javier garcia - verdugo sanchez - six sigma training - w4 reliability

/3710 BB W4 Reliability 05, D. Szemkus/H. Winkler

Reliability

Introduction

Week 4

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Page 2/3710 BB W4 Reliability 05, D. Szemkus/H. Winkler

The following issues will be discussed:• What does reliability mean?• What is the role of reliability in the company?• How do we differentiate between early life failures „infant

mortality“, random and wear out failure modes?• Reliability and Six Sigma• Understanding the basic application of the Weibull analysis• Analysis of life time, generation of simple Weibull plots• Calculation of

• Failure rate – MTTF / MTBF• Probability of success (surviving) (Ps)• Probability of failure (Pf)• Reliability of parallel und serial systems

• Development of understanding about the reliability allocation• Application of reliability allocations in system - designs

About this Module…


What is Reliability ?

Reliability is the probability, that a product or a system…

• …does not work as intended

• …within specified limits

• …under determined conditions

• …over a predetermined time frame


What is Classic Reliability ?

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Reliability in a Weibull Distribution

• The probability, that a part or system fails…• After a specified time• In a defined environment

We say, R(T0) = Pr(T>T0)

What can be the causes for an early failure or breakdown?


Why is Reliability so Important ?

• Customers expect reliability

• It saves the customer money

• A deciding factor to

• …hold customers

• …win back lost customers

• …win new customers

• It save us money


• Costs to correct one single defect:

– €34 during development

– €177 before procurement

– €368 before production

– €17,000 before shipment

– €690,000 at the customer

• The cost to correct a satellite are much higher…

Cost data from 1991 EuroPACE Quality Forum, Horoshi Hamada, President of Ricoh

The consideration and development of reliability has to be performed early in the product development

What are the Costs of a Reliability Problem ?


Reliability – 3 Phases

Product failure can occur in three phases

•The first phase we call it the „infant mortality“ period, characterized by a high failure rate at the beginning, its decreasing over time.

•The second phase is characterized by random failures. Failure possibilities are independent of time.

•The third phase we call it wear out period, characterized by an increasing failure rate over time.

First Phase“infant mortality”

Third Phasewear out

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Second Phase- Design Life Time -


Reliability Consideration – Phases 1 & 3

For the reliability calculation both areas have to be included:

1. Infant mortality → Corrective actions, usually a design change. Characteristically is the tendency to a decreasing failure rate after the field implementation (not predictable defects)

2. Wear out → Corrective actions are normally parts or components replacement (predictable defect)

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Requirement

Minimal design life (hours / years)

random

Infant mortalitywear out

AcceptableNot acceptable


System Planning & Requirement Definition

• Serial reliability:

The reliability of one single component influences the reliability of the system if serial connected.

The failure of one component results in a failure of the complete system.

Basics for reliability of components

R4

R1

R2

R3

V+

V-

V out

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+

R1 R2 R3

R4 X1

Example: Electrical circuit Block diagram for reliability


• Parallel reliability:

The system is functioning also of a failure of some components.

Computer1

Computer2

Computer3

Computer 1, 2, and 3have the same function, parallel connected.Only 1 computer of 3 is needed for a proper function.

Example:

Basics for reliability of components



Probability of success

• Reliability → Probability of success (Ps):

Definition: The probability of success or survival (Ps) is the probability that a component or system is in operation up to a determined point of time.

Ps = 1 for a perfect reliable system

Ps = 0 for a total unreliability System

• Unreliability → Probability of failure (Pf):

Definition: The probability of failures (Pf) is the probability that a component or system fails or does not work anymore before a determined point of time.

Ps + Pf = 1for all systems



• Exponential distribution function

e = natural Logarithm (2,718281828)

λ = failure rate

t = time, mostly expressed in hours

• MTBF: Mean Time Between Failures

Average failure time or reciprocal

value of the failure rate


tePs λ−=

MTBF

1=λ



h

Failure0002.0

Failureh

5000

11===

MTBFλ

4966.0)3500)(0002.0( === −λ− eePs t


Example 1:

The MTBF of a systems is 5000 h. What is the probability, that the system is still in operation at 3500 h?



Serial systemSystem components are serial connected, so that the failure of one component result in a failure of the whole system.

component

2component

3component

1

Ps(System) = Ps(1) x Ps(2) x Ps(3) x …



Example 2: Simple serial system

Each of the 3 components (system) has a MTBF of 5000 h. What is the probability, if serial connected, that the system is still in operation after 1000 h?

component 2MTBF = 5000 h



h

Failure0002.0=λ

8187.0)1000)(0002.0(

)3()2()1( ==== −ePsPsPs

549.0)3()2()1()( =××= PsPsPsPs System



Example 2: alternative solution

Because the 3 components are build in series, we can sum the individual failure rates before the calculation of the value Ps(System)

h

Failuresystem 0006.0321 =++= λλλλ

h

Failure0002.0=λ

549.0)1000)(0006.0(

)( == −ePs System



Simple parallel systemSystem components are connected „or“ that a failure of one component does not result in a failure of the complete system .

component

2

component

1

Ps(System) = 1 – (Pf(1) x Pf(2))



Example 3:

Two components are parallel connected, each has a MTBF of 5000 h. What is the probability that the complete system is still in operation after 3500 h?



0002.01

==λMTBF

4966.0)3500)(0002.0(

21 === −ePsPs

7466.0)4966.01)(4966.01(1*1 21 =−−−=−= PfPfPssystem



Serial - parallel systemsThe reliability of more complex systems can be calculated with a so called serial and parallel combination technique.

A/B/C D/E F A/B/C/D/E/FB

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Example 4: The complex Model in Step 1 can be reduced in accordance to step 2 and than again in accordance to step 3



Additional analysis techniques for systems

B

A

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D…

AB

A

C

B

A

C

DB

A

D

CE

X components, Y required Dependent elements Time dependent failure rates (simple)

Time dependent failure rates (complex) Reparable Systems

Method:Binomial distribution

Method:Markov Modeling

Method:•Calculation of probability distributions•Mont Carlo Simulation

Method:Monte Carlo Simulation

Method:Markov ModelingMonte Carlo Simulation



RELIABILITY PREDICTION• Prediction is based on a model combining failure rates of

the individual components and/or subsystems to provide an overall picture of product/equipment reliability

• Most models are built on an exponential (constant) failure rate that is additive

• The process of modeling requires understanding of component/subsystem reliability, use, and stress levels

Conclusion

• Provides a ball park estimate of failure rates and serves as a comparison between products

• Provides guidance for the selection of components - It is highly recommended that you thoroughly understand the reliability of high failure rate parts and subsystems

• Highlights the stress levels on each part - It is highly recommended that a thorough stress level review be done for each component, joint, fastener, connector, etc.


Example 5:

A serial system contains 3 components. What should be the required MTBF for component 1, that the overall system achieves a Ps = 0,85 at 1000 operating hours?

component 2MTBF = 20.000 h

Ps = 0,951

component 3MTBF = 12.500 h

Ps = 0,923

component 1MTBF = ?



Failure Mechanism

Over stressing:

• Mechanic•Disruption•Overload

•Thermal•Electrical

•Electrostatic charging•Chemical

•Contamination•Others, incl. radiation etc.

Wear out:

• Mechanic•Endurance stress•Wear

•Thermal•Electrical•Chemical

•Corrosion•Polymerization•Diffusion

•Others


Definition of Ps…

Ps = Probability of success

Example:

The marketing department likes to operate some LEDswith 13 V (designed for 6,3 V) in order to get a brighter bill board for an exhibition.

Question, what life time can we expect life at a voltage of 13 V until 10% of the LEDs failed?


The Weibull - Analysis

Weibull- Basics

• Each Weibull – Plot presents a failure of the same failure type (failure mode / phase)

• To define the failure time precise three requirements have to be fulfilled:

• The failure time has to be measured clearly

• A consistent metric for the expired time

• The meaning of the failure who is causing the break down must be clearly defined


Stat

>Reliability/Survival

>Distribution Analysis (Right Censoring)

>Distribution ID Plot

Stat



>Distribution ID Plot

Simple and short example:The time to failure is measured for 2 products. 18 samples of product A shows a variation between 10 – 66 hours.Lets generate with these numbers some distribution plots.

1. Check if Weibull distribution fits.


RELIABILITY1.mtw


The Anderson-Darling statistic indicates that a smaller value has a better fit of the

data. The default setting result in Pearson

correlation coefficients. Here the best fit is 1 or –1.

For these data the Weibull distribution fits. Normal and Lognormal can be taken

as well.


T T F A

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T T F AP

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T T F A

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T T F A

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C orrelation C oefficientWeibull0,986

Lognormal0,974

Exponential*

Normal0,981

Probability Plot for TTF ALSXY Estimates-Complete Data

Weibull Lognormal

Exponential Normal

T T F A

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T T F A

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T T F A

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T T F A

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A nderson-Darling (adj)Weibull0,983

Lognormal1,109

Exponential2,736

Normal1,040

Probability Plot for TTF AML Estimates-Complete Data

Weibull Lognormal

Exponential Normal

Option: Maximum Likelihood


Simple and short example:

2. Set up the graphic

You can define the min & max value for the x- coordinate for better

visibility.


Stat



>Parametric Distribution analysis

Stat





TTF A

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Table of Statistics

Median 34,9921IQ R 26,3116Failure 18C ensor 0A D* 0,898

Shape

C orrelation 0,986

2,04782Scale 41,8503Mean 37,0755StDev 18,9726

Probability Plot for TTF A

Complete Data - LSXY EstimatesWeibull - 95% CI


BetaEta



The values Beta and Eta – the meaning

• The Beta (β) value indicates the slope of the calculated straight line which is linked to the failure mechanism. Within the Minitab graphic you find the Beta value under „Shape“.

• The Eta (η) value is also calculated by Minitab (as Scale) and presents the characteristic design life. That is the intersection on the line corresponding 63,2 % with the calculated straight line. With other words, 63,2 % of the parts will fail at that characteristic design life!

At β = 1 means η the characteristic design lifeMTTF (Mean Time to Failure) or MTBF (Mean Time Between Failure)



The meaning of the Beta (β) value / the slope

• What is the size of the Beta value in our example and what is the conclusion in respect the failure cause?

• A β < 1 indicates to a “infant mortality” early failure rate

• Insufficient „burn-in“ or „stress screening“

• Production problems, wrong assembly, quality control

• Overhaul problems

• A β ≈ 1 indicates to a random failure

• Maintenance failure, human error

• Defects due to natural influence, „FOD“

• Combination of 3 or more failure reasons (different β)

• Intervals between failures



• A 1 < β < 4 indicates to a failure due to early wear out

• Low Cycle Fatigue

• Mostly bearing defects

• Corrosion, Erosion

• A β > 4 indicates to an old age (sudden) wear out

• Stress corrosion

• Material conditions

• Material break out, similar to ceramic

The meaning of the Beta (β) value / the slope



What do we understand of „B“ design life?

• „B“ design life (e.g. B10, B50, etc.) refers to the time at 10% or 50%, etc. of the parts (components) did fail. The „TTF A“ design life can be read off on the x- axis of our plot.

• List the numbers for „TTF A“ from our example:

• B1

• B10

• B50

• If the warranty time is 20 hours, how much % of the parts do we expect to fail up to this point of time?


Values from the Session Window in Minitab:

B1 = 4,4B10 = 13,9B50 = 35,0B90 = 62,9

After 20 hours about 20% have failed

The Weibull - Analysis Standard 95,0% Normal CI

Percent Percentile Error Lower Upper1 4,42708 2,32142 1,58407 12,37262 6,22574 2,82416 2,55896 15,14673 7,60788 3,13729 3,39040 17,07174 8,77741 3,36320 4,14205 18,60025 9,81277 3,53796 4,84054 19,89256 10,7540 3,67882 5,50025 21,02607 11,6247 3,79550 6,13003 22,04468 12,4403 3,89402 6,73587 22,97589 13,2115 3,97840 7,32200 23,8384

10 13,9460 4,05147 7,89162 24,645320 20,1186 4,44800 13,0439 31,030530 25,2967 4,58931 17,7271 36,098440 30,1468 4,66300 22,2629 40,822750 34,9921 4,75897 26,8044 45,680960 40,1013 4,96171 31,4659 51,106670 45,8211 5,38916 36,3876 57,700380 52,7986 6,25718 41,8549 66,603890 62,8893 8,16007 48,7676 81,100491 64,2785 8,47424 49,6417 83,231092 65,7951 8,82996 50,5777 85,591093 67,4713 9,23788 51,5913 88,239394 69,3537 9,71355 52,7050 91,261495 71,5132 10,2809 53,9530 94,788896 74,0666 10,9798 55,3909 99,039197 77,2284 11,8845 57,1198 104,41698 81,4671 13,1599 59,3583 111,81199 88,2220 15,3251 62,7645 124,005


Simple and short example:Lets compare the two product designs. Now we want to see if the modification results in a significant difference for time to failure.

Analyze it with the support of Weibull Plots


Stat





TTF

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Table of Statistics

18 04,51847 101,793 0,982 26 0

Shape Scale C orr F C2,04782 41,850 0,986

ProductTTF ATTF B

Probability Plot for TTF

Complete Data - LSXY EstimatesWeibull - 95% CI

Beta

Eta


What do you conclude from the analysis?


Definition of Ps…

Ps = Probability of success

Example:

The marketing department likes to operate some LEDswith 13 V (designed for 6,3 V) in order to get a brighter bill board for an exhibition.

Question, what life time can we expect life at a voltage of 13 V until 10% of the LEDs failed?

Failure time of the LEDs: 867, 802, 882 und 935 sec.

What failure type results from the Beta value?

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