reliability extending the quality concept. kim pries asq cqa cqe cssbb cre apics cpim director...
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Reliability
Extending the Quality Concept
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Kim Pries
ASQ CQA CQE CSSBB CRE
APICS CPIM
Director of Product Integrity & Reliability for Stoneridge TED
Background in metallurgy & materials science
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Summary Slide
What is reliability? Reliability data Probability distributions Most common distribution Weibull mean Citation Shapes of Weibull
Scale of Weibull Location of Weibull Gamma distribution Non-parametric data fit
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What is reliability?
Reliability is the “quality concept” applied over time
Reliability engineering requires a different tool box
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Reliability data
Nearly always “units X to failure,” where units are most oftenMilesHours (days, weeks, months)
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Probability distributions
Exponential“Random failure”
Log-normal Weibull Gamma
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Most common distribution
Weibull distribution
Equation
eta = scale parameter,
beta = shape parameter (or slope),
gamma = location parameter.
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Weibull mean
Also known as MTBF or MTTF Need to understand gamma function
11mean
1
0
x nn e x dx
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Citation
Using diagrams from Reliasoft Weibull++ 7.x
A few from Minitab
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Shapes of Weibull
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Scale of Weibull
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Location of Weibull
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Gamma distributionReliaSoft Weibull++ 7 - www.ReliaSoft.com
Probability - Gamma
Time, (t)
Un
re
lia
bilit
y, F
(t)
6.000 2000.000404.800 803.600 1202.400 1601.2000.010
0.500
5.00010.000
50.000
99.990
0.010
Probability-Gamma
Folio1\Data 1Gamma-2PRRX SRM MED FMF=2986/S=0
Data PointsProbability Line
9/5/20066:58:57 AM
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Non-parametric data fit
Months to failure
Perc
ent
403530252015105
100
80
60
40
20
0
Shape 3.368Scale 23.57N 514
Empirical data fit
Failure to timeWeibull
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Summary Slide
Accelerated life testing Accelerated Life Testing Highly accelerated life
testing Multi-environment
overstress MEOST, continued Step-stress HASS and HASA
Achieving reliability growth
Reliability Growth-Duane Model
Reliability Growth-AMSAA model
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Accelerated life testing
1.00
5.00
10.00
50.00
90.00
99.00
10.00 1000.00100.00
ReliaSoft ALTA 6.0 PRO - ALTA.ReliaSoft.com
Probability Weibull
Time
Unre
liability
9/5/2006 07:01CompanyUser's Name
Arrh/WeibData 1
400406
F=5 | S=0416
F=6 | S=0426
F=6 | S=0
Beta=2.9658, B=1.0680E+4, C=2.3966E-9
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Accelerated Life Testing
Can be used to predict life based on testing
A typical model looks like
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Highly accelerated life testing
No predictive value Reveals weakest portions of design Examples:
Thermal shockSpecial drop testingMechanical shockSwept sine vibration
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Multi-environment overstress
Derate components Study thermal
behavior Scan Finite element analysis
Modular designs DFM Mfg line ‘escapes’ RMAs
Robust…high S/N ratio
Design for maintainability
Product liability analysis
Take apart supplier products
FFRs
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MEOST, continued Test to failure is goal Combined stress environment Beyond design levels Lower than immediate destruct level Example:
Simultaneous Temperature Humidity Vibration
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Step-stress
Cumulative damage model
Harder to relate to reality
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HASS and HASA
Screening versus sampling Small % of life to product Elicit ‘infant mortality’ failures Example:
Burn-in
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Achieving reliability growth
Detect failure causes Feedback Redesign Improved fabrication Verification of redesign
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Reliability Growth-Duane Model
Cruder than AMSAA model
Shows same general improvement
1.00
10000.00
10.00
100.00
1000.00
100.00 1000.00
ReliaSoft's RGA 6 - RGA.ReliaSoft.com
Cumulative Number of Failures vs Time
Time
Cum
. N
um
ber
of F
ailure
s
9/12/2006 11:01Stoneridge TEDKim Pries
DuaneData 1DevelopmentalLS
Alpha=-1.9467, b=18364.7224
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Reliability Growth-AMSAA model
Cumulative failures
Initially very poor
Improves over time
1.00
10000.00
10.00
100.00
1000.00
100.00 1000.00
ReliaSoft's RGA 6 - RGA.ReliaSoft.com
Cumulative Number of Failures vs Time
Time
Cum
. N
um
ber
of F
ailure
s
6/22/2006 14:27CompanyUser Name
Crow-AMSAA (NHPP)Data 1MLE
Beta=1.3304, Lambda=0.7674
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Summary Slide
Effects of design Effects of manufacturing Can’t we predict? Warranty Warranty Serial reliability Parallel reliability
(redundancy)
Other tools Software reliability
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Effects of design
Usually the heart of warranty issues Counteract with robust design
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Effects of manufacturing
Manufacturing can degrade reliability Cannot improve intrinsic design issues
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Can’t we predict?
MIL-HDBK-217FNo parallel circuitsElectronics onlyExtremely conservative
Leads to over-engineering Excessive derating Off by factors of at least 2 to 4
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Warranty
1-dimensionalExample: miles only
2-dimensionalExample:
Miles Years
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Warranty
Non-renewing Pro-rated Cumulative
Multiple items Reliability improvement
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Serial reliability
Simple product of the probabilities of failure of components
More components = less reliability
1
n
ii
serial reliability x
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Parallel reliability (redundancy)
Dramatically reduces probability of failure
1
1 (1 )n
ii
parallel reliability x
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Other tools
FMEA Fault Tree Analysis Reliability Block Diagrams
Simulation
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Software reliability
Difficult to prove Super methods
B-method ITU Z.100, Z.105, and Z.120Clean room
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Summary Slide
What about maintenance? Pogo Pins Pogo Pins (product 1) Pogo Pins (Product 2) Pogo Pin conclusions Preventive vs. Predictive
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What about maintenance?
Same math Looking for types of wear and other failure
modes
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Pogo PinsReliaSoft Weibull++ 7 - www.ReliaSoft.com Probability Density Function
Time, (t)
f(t)
0.000 4.0000.800 1.600 2.400 3.200
0.000
0.300
0.060
0.120
0.180
0.240
Pogo Failures++\Data 1Weibull-3PRRX SRM MED FMF=526/S=0
Pdf Line
Kim PriesStoneridge TED12/12/200512:17:15 PM
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Pogo Pins (product 1)
ESC_Pogo
4530150
0.6
0.4
0.2
0.0
ESC_Pogo
Perc
ent
100.0010.001.000.100.01
99.9
90
50
10
1
ESC_Pogo
Perc
ent
4530150
100
50
0
ESC_Pogo
Rate
4530150
0.6
0.4
0.2
0.0
Table of Statistics
Median 2.74296IQR 6.81390Failure 138Censor 0AD* 5.296
Shape 0.682757Scale 4.69196Mean 6.08597StDev 9.16024
Probability Density Function
Survival Function Hazard Function
Distribution Overview Plot for ESC_PogoML Estimates-Complete Data
Weibull
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Pogo Pins (Product 2)
4WD_Pogo
6040200
0.6
0.4
0.2
0.0
4WD_Pogo
Perc
ent
100.00010.0001.0000.1000.0100.001
99.9
90
50
10
1
4WD_Pogo
Perc
ent
6040200
100
50
0
4WD_Pogo
Rate
6040200
0.6
0.4
0.2
0.0
Table of Statistics
Median 2.95918IQR 8.01387Failure 96Censor 0AD* 3.925
Shape 0.638638Scale 5.25305Mean 7.32163StDev 11.9253
Probability Density Function
Survival Function Hazard Function
Distribution Overview Plot for 4WD_PogoML Estimates-Complete Data
Weibull
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Pogo Pin conclusions
Very quick “infant mortality” Random failure thereafter Difficult to find a nice preventive
maintenance schedule Frequent inspection
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Preventive vs. Predictive
Preventive maintenanceFix before it breaksStatistically based intervals
Predictive maintenanceDetect anomaliesAlways uses sensors
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The future
Combinatorial testingDesigned experiments
Response surfaces Analysis of variance Analysis of covariance
Eyring modelsMultiple environments