introduction to reliability - dsiac.org · •reliability engineering & design for reliability...
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GEORGE P. HANSEN, PH.D.
August 9, 2016
INTRODUCTION
TO RELIABILITYDistribution Statement A: Approved for public release; distribution is unlimited.
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sponsored by the Defense Technical Information
Center (DTIC) with policy oversight provided by the
Office of the Under Secretary of Defense (OUSD)
for Research and Engineering (R&E). DSIAC is
operated by the SURVICE Engineering Company
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The main question is, when?
How long can we count on it?
How does it happen?
Can we aid or design it to last longer?
EVERYTHING EVENTUALLY FAILS
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What is Reliability?
Probability that a thing will perform its intended function for a
specified time under defined conditions without failure or
performance degradation.
Consider performance life times the way an insurance actuary
looks at human populations.
• We don’t know exactly when an individual will fail.
• Given that it has survived till now, we can estimate its chance of continued
survival.
End users define intended function, time and use conditions.
Design engineers ensure it meets these requirements.
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Reliability is always comprised of four key factors:
What is Reliability?
• Often multiple.
• Rank and pick most
important.
• Consider use frequency.
Function
• Often multiple and
complex.
• Rank and pick most
important.
• Consider unexpected or
infrequent devastating
events.
• Consider usage
conditions, habits,
random accidents.
Environment
• Duration, cycles, duty
cycles, hours, miles.
• Can be several points,
depending on strategy.
Function
Probability of Success (or Failure)
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What is Reliability?
• Judicious material selections
• De-rating materials, components and
subsystems
• Innovative use of redundancy or backup
• Designing maintenance requirements
• Other strategies…
Reliability engineering involves
improving reliability by:
• Identifying all potential design failure
modes and mechanisms.
• Testing a “large number” of items to failure
and measuring failure times for each failure
mode.
• Quantifying probability of failure for a given
time in the product usage life.
Reliability assessment involves:
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What is Reliability?
Quantified risk of product, component or material failure
Known warranty and legal liabilities
Known maintenance and repair liabilities
• Reduced spare parts inventory & cost
• Reduced maintenance labor cost
• Reduced unscheduled downtime
• Increased production stability & efficiency
Customers perceive reliability as product quality
• Longer equipment life
• More consistent performance
Reliability techniques can be applied to assessing performance of products, production processes, infrastructure, services…
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Benefits of Reliability
7
Lost revenues,
AVOIDED
Damaged reputation,
AVOIDED
Lost time away from
productive efforts,
AVOIDEDhttps://www.usatoday.com/story/money/cars/2014/04/23/gm-first-quarter-earnings-recall-charges-loss/8074051/
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8
Sound reliability engineering practices must
include knowledge of the failure physics of all
components, modules and interconnection
assemblies in a system. Knowledge of life-
limiting failure mechanisms, and how these
mechanisms will behave in the intended use
environment, is also necessary. Only in this
manner can robust designs be ensured.
RIAC EPRD-2014, Introduction p. 1.
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TEST YOUR
PRODUCTSBEFORE YOUR CUSTOMERS DO.
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In reliability engineering
failures are…
NOT OPTIONAL, THEY ARE
ESSENTIAL!
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Failure Processes:
Generally start at point defects
• Localized areas of high chemical energy or mechanical stress.
• Starting point is called a primary failure.
Micro-failures cascade to macroscopic dimensions
• System responds to applied mechanical, thermal, electrical and
chemical stresses by various mechanisms which reduce its
internal energy.
• These processes drive failures and the failure cascade.
• Subsequent cascading events are called secondary failures.
How is the starting point related to stress factors?
The event cascade is associated with the failure
mechanism; the rate of this process is a function of
environmental factors.
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Failure Analysis & Prediction:
• Systematic determination
of the causes of a failure
with the intention to
prevent its recurrence
• Retrospective
• Failure has occurred
RCA – Root Cause Analysis
• Systematic determination
and prioritization of
possible failures to prevent
them from occurring and
mitigating their effects
• Prospective
• Failures may occur
FMEA – Failure Mode Effects Analysis
RCA
BEHIND
FMEA
AHEAD
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Important Considerations in Assessing Failures
Common factors to consider in conducting failure analysis:
• Inherent (common cause) or event-related (special cause)
• Primary and secondary mechanistic contributions
• Variations in materials, components and the manufacturing process
• Environmental, operational factor interactions
• Operating hours till failure
• Variations within system operating conditions
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Important Considerations in Assessing Failures
• Maintenance records
• Times to failure
• Failure mechanisms
• Environmental stresses
• Operational stresses
Be cautious that
there are many more
factors affecting
reliability than can
be realistically
identified.
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Obtaining Failure Distributions
• Operate product.
• Monitor performance over time.
• Determine when failures occur
− Or when product drifts out of
specifications.
− Failures need not be catastrophic.
− Multiple failure modes may be
active
o All need to be monitored.
o Not necessarily follow equal or similar
temporal distributions.
Life Test
• Failure times are accelerated by
stressing product at elevated
levels.
• ALT stress(es) should not induce
unnecessary failure modes.
• Acceleration stress factor
should be in correspondence
with actual usage stress.
Accelerated Life Test
Often we do not
have the luxury of
controlled in-house
tests, accelerated or
otherwise. What
then?
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A Brief Word on Censoring
Product life tests
provide “exact” failure times.
Even ALT’s require
very long times to complete.
Censoring techniques are used
to reduce test time, or to incorporate
field failure data where access to
products is limited.
CENSORING STRATEGIES:
• Yield population parameters
quickly.
• Commensurate loss of
confidence in the estimates.
IMPACT MUST BE EVALUATED
AND UNDERSTOOD.
• Systematic or random?
• Systematically missing data
can introduce undesirable bias.
COMMON CENSORING STRATEGIES:
• Left censoring
• Right censoring
• Interval censoring
• Type I censoring
• Type II censoring
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Common Failure Distributions
NORMAL
Failure times normally
distributed.
• Used to model wear
out stage.
• Light filaments,
electrical insulation.
• Models properties
such as strength,
elongation, impact
resistance.
EXPONENTIAL
Failure times randomly
distributed.
• Only distribution to
which MTTF applies.
LOGNORMAL
Log of failure times
normally distributed.
• μ and σ are the log
mean and log
standard deviation.
• Commonly used to
model wear out
stage.
• Metal fatigue, solid
state components,
electrical insulation.
WEIBULL
Two or three parameter
exponential function
that can flexibly model
infant mortality, useful
life, or wear out
depending upon
parameters found
upon fitting to data.
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MEAN, AVERAGE:MEDIAN:
The probability density function (PDF)
for a variable is defined by:
The cumulative distribution function
(CDF) for the quantity is defined as:
P(X) GIVES:
The proportion of population
with value less than x,
The probability of having a
value less than x.
Probability Density Distributions & Cumulative Density Distributions
( ) ( )x
P x p t dt
Probability
( ) thatb
ap t dt
a x b
( ) ( ) 1P x p t dt
WHEN NORMALIZED
( ) ( ) 0.5M
P x p t dt
•( ) ( )P x t p t dt
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Weibull Distribution
Probability Density Function (PDF)
−Time is the predictor variable.
−PDF gives the relative likelihood of failing by age t.
Cumulative Distribution Function (CDF)
−CDF gives the fraction of a population that fails by time t.
Reliability Distribution Function (RDF) R(t) = 1- F(t)
−RDF gives the fraction of a population surviving beyond
time t.
Percentile
−Lifetime associated with a desired failure probability.
−τ0.632 ≈ η (characteristic life).
Parameters:
−β, slope or shape parameter (measures dispersion)
−η, characteristic life or scale parameter
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Weibull Probability Distribution Function
Increasing Shape Parameter
1
1
( )
1
ln(1 )
t
t
t
P
tf t e
F t e
R t e
P
Increasing Scale Parameter
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Weibull Distribution
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Probability - Weibull
Folio1\Beta 2.0 Eta 1000:
Folio1\Beta 1.0 Eta 100:
Folio1\Beta 0.5 Eta 1:
Time, (t)
Un
re
lia
bilit
y, F
(t)
1.E-3 100001.E-2 1.E-1 1 10 100 10000.1
0.5
1.0
5.0
10.0
50.0
90.0
99.9
0.1
Probability-Weibull
Folio1\Beta 0.5 Eta 1Weibull-2PRRX SRM MED FMF=100/S=0
Data PointsProbability Line
Folio1\Beta 1.0 Eta 100Weibull-2PRRX SRM MED FMF=100/S=0
Data PointsProbability Line
Folio1\Beta 2.0 Eta 1000Weibull-2PRRX SRM MED FMF=100/S=0
Data PointsProbability Line
4/28/20149:04:02 AM
Increasing β and η
ReliaSoft Weibull++ 7 – www.ReliaSoft.com
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NameProbability
Distribution
Cumulative
DistributionMean
Standard
Deviation
Normal
Lognormal
Exponential
Logistic
Gamma
Gumble
Time is the predictor variable in all cases.
Other Useful Distributions
/ 61
exp expx x
1 exp exp
x
2 2( ) /(2 )1
2
xe
2
11 erf
2 2
x
2
2
1 (ln )exp
22
x
x
1 1 ln1 erf
2 2 2
x
2 /2e 2 221e e
xe 1 xe 1
1
2
1x x
s se s e
1
1x
se
3
s
11
( )
x
k
kx e
k
1,
( )
xk
k
k k
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Failure Rate Across the Life of Product Population
is the Sum of Three Categories
Establishing how failures are distributed over time is central to every determination of product reliability.
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Reliability Engineering
Apply External
Stresses
Determine Unit
Operating Limits
Determine Unit
Destruction Limits
Identify/Correct
Failures
Develop Test Plan
HALTImprove Robustness
Apply External
Stresses
(< Destruct Limit)
Collect Reliability
Data
Change Stress
Level
Use Model to Extrapolate
Reliability at Nominal
Level (Verify Goals Met)
HASTProve Reliability Goals
Redesign
and Retest
Stage 1
Prototype
Stage 2
Prototype Product
Apply External
Stresses
Remove DOA and
Early Life Failures
Ship Product
HASSScreening to reduce DOAs
Reliable
Product
Operating Margins
Destruct MarginsLife Distribution
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Design, Test, Buttress, Fortify, Reiterate
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RELIABILITY
ENGINEERING
WHERE POSSIBLE,
LEARN FROM HISTORY
Consider the
Iron Pillar of Delhi
(ca. 414 CE)
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RELIABILITY
BENEFITS FROM
THOUGHT
BETTER THAN
AFTERTHOUGHT
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Next Steps
• MTBF, failure rates and censoring
• Reliability engineering & design for reliability
• Product life testing & reliability growth
• Accelerated life testing
• Experimental design and reliability
• Failure rates and censoring
• RCA, FMEA & FRACAS
• Risk analysis and management
• Analysis of product returns and field failure data
Please select and rank your top three
choices for additional webinar topics:
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QUESTIONS?DSIAC is Available for Advanced and/or
Classified Training and our Subject Matter
Experts are Available to Answer your
Technical Questions and Support
Contracted Analysis Tasks
CONTACT BRIAN BENESCH
(443) 360-4600
THANK YOU!
Brian.Benesch@dsiac.org
Brian.a.Benesch.ctr@mail.mil
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