,002 0,002 0,001 0,001 0,487 0,0040,004 0,006 0,018 0,002 0,001 0,048 0,036 0,044 0,014 0,014 0,010 0,015 0,019 0,007 0,007 0,007 0,007 0,001 0,001 0,008 0,008 0,007 0,007 2,433 0,0200,000 0,001 0,002 0,000 0,000 0,006 0,004 0,005 0,002 0,002 0,001 0,002 0,002 0,007 0,007 0,007 0,007 0,000 0,000 0,001 0,001 0,001 0,001 0,041 0,0020,009 0,014 0,044 0,005 0,003 0,116 0,086 0,105 0,033 0,033 0,025 0,036 0,044 0,131 0,131 0,131 0,131 0,003 0,003 0,020 0,020 0,017 0,017 0,811 0,0472,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 1,000 1,000 1,000 1,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,0000,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,100 0,100 0,100 0,100 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030

1,0000,070

1,0000,065

1,0000,001

1,0000,001

FP2 : Needle insertion speedFP3 : Mounting torqueFP4 : De-mounting torqueFP7 : Loading force

Product concept

MR DP

Engineering design : Geometry and assembly process

PP

Tools and equipment design and production establishment

VMF Case Study

MR3 MR2 MR19,84 6,60 7,10 Nominal

9 6 6 Var

Load

ing

Forc

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mfor

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Injec

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omfor

t

Ease

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untin

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Var Nominal

0,38 3,22 FR7

121,33 200,06 FR4

200,06 FR3121,33

FR269,61 818,36

DP5 DP6 DP7 DP8-a DP8-b DP8-c DP9 DP10-a DP10-b DP11 DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20 DP21 DP22 DP23 DP24 DP25 DP26 DP27 DP37 DP66 DP67Nominal 3,00 0,07 0,07 4,70 14,60 1,55 1,00 38,62 28,83 34,95 11,07 11,06 8,35 12,05 14,80 43,60 43,60 43,60 43,60 0,90 0,90 6,50 6,50 5,60 5,60 2703,00 15,65 0,02 0,00

Tol 0,08 0,01 0,01 0,09 0,14 0,07 0,06 0,19 0,17 0,19 0,13 0,13 0,30 0,26 0,14 0,50 0,50 0,50 0,50 0,05 0,05 0,11 0,11 0,10 0,10 3,00 0,14 0,00 0,00

Nominal

0,003 m2 / DP 6

0,025 m1 / DP66

0,07 Sk2 / DP7

0,07 Sk1 / DP6

0 Tc

0,8 Humidity

21 Temp

10 CT3

100 HP3

90 MT3

6 CT2

95 HP2

70 MT2

5 CT1

120 HP1

60 MT1

0,00-0,02

0,3643,680,000,00

1,190,46

20,20 2772,35 2772,35 10,10 -10,10 -10,10 10,10 -10,10 10,10 -10,10 10,10 10,10 -15321,44 -15321,441,66 22,18 22,18 0,96 -1,40 -0,66 0,57 -1,95 1,77 -1,89 1,28 1,28 -15,32 -15,32

-221,85 4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,37-30,97 2,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,372,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

19,36 12,01 0,07 0,07 0,07 -0,07 -0,07 -0,07 -0,070,15 0,10 0,01 0,01 0,01 -0,01 -0,01 -0,02 -0,02

#DIV/0! -0,068 -0,172 -0,028 -0,018-0,272 -0,341 -0,860 -0,141 -0,0910,021 0,027 0,067 0,011 0,0070,213 0,267 0,674 0,110 0,0710,024 0,030 0,076 0,012 0,0080,024 0,030 0,076 0,012 0,008

-0,051 -0,103 -0,017 -0,011 -0,073 -0,085 -0,105 -0,004 -0,004 -0,004 -0,004 -0,011 -0,011 -0,071 -0,071 -0,061 -0,061 -3,784-0,256 -0,517 -0,084 -0,054 -0,364 -0,427 -0,524 -0,022 -0,022 -0,022 -0,022 -0,054 -0,054 -0,354 -0,354 -0,305 -0,305 -18,921

0,023 0,045 0,007 0,005 0,032 0,037 0,046 0,002 0,002 0,002 0,002 0,005 0,005 0,031 0,031 0,027 0,027 0,946

0,225 0,454 0,074 0,048 0,320 0,375 0,461 0,015 0,015 0,015 -0,004 0,048 0,048 0,311 0,311 0,268 0,268 9,461

0,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 -0,022 0,007 0,007 0,043 0,043 0,037 0,037 0,0810,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 0,005 0,007 0,007 0,043 0,043 0,037 0,037 0,081

-0,056 -0,042 -0,051 -0,016 -0,016 -0,027-0,281 -0,210 -0,254 -0,081 -0,081 -0,1370,036 0,002 0,029 0,010 0,010 0,0120,357 0,024 0,286 0,102 0,102 0,1230,069 0,023 0,027 0,020 0,020 0,0240,069 0,023 0,027 0,020 0,020 0,024

0,001 0,001 0,004 0,000 0,000 0,010 0,007 0,009 0,003 0,003 0,002 0,003 0,004 0,001 0,001 0,001 0,001 0,000 0,000 0,002 0,002 0,001 0,001 0,487 0,0040,004 0,006 0,018 0,002 0,001 0,048 0,036 0,044 0,014 0,014 0,010 0,015 0,019 0,007 0,007 0,007 0,007 0,001 0,001 0,008 0,008 0,007 0,007 2,433 0,0200,000 0,001 0,002 0,000 0,000 0,006 0,004 0,005 0,002 0,002 0,001 0,002 0,002 0,007 0,007 0,007 0,007 0,000 0,000 0,001 0,001 0,001 0,001 0,041 0,0020,009 0,014 0,044 0,005 0,003 0,116 0,086 0,105 0,033 0,033 0,025 0,036 0,044 0,131 0,131 0,131 0,131 0,003 0,003 0,020 0,020 0,017 0,017 0,811 0,0472,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 1,000 1,000 1,000 1,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,0000,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,100 0,100 0,100 0,100 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030

1,0000,070

1,0000,065

1,0000,001

1,0000,001

FP2 : Needle insertion speedFP3 : Mounting torqueFP4 : De-mounting torqueFP7 : Loading force

MR DP

PP

VMF Case Study

Right now you are probably thinking…Either:“that’s pretty neat, surprised that hasn’t been tried before”

Or:“That looks like a more complicate QFD… and we hate doing QFDs so that’s not going to work”

- Too many DPs in our design- Information not available- Design keeps changing and that matrix

does not seem agile enough to return value (cost vs benefit)

“Too many DPs in our design”

It is very easy to have DPs, Parts and even Sub-assemblies in the same framework. It scales and modularises very easily!

With a kinematics module there can be a simple transition between bodies, parts and surfaces useful for interface and constraints management

MR3 MR2 MR19,84 6,60 7,10 Nominal

9 6 6 Var

Load

ing

Forc

e co

mfor

t

Injec

tion c

omfor

t

Ease

ofmo

untin

g

Var Nominal

0,38 3,22 FR7

121,33 200,06 FR4

200,06 FR3121,33

FR269,61 818,36

DP5 DP6 DP7 DP8-a DP8-b DP8-c DP9 DP10-a DP10-b DP11 DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20 DP21 DP22 DP23 DP24 DP25 DP26 DP27 DP37 DP66 DP67Nominal 3,00 0,07 0,07 4,70 14,60 1,55 1,00 38,62 28,83 34,95 11,07 11,06 8,35 12,05 14,80 43,60 43,60 43,60 43,60 0,90 0,90 6,50 6,50 5,60 5,60 2703,00 15,65 0,02 0,00

Tol 0,08 0,01 0,01 0,09 0,14 0,07 0,06 0,19 0,17 0,19 0,13 0,13 0,30 0,26 0,14 0,50 0,50 0,50 0,50 0,05 0,05 0,11 0,11 0,10 0,10 3,00 0,14 0,00 0,00

Nominal

0,003 m2 / DP 6

0,025 m1 / DP66

0,07 Sk2 / DP7

0,07 Sk1 / DP6

0 Tc

0,8 Humidity

21 Temp

10 CT3

100 HP3

90 MT3

6 CT2

95 HP2

70 MT2

5 CT1

120 HP1

60 MT1

0,00-0,02

0,3643,680,000,00

1,190,46

20,20 2772,35 2772,35 10,10 -10,10 -10,10 10,10 -10,10 10,10 -10,10 10,10 10,10 -15321,44 -15321,441,66 22,18 22,18 0,96 -1,40 -0,66 0,57 -1,95 1,77 -1,89 1,28 1,28 -15,32 -15,32

-221,85 4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,37-30,97 2,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

4,06 4,06 333,43 333,43 15,39 15,39 -53,59 -53,59 0,07 235,372,03 2,03 18,21 18,21 1,63 1,63 -5,40 -5,40 0,22 33,48

19,36 12,01 0,07 0,07 0,07 -0,07 -0,07 -0,07 -0,070,15 0,10 0,01 0,01 0,01 -0,01 -0,01 -0,02 -0,02

#DIV/0! -0,068 -0,172 -0,028 -0,018-0,272 -0,341 -0,860 -0,141 -0,0910,021 0,027 0,067 0,011 0,0070,213 0,267 0,674 0,110 0,0710,024 0,030 0,076 0,012 0,0080,024 0,030 0,076 0,012 0,008

-0,051 -0,103 -0,017 -0,011 -0,073 -0,085 -0,105 -0,004 -0,004 -0,004 -0,004 -0,011 -0,011 -0,071 -0,071 -0,061 -0,061 -3,784-0,256 -0,517 -0,084 -0,054 -0,364 -0,427 -0,524 -0,022 -0,022 -0,022 -0,022 -0,054 -0,054 -0,354 -0,354 -0,305 -0,305 -18,921

0,023 0,045 0,007 0,005 0,032 0,037 0,046 0,002 0,002 0,002 0,002 0,005 0,005 0,031 0,031 0,027 0,027 0,946

0,225 0,454 0,074 0,048 0,320 0,375 0,461 0,015 0,015 0,015 -0,004 0,048 0,048 0,311 0,311 0,268 0,268 9,461

0,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 -0,022 0,007 0,007 0,043 0,043 0,037 0,037 0,0810,031 0,063 0,010 0,007 0,044 0,052 0,063 0,005 0,005 0,005 0,005 0,007 0,007 0,043 0,043 0,037 0,037 0,081

-0,056 -0,042 -0,051 -0,016 -0,016 -0,027-0,281 -0,210 -0,254 -0,081 -0,081 -0,1370,036 0,002 0,029 0,010 0,010 0,0120,357 0,024 0,286 0,102 0,102 0,1230,069 0,023 0,027 0,020 0,020 0,0240,069 0,023 0,027 0,020 0,020 0,024

0,001 0,001 0,004 0,000 0,000 0,010 0,007 0,009 0,003 0,003 0,002 0,003 0,004 0,001 0,001 0,001 0,001 0,000 0,000 0,002 0,002 0,001 0,001 0,487 0,0040,004 0,006 0,018 0,002 0,001 0,048 0,036 0,044 0,014 0,014 0,010 0,015 0,019 0,007 0,007 0,007 0,007 0,001 0,001 0,008 0,008 0,007 0,007 2,433 0,0200,000 0,001 0,002 0,000 0,000 0,006 0,004 0,005 0,002 0,002 0,001 0,002 0,002 0,007 0,007 0,007 0,007 0,000 0,000 0,001 0,001 0,001 0,001 0,041 0,0020,009 0,014 0,044 0,005 0,003 0,116 0,086 0,105 0,033 0,033 0,025 0,036 0,044 0,131 0,131 0,131 0,131 0,003 0,003 0,020 0,020 0,017 0,017 0,811 0,0472,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 1,000 1,000 1,000 1,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,0000,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,100 0,100 0,100 0,100 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030 0,030

1,0000,070

1,0000,065

1,0000,001

1,0000,001

FP2 : Needle insertion speedFP3 : Mounting torqueFP4 : De-mounting torqueFP7 : Loading force

MR DP

PP

CFDFEACAT

MFAPCDB/GMσD

User Studies

“The information is not available”

DOE

“The design keeps changing and the matrix does not seem agile enough to

return value (cost vs benefit)”

Start Q2 by entering the Product Requirements Specification

• RCI (Requirements completeness Index)

• Number of requirements

• Weighting values (a primitive Q1 sensitivity)

• Blank spots

FP to Part Relations

FP to DP developmentFR2 x x ?FR3 ? x x xFR4 x x xFR7 x x x x

DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20FR2 > >FR3 < x xFR4 < x xFR7 > < x x

DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20FR2 > >FR3 -221,8482 4,0566 4,0566FR4 < x xFR7 -0,0736 < x x

DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20

69,61355 818,3569 FR2 10,1020 >121,3275 200,0609 FR3 -221,8482 4,0566 4,0566121,3275 200,0609 FR4 < x 4,0566

0,38455 3,224628 FR7 -0,0736 -0,0736 -0,0736 -0,0736

Limits Nominal DP12 DP13 DP14 DP15 DP16 DP17 DP18 DP19 DP20

Nominal 11,065 11,062 8,35 12,05 14,8 43,6 43,6 43,6 43,6Tolerance 0,126566 0,126555 0,29939 0,261028 0,139598 0,5 0,5 0,5 0,5

The purpose of the VMF for designFP

DP

PP

CSRobustDesign

• Make better trade-off decisions• Reduce perceived quality loss• Identify Coupling• Allocate user studies, simulation

resources and DOEs.• Robustness Optimisation• Allocate Tolerances• Absorb variation with assembly

processes• Decide measurement protocol

and process flexibility

The purpose of the VMF for production

• To adjust controlled parameters to compensate for variations identified by measurements

• To give production control of product performance and not just single dimensions

• To allow predict the product performance based on current PP settings and measurements

FP

DP

PP

CSRobustness

Achievement

Some key features

The total variation of a parameter is equal to the sum of the related contributions in the next quadrant

Sensitivity

Contribution

38

Different ways to derive the (local) sensitivity index

Nominal Range Sensitivity (NRS) 𝑁𝑁𝑁𝑁𝑁𝑁 =∆𝑓𝑓 𝑋𝑋∆𝑥𝑥

Partial derivative 𝑁𝑁𝑖𝑖 =𝜕𝜕𝑓𝑓 𝑋𝑋𝜕𝜕𝑥𝑥𝑖𝑖

Nominal range sensitivity (NRS) relative to perturbation 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 =

𝑓𝑓 𝑥𝑥1, … , 𝑥𝑥𝑖𝑖 � 1 + ∆𝑖𝑖 , … , 𝑥𝑥𝑛𝑛𝑓𝑓 𝑋𝑋 − 1

∆𝑖𝑖

Normalized partial derivative 𝑁𝑁𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚𝑛𝑛 =𝜕𝜕𝑓𝑓 𝑋𝑋𝜕𝜕𝑥𝑥𝑖𝑖

�𝑥𝑥𝑖𝑖𝑓𝑓 𝑋𝑋

Euclidean distance(Robustness radius) 𝑟𝑟𝐸𝐸 = min

𝑋𝑋𝑗𝑗: 𝑓𝑓𝑖𝑖𝑗𝑗 𝑋𝑋𝑗𝑗 =𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 ⋁ 𝑓𝑓𝑖𝑖𝑗𝑗 𝑋𝑋𝑗𝑗 =𝑓𝑓𝑚𝑚𝑖𝑖𝑚𝑚𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑛𝑛𝑛𝑛𝑚𝑚 𝐷𝐷−1 𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑛𝑛𝑛𝑛𝑚𝑚

𝑇𝑇

Reference: Göhler SM, Eifler T, Howard TJ. Robustness Metrics: Consolidating the Multiple Approaches to Quantify Robustness. J Mech Des. 2016; in press (November).

VMF.v1

VMF.v2

Variational contribution and global sensitivity index

Worst-case contribution 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =∆𝑓𝑓 𝑋𝑋∆𝑥𝑥 � (𝑥𝑥𝑈𝑈𝑈𝑈𝑈𝑈 − 𝑥𝑥𝑈𝑈𝑈𝑈𝑈𝑈)/2

Worst-case contribution normalised 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =𝜕𝜕𝑓𝑓 𝑋𝑋𝜕𝜕𝑥𝑥𝑖𝑖

�𝑑𝑑𝑥𝑥𝑖𝑖𝑑𝑑𝑓𝑓

ANOVA HDMR decomposition, based on conditional variance

V y = �i=1

n

Vi + �i=1

n−1

�j=i+1

n

Vij + ⋯+ V12…n

𝑁𝑁𝑖𝑖 =𝑉𝑉𝑖𝑖 𝐸𝐸~𝑥𝑥𝑖𝑖 𝑦𝑦|𝑥𝑥𝑖𝑖

𝑉𝑉 𝑦𝑦

Reference: Göhler SM, Eifler T, Howard TJ. Robustness Metrics: Consolidating the Multiple Approaches to Quantify Robustness. J Mech Des. 2016;in press (November).

VMF.v1

VMF.v2

Output Robustness KPIsYield rate P = Pr 𝐿𝐿𝑁𝑁𝐿𝐿𝑗𝑗 ≤ 𝑓𝑓𝑗𝑗 𝑋𝑋 ≤ 𝑈𝑈𝑁𝑁𝐿𝐿𝑗𝑗|𝐿𝐿𝑁𝑁𝐿𝐿𝑘𝑘≠𝑗𝑗 ≤ 𝑓𝑓𝑘𝑘≠𝑗𝑗 𝑋𝑋 ≤ 𝑈𝑈𝑁𝑁𝐿𝐿𝑘𝑘≠𝑗𝑗| …

VarianceANOVA HDMR decomposition

Variance

Standard Deviation

(for independent variables)

V y = �i=1

n

Vi + �i=1

n−1

�j=i+1

n

Vij + ⋯+ V12…n

𝑉𝑉 𝑦𝑦 = � 𝑓𝑓 𝑋𝑋 − 𝐸𝐸 𝑦𝑦 2 � 𝑝𝑝 X 𝑑𝑑X

σ = V = � f X − E y 2 � p X dX

𝑉𝑉 𝑓𝑓 𝑋𝑋 = �𝑖𝑖=1

𝑁𝑁𝜕𝜕𝑓𝑓𝜕𝜕𝑥𝑥𝑖𝑖

2

𝜎𝜎𝑖𝑖2

Product Robustness Index (PRI)𝑈𝑈𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑓𝑓 𝑉𝑉𝑉𝑉𝑟𝑟𝑐𝑐𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑉𝑉𝑉𝑉𝑟𝑟𝑐𝑐𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑁𝑁𝑉𝑉𝑐𝑐𝑅𝑅𝑅𝑅

Reference: Göhler SM, Eifler T, Howard TJ. Robustness Metrics: Consolidating the Multiple Approaches to Quantify Robustness. J Mech Des. 2016;in press (November).

RDD15

VMF Software(beta version due end of 2016)

• The matrix will not be for data entry but will be one of several front-end views

• Sensitivities will not be single values but instead based on transfer functions to allow for the modelling of interaction effects.

• For contribution a Monte-Carlo plug-in will be used with surrogate models pulled from various other software for the transfer functions.

Cases

1. Pen Mate

2. Vaavud Wind Reader

3. Radiometer MEGA VMF Project

3.1. VMF StructureBuilding a VMF Software demonstrator to model existing Sensor currently in trial production setting

3.2. VMF Build MethodologyIncremental and radial redesign of BGA using the VMF to manage, guide and evaluate robustness throughout the process

Closing statementWe believe, but with open minds, that:

• A VMF can be created for any product

• It is possible to have a net benefit at every stage of the build process of the VMF and we will know the robustness of our designs like never before.

• When implemented, it will mean that project members from all disciplines will face the same direction with respect to achieving product quality.

?

What Next?• After lunch, meet down stairs in s09 for the workshop at 13:15

• Your team number is indicated on you name badge – please sit at your allocated table with your team.

• We will be tightly packed into the room so don’t spread out!

• Enjoy your lunch!