(microsoft powerpoint - tillf\366rlitlighet variation och rdm.ppt
TRANSCRIPT
CHALMERS
Välkomna!till workshop
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till workshop
ROBUST KONSTRUKTIONSMETODIK FÖR ÖKAD TILLFÖRLITLIGHET
-Tillförlitlighet och variation
CHALMERS
Tillförlitlighet, variation
och robusthet
Bo Bergman SKF Professor
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robusthet
Bo BergmanSKF Professor Quality SciencesDivision of Quality Sciences
Chalmers University of Technology
SE-412 96 Gothenburg, Sweden
Phone: +46 31 772 8180
E-mail: [email protected]
CHALMERS
The Kano Model
CustomerSatisfaction
Expected
Attractive
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Degree offulfilment
Must – be
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History (industry)
AssemblyIntegrationSpecialisation
ProcessLearningVariation
OrganizationContinuous Improvement
JapanisationQuality Drivenorganisationdevelopemnt
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Japanese Export
. . . . .
ManyDialects..Six SigmaLean…
Quality Drivenorganizationdevelopment
S D
PA
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Demings Profound Knowledge +
• Understanding Variation– Not only handling and reduction
• Psychology – Not only individual but also organisation and social
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– Not only individual but also organisation and social
• Knowledge Theory– How knowledge determines what we can observe and interpret, and how new knowledge is created
• Systems Thinking– The Complexity Growth
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The World is full of Variation
• Big Bang (from variation, a quantum fluctuation, and in
variation)
• Physical Reality (Thermodynamics, Statistical
mechanics, Quantum Mechanics)
• Biological Reality (Evolution: Replication and
Facts about the world:
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• Biological Reality (Evolution: Replication and
Increased and reduced variation)
• Humans and Human Artefacts (We find
variation everywhere!)
CHALMERS
Reliability and Safety-
must be qualityCustomer
Satisfaction
Expected
Attractive
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Degree offulfilment
Must – be
CHALMERS
Why do we have failures?
Due to variation!
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CHALMERS
Reliability in a World Full of Variation
Variation: For good and for bad
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Without VariationNo World!Life is Variation!
Variation CreatesProblems:- Deviations- Disturbances- Noise
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early failure period
best period
wear-out period
z(t)
The Bathtub Curve
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constant failure ratet
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Innervariation
early failure period
best period
wear-out period
z(t)
Manufacturingvariation
Usagevariation
Un-reliability due to Variation
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variationDeteriorationconstant failure rate
t
Manufacturingvariation
variation
Production Processes
Under Statistical Control?
Usage Environment
Under Statistical Control?
Usually NOT!!!
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A Critique of Reliability Theory Assumptions
• Probability models under the assumption:
• Processes under statistical control?– Probably not!!!
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– Probably not!!!
• Lagging indictors of reliability performance– The design is created before testing
– Usage feedback is even much later
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Back to Basics
Work with the failure mechanisms
and their relations to Variation!
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and their relations to Variation!
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Six Sigma:
VariationRed c
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Reduction
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Chance vs Assignable causes of variation
Time Time Time
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a process withassignable causes
a stable process a stable morecapable process
Processes
Out of statistical In Statistical Control
Control
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Manufacturing controls process capabilitiesProcess
Capability
Engineering controlstolerances
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defects
Lower
tolerance limitUpper
tolerance limit
Quality Deficiency CostsExpensive components
Relation to Six Sigma
CHALMERS
),...,,,( 21= nxxxfy
DFSS and Six Sigma
DfSS
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...2
2
2
2
2
1
2
21+
∂
∂+
∂
∂= xxy
x
y
x
yσσσ
Six Sigma
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Variation/Robust Design
Quality Loss
L(y)
Quality Loss
L(y) Quality Loss
L(y) Quality Loss
L(y)
a b
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TargetValue
LTL UTL
y
TargetValue
LTL UTL
y
Target Value LTL UTL
y Target Value LTL UTL
y
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P-diagram
Noise factors
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Product
Process
SystemSignal
factorsControl
factors
Response
Ideally)(xfy = but
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Targeted Effects of Variation Reduction
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The effects of variation focused in Design for Six Sigma programs;
based on 25 responses.
Ida G?
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Robust Design Methodology
Sources of Variation
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ResultsPRODUCTor
PROCESS
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Failure Experiences and RemediesThe Growth of Reliability Engineering
• Early Problems– “Elevators” in mines; Rail Road Accidents; Fatigue Problems; Rocket Problems (fortunately); Electronics Problems (esp. in the US Navy); etc.
• Aircraft Safety and Availability– Improvements based on a serious feedback process
• Life Cycle Cost based Acquisitions
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• Life Cycle Cost based Acquisitions– Defence Industry, Process Industry
• Competitiveness– Automobile Industry– AC equipment producers (Garvin, 1988)
• Today, most industries have been forced to realise the problem
• Warranty costs – often as high as 50% of the Development costs
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Aim of Reliability efforts
Causes• Find• Estimate• Reduce• Eliminate
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Consequences
Fault
• Reduce• Eliminate
• Find• Estimate• Reduce• Eliminate
ExperienceFeed-back
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Stress & StrengthDemand and Capacity
Stress Strength
Probability density
Bo Bergman SKF Professor
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••••• •• •
•••
••••••
••
•
•
•• •
•
• •••
•••
•
••
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Failure Mode Avoidance
• Lusser (in the 1950-ties)– Robert Lusser
• The V1 rocket
• Lusser´s Law
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• Lusser´s Law
• Starfighter F104 (“widowmaker”)
• Missile development criteria
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Reliability, Stress, and Strength
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Lusser, 1955
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Failure Mode Avoidance
• Lusser (in the 1950-ties)– Robert Lusser
• FMEA– Failure Mode and Effects analysis– Physics of Failure
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– Physics of Failure
• Clausing (Xerox/MIT)– Operating Window
• Pat O´Connor• Taguchi• Davis (Ford)
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Failure Mode Avoidancein Robust Design Methodology
Ideal Function
Response
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Signal
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Failure Mode Avoidance
Ideal Function
Response
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Signal
S/N ratio
An Engineering
Measure of Reliability?
CHALMERS
Failure Mode Avoidance
• Lusser (in the 1950-ties)– Robert Lusser
• FMEA– Failure Mode and Effects analysis– Physics of Failure
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– Physics of Failure
• Clausing (Xerox/MIT)– Operating Window
• Pat O´Connor• Taguchi• Davis (Ford)• Frame: DfSS e.g Park, Creveling et al. ….
CHALMERS
P-diagram
Noise factors
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Product
Process
SystemSignal
factorsControl
factors
Response
Ideally but
CHALMERS
Product representation as a System of P-Diagrams
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CHALMERS
Robust Design
• System design
– Decide on the products characteristics so that the requirements are fulfilled and it can be produced easily. Creative Robustness should be looked for!
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easily. Creative Robustness should be looked for!• Parameter Design
– Find a set-up of the construction parameters that make the product independent of disturbances.
• Tolerance Design
– Decide on tolerances, but strive for the target value
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Creative solutions: some illustrations
The self aligning bearing
A Creative
Reliability
Improvement
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Improvement
1907
1995
Sven Wingquist
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Inspiration
• Creative yesterday – commonplace today
Replacing the chain with a wire
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DFA - solutions
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Poka-Yoke Principles
1. Make it easier for the person to do the right thing than the wrong thing
2. Make mistakes obvious to the person immediately so that some
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2. Make mistakes obvious to the person immediately so that some correction can be made on the spot
3. Allow the person to take corrective action or stop before any irreversible step occurs
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How to create a robust design?
y
y
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xx0
y0
x1
X1 results in less variation in y
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Transfer function
1. Is the transfer function known to the experimenter?
? ? ?)*,,( NCNCfy =
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1. Is the transfer function known to the experimenter?
2. Is it possible to use Design of Experiments to estimate
the transfer function ?
3. Is the transfer function possible to estimate by use
of simulation?
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Pump design – transfer function known
Tubing
Flow rate (F) (l/min)
Transfer function:
F = (3.141 x R2 x L - B) N
One wayvalve
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Piston
F = (3.141 x R2 x L - B) N
R = Piston radius (dm)
L = Stroke length (dm)
B = Back flow (l)
N = Motor speed (rpm)
Customer requirement: F=10±0.75l/min
CHALMERS
Pump design
Factors Nominal value Standard Deviation
Radius 0.2-0.8 dm 0.001
Stroke length 0.2-0.8 dm 0.002MA
KE
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Stroke length 0.2-0.8 dm 0.002
Back flow 0.001-0.004 l 0.00005 0.00002
N (rpm) 50-100rpm 2 1
Low cost High cost
(Inlet Valve)
BU
Y
(Electrical motor)
CHALMERS
The tolerance design approach
First Design
• Piston Radius R =0.4 dm
• Stroke length L=0.4 dm
• Back flow B=0,002 l (low cost)
• Motor speed N=50rpm (low cost)
The target is 10 l/min, but
• 3 sigma process
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• Motor speed N=50rpm (low cost)
Tightening the specifications of the motor (the high cost type)
gives better performance
• 5 sigma process
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A robust design approachThe effect of the factors on
the mean and the variance of the flow
Variance
(flo
w)
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Variance
Mean
(flo
w)
R B NL0.2
0.8
0.0
01
500.2
0.8
0.0
04
100
R B NL0.2
0.8
0.0
01
500.2
0.8
0.0
04
100
CHALMERS
A robust design approach
• Set R and L as low as possible, i.e. R=L=0,2dm
• Use low cost back flow (B)
• Bring the flow rate to target (F=10 l/min) by adjusting N
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• The resulting performance is:
– Almost a 5 sigma process!
• As N≤100, keep R low and increase L until F=10 l/min
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Manufacturing process of composite material
y – bending strenght response variable
A – curing temperature
B – pressure
C – holding time
control factors
(process variables)
D – proportion of hardener
y = f (A,B,C,D,E,F,G,H)?
Composite material experiment: transfer function unknown
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• Four different process conditions• Eight batches of raw material
D – proportion of hardener
E – thermo-plastic content
F – proportion of epoxy
G – material ageing
H – process type
noise factors
?
CHALMERS
Experimental designD E F G H-1 -1 -1 1 -1 2075
1 -1 -1 1 1 2117
-1 1 -1 -1 1 2221
1 1 -1 -1 -1 2227
-1 -1 1 -1 1 2201
1 -1 1 -1 -1 2179
-1 1 1 1 -1 1988
1 1 1 1 1 1858
-1 -1 -1 1 -1 1829
1 -1 -1 1 1 1978
-1 1 -1 -1 1 2111
1 1 -1 -1 -1 2205
-1 -1 1 -1 1 2127
A B C 1 -1 1 -1 -1 2106
Process variables (control factors)A Curing temperature
B Pressure
C Holding time
Incoming material (noise factors)D Proportion of hardener
E Thermo-plastic content
F Proportion of epoxyProcess
Product
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A B C 1 -1 1 -1 -1 2106
-1 -1 1 -1 1 1 1 -1 1870
1 -1 -1 1 1 1 1 1 1879
-1 1 -1 -1 -1 -1 1 -1 2245
1 1 1 1 -1 -1 1 1 2242
-1 1 -1 -1 1 2245
1 1 -1 -1 -1 2258
-1 -1 1 -1 1 2206
1 -1 1 -1 -1 2207
-1 1 1 1 -1 2053
1 1 1 1 1 2188
-1 -1 -1 1 -1 2219
1 -1 -1 1 1 2145
-1 1 -1 -1 1 2174
1 1 -1 -1 -1 2265
-1 -1 1 -1 1 2241
1 -1 1 -1 -1 2187
-1 1 1 1 -1 2208
1 1 1 1 1 2181
F Proportion of epoxy
G Material aging
H Type of process
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-1
0
1
2
3
-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0
Sta
ndar
d d
evia
tio
n
-1
0
1
2
3
-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0
Sta
ndar
d d
evia
tio
n
-
1
0
1
2
3
-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0
Sta
ndar
d d
evia
tio
nB
G
BG
Identification of location effects
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-3
-2
Contrasts
Sta
ndar
d d
evia
tio
n
-3
-2
Contrasts
Sta
ndar
d d
evia
tio
n
-
3
-
2
Contrasts
Sta
ndar
d d
evia
tio
n
G
• Location effects B, G and BG was determined to be active based
on engineering knowledge and the normal plots
Process factors Factors and interactionsassociated with incoming material
Interactions between ”process factors”and ”incoming material factors”
CHALMERS
Model
( )
ˆ( , ) 2132 72 65 46
2132 72 46 65
y B G B G BG
B B G
= + − + =
+ + −
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( )2132 72 46 65B B G+ + −
B ≈ 1.4
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Conclusions
• The storage time of the incoming material (G) is causing variation in the bending strength of the composite
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bending strength of the composite material.
• If the pressure (B) is set at high level the bending strength is made insensitive to the storage time.
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Robust Testing
TheDesign
Variation of
Noise factors
N1 N2 …. Nn
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DesignNoise factors
Evaluate the Design