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Reliability
Extending the Quality Concept
Kim Pries
ASQ CQA CQE CSSBB CRE
APICS CPIM
Director of Product Integrity & Reliability for Stoneridge TED
Background in metallurgy & materials science
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
What is reliability?
Reliability is the “quality concept” applied over time
Reliability engineering requires a different tool box
Reliability data
Nearly always “units X to failure,” where units are most oftenMilesHours (days, weeks, months)
Probability distributions
Exponential“Random failure”
Log-normal Weibull Gamma
Most common distribution
Weibull distribution
Equation
eta = scale parameter,
beta = shape parameter (or slope),
gamma = location parameter.
Weibull mean
Also known as MTBF or MTTF Need to understand gamma function
11mean
1
0
x nn e x dx
Citation
Using diagrams from Reliasoft Weibull++ 7.x
A few from Minitab
Shapes of Weibull
Scale of Weibull
Location of Weibull
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
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
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
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
Accelerated Life Testing
Can be used to predict life based on testing
A typical model looks like
Highly accelerated life testing
No predictive value Reveals weakest portions of design Examples:
Thermal shockSpecial drop testingMechanical shockSwept sine vibration
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
MEOST, continued Test to failure is goal Combined stress environment Beyond design levels Lower than immediate destruct level Example:
Simultaneous Temperature Humidity Vibration
Step-stress
Cumulative damage model
Harder to relate to reality
HASS and HASA
Screening versus sampling Small % of life to product Elicit ‘infant mortality’ failures Example:
Burn-in
Achieving reliability growth
Detect failure causes Feedback Redesign Improved fabrication Verification of redesign
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
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
Summary Slide
Effects of design Effects of manufacturing Can’t we predict? Warranty Warranty Serial reliability Parallel reliability
(redundancy)
Other tools Software reliability
Effects of design
Usually the heart of warranty issues Counteract with robust design
Effects of manufacturing
Manufacturing can degrade reliability Cannot improve intrinsic design issues
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
Warranty
1-dimensionalExample: miles only
2-dimensionalExample:
Miles Years
Warranty
Non-renewing Pro-rated Cumulative
Multiple items Reliability improvement
Serial reliability
Simple product of the probabilities of failure of components
More components = less reliability
1
n
ii
serial reliability x
Parallel reliability (redundancy)
Dramatically reduces probability of failure
1
1 (1 )n
ii
parallel reliability x
Other tools
FMEA Fault Tree Analysis Reliability Block Diagrams
Simulation
Software reliability
Difficult to prove Super methods
B-method ITU Z.100, Z.105, and Z.120Clean room
Summary Slide
What about maintenance? Pogo Pins Pogo Pins (product 1) Pogo Pins (Product 2) Pogo Pin conclusions Preventive vs. Predictive
What about maintenance?
Same math Looking for types of wear and other failure
modes
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
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
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
Pogo Pin conclusions
Very quick “infant mortality” Random failure thereafter Difficult to find a nice preventive
maintenance schedule Frequent inspection
Preventive vs. Predictive
Preventive maintenanceFix before it breaksStatistically based intervals
Predictive maintenanceDetect anomaliesAlways uses sensors
The future
Combinatorial testingDesigned experiments
Response surfaces Analysis of variance Analysis of covariance
Eyring modelsMultiple environments