INTRODUCTION TO RELIABILITY - dsiac.org · •Reliability engineering & design for reliability •Product life testing & reliability growth •Accelerated life testing •Experimental

GEORGE P. HANSEN, PH.D.

August 9, 2016

INTRODUCTION

TO RELIABILITYDistribution Statement A: Approved for public release; distribution is unlimited.

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Office of the Under Secretary of Defense (OUSD)

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UNCLASSIFIED | Distribution Statement A: Approved for public release; distribution is unlimited.

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


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.


Reliability is always comprised of four key factors:


• 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)



• 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:



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…


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/


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.


TEST YOUR

PRODUCTSBEFORE YOUR CUSTOMERS DO.


In reliability engineering

failures are…

NOT OPTIONAL, THEY ARE

ESSENTIAL!


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.


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


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


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.


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?


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


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.


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


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


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


Weibull Distribution

ReliaSoft Weibull++ 7 - www.ReliaSoft.com

Probability - Weibull

Folio1\Beta 2.0 Eta 1000:



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





4/28/20149:04:02 AM

Increasing β and η

ReliaSoft Weibull++ 7 – www.ReliaSoft.com


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


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.


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


Design, Test, Buttress, Fortify, Reiterate


RELIABILITY

ENGINEERING

WHERE POSSIBLE,

LEARN FROM HISTORY

Consider the

Iron Pillar of Delhi

(ca. 414 CE)


RELIABILITY

BENEFITS FROM

THOUGHT

BETTER THAN

AFTERTHOUGHT


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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Classified Training and our Subject Matter

Experts are Available to Answer your

Technical Questions and Support

Contracted Analysis Tasks

CONTACT BRIAN BENESCH

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THANK YOU!

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Documents

INTRODUCTION TO RELIABILITY - dsiac.org · •Reliability engineering & design for reliability •Product life testing & reliability growth •Accelerated life testing •Experimental