Post on 16-Oct-2020
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
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
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
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
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!