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

Pdf

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

PDF

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

PDF

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