avinash dharmadhikari tata motors limitedsresa.org.in/l7-reliability-engineering.pdf1 tata motors...

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1 TATA MOTORS LTD. Confidential. For discussion purpose only

Reliability Engineering*

Avinash Dharmadhikari

TATA MOTORS LIMITED

*Background material for presentation at BARC-7th Dec 2012


29th July

JRD Quality awards: Tata Business Excellence Model

On 29th July 2007:

Mr. Tata ended his address by quoting the President of

Toyota Motor Corporation –

“What we want to be is the best motorcar

company, being the largest is incidental.”

Workshop on 'Reliability and Life Assessment of Electronic Systems - Methods & Techniques'

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Quality

Customers perception of the product


Reliability

Reliability: Quality over time “The ability of an item to perform a required function under stated conditions for a stated period of time”


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How do customers talk about reliability?

“A system that does what I want (function), when and where I want

to use it (conditions), for as long as I want to use it (time)”

“No surprises - no unscheduled downtime” “Get me up and running quickly when failures occur”


Reliability: Stated in more precise measurable terms

“Probability that a system will perform its intended function

for a specified time t under stated operating conditions”

R(t): reliability at time t


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Design for reliability Process of building reliability into Design

Now

Target

Compliants!


IDENTIFY DESIGN VALIDATE

VERIFY

ANALYSE

MONITOR AND CONTROL

CONCEPT DESIGN & DEVELOPMENT

MANUFACTURING AND FIELD

RELIABILITY MANAGEMENT


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IDENTIFY

The present status of reliability

Customers expectations

Environmental / usage conditions

Technology limitations / constraints

Required reliability

Gap


Data sources: present status of reliability using:

•field failures •Internal / supplier rejections •Third party surveys


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IDENTIFY: TOOLS

HOUSE OF QUALITY-QFD,

BENCH MARKING

WARRANTY DATA ANALYSES

RELIABILITY EVALUATION

RELIABILITY APPORTIONMENT (ALLOCATION)


A stage when detail design actions like drawings, circuit layouts,

supplier selection begin.

DESIGN


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DESIGN: Tools

•Fault Tree Analysis (Historical data support)

•DFMEAs: Product, system, subsystem, components

SEVERITY, OCCURANCE, DETECTION

RPN = S * O * D

AIAG FMEA - 2008


ANALYSE

First cut rough estimates of product life / reliability / durability / serviceability


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ANALYSE: Tools

•Digital validation:

Strength, tolerance, thermal, NVH, durability

•Reliability block diagrams

•Reliability predictions:

based on historical data / standard data bases

DOE- Parameter design & Tolerance design at digital level


VERIFY

• Manufacture: ‘PROTO’ as per drawing

• Verify does it meet designer’s intentions

(fitment, functions, performances)

Iterative process where the design weaknesses are to be captured

and re-designing and re-analyses are done where ever needed.


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VERIFY: Tools

Proto: Characteristic matrices, Process flow charts,

PFMEAs

Highly accelerated physical tests ( HALT)

Accelerated tests

Test till failure using customer cycle and environment

Degradation tests using customer cycle and

environment


VERIFY: Statistical tools:

Sample size determination

DOE

Analyses of data

Prediction of reliability growth

DESIGN REVIEWS BASED ON TEST RESULTS (DRBTR)


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VALIDATION:

Ensure that products made at production rate using final drawings meet customer requirements

VALIDATION: Tools

•All tools of ‘verification’ stage

•Production PFDs, PFMEAs and Control plans

•comparative analysis


MONITOR AND CONTROL

Assurance of quality over the period of time


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MONITOR AND CONTROL: Tools

•Acceptance sampling schemes,

•On line control charts,

•Audits / Ongoing reliability testing

•Cp, Cpk studies,

•8 D analyses based on field/ EOL complaints

•TGW /TGR leanings


• Requirements flow from Vehicle down to Components

• Verification/Validation flow from Components up to Vehicle

Vehicle

Systems

components Rate of Production prototypes

Vehicle

Systems

VoC:QFD, Performance, Model, performance needs

VoB: HoQ, Functionals, assemblies Model, functional needs, Analysis

VoB: HoQ, material, dimensions, Model, fitment needs, Analysis

HALT,ALT Test to failure with degradation, screening DOE, Model Prediction

Systems

Functionals, assemblies Model, DOE with noise factors, predictions

Vehicle

Performance, Model, prediction of VoC

,ALT, Goal posts, Test to failure with degradation, correlations with proto, controls Model, Predict

Physical testing, Multiple samples Correlations with proto-systems, controls, Model, predictions

Controls, Performance in customer environment, Model prediction of VoC

Mass production:

controls

Concept, design, analysis, verify, validate, produce

Model: statistical & Engineering


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?

Reliability Modeling


Data sources:

Digital Physical

OLD

NEW

Lab

Product

field

old product and new product

Establish correlations using old models, predict on new model


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Data types: Material, Dimensions/profiles Fitments,

Data types

1. Piece-to-piece variation

2. Changes to component

characteristics over time

3. Customer duty cycle

4. Climate & road conditions

5. Environment created by

neighboring components

in the system.

•Gaps/flushness

•Functions, NVH /BSR

•Thermals/electrical surge

•Performance

•Reliability

•Durability

•Repair/replacement times

•Life


A look at Human Life Data: Unit- Age in years


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27 TATA MOTORS LTD. Confidential. For discussion purpose only 27

Bath-Tub Curve (of human mortality rate*)

*Source: National Vital Statistics Reports, Vol. 48, No.18

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

1 10 100 Age (years) - log. scale

Ha

za

rd

20 40

infant

mortality

hand-guns,

drugs,

automobiles,

childbirth

older age

healthy leaving

5



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Life of a Physical product


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Continuous

• Time

• Mileage

• Cycles

Discrete

• Number of spot welds in a frame

• Number of corrosion spots per unit area of sheet metal

Life Variables

Behavior of random variables is described by means of mathematical functions,

which include: density function, distribution function, reliability function, hazard

rate and cumulative hazard function


Consider a histogram of failure times, t, for a large population of nominally identical parts.

t

f(t)

A mathematical model that approximates the behavior of this histogram is know as the density function and is denoted by f(t).

Distribution Function and Reliability Function

t=t0

t

F(t)

1

F(t0)

t=t0

The distribution function, F(t), represents a proportion of parts failing before a given time t.

F(t0)

The reliability function, R(t), represents a proportion surviving beyond a given time t.

R(t)

R(t0)

R(t0)

animation


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CDF Animation Insert.ppt

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Schematic of the reliability definition

IPTV 100 at 150,000

kms

IPTV in first 6, 12 & 18 months


Hazard Function

(Instantaneous Failure Rate)

The Hazard rate, h(t), describes the possibility to fail in the next small interval from t0 to t0+Dt, given the survival up to t0

, with an approximate probability of f(t0)*Dt.

Mathematically, the hazard rate is the ratio of the density function to the reliability function: h(t)= f(t)/R(t).

In simpler terms, the hazard rate:

number of part failures at a point in time number of parts at risk at that time

f(t)

t

R(t0)

t=t0

t

h(t)

Dt f(t0)

t=t0

h(t0)

animation

The Hazard (failure rate) can take various forms: increasing (IFR), decreasing (DFR), constant (CFR) and non-monotonous (e.g., first decreasing, then constant, then increasing). Shown on the left is an increasing failure rate (IFR) case.


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Bath-Tub Curve (of a mechanical part failure rate)

h(t)

t infant mortality

noise factor #1: piece-to-piece variation

DFR CFR IFR

Primarily manufacturing

issues

Design issues revealed

under random stress; also, most solid-

state electronics

Design issues related to

wear out or degradation

due to fatigue, corrosion,

wear, creep

random failures

noise factors #3,4,5: customer duty cycle, internal & external environment

wear out

noise factor #2: changes over time/mileage of design strength


Reliability field

Reliability criteria

Nuclear Aerospace Automotive Medical

# units in the field 00’s 000’s 00000000’s 00000000’s

Quality of field records

Failed Units

Unfailed Units

excellent

excellent

excellent

excellent

fair

none

reasonable->good

none

Units lost to follow-up no no yes often

Noise space moderate moderate complicated complicated

Competing risks no no yes yes

Key reliability strategy redundancy,

intervention

redundancy,

intervention

robustness,

some intervention

intervention

Scientific context deductive deductive Deductive/inductive Deductive/inductive

Key reliability measure probability of

failure

probability of

failure

distance to failure

modes

Local: relative risk of

disease

Design improvement yes yes yes Yes to some extent

Reliability criteria

Is Automotive field closer to Medical or to Nuclear/Aerospace?


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Cumulative Hazard Function

In many cases, the hazard rate estimated from data is subject to “noise” fluctuations, which complicate the recognition of its trend (i.e., IFR, DFR, CFR, etc.) The Cumulative hazard function, H(t), is the integral of the hazard function and is used to “smooth out” the fluctuations of the hazard rate. 0.000

0.0010.0020.0030.0040.0050.0060.0070.0080.009

0 5 10 15 20

time, t

Haza

rd, h(t

)

0.000

0.020

0.040

0.060

0.080

0.100

0.120

Cum

Haza

rd, H

(t)

H(t) = t

0

h(u)du


Cumulative Hazard Function (cont’d)

Cumulative hazard is always a non-decreasing function of time. If the cumulative hazard is concave, the respective failure rate is an DFR; if it’s convex - the respective failure rate is a IFR; if it’s linear – the respective failure rate is a CFR.

t

H(t)

t

h(t)

animation

IFR CFR

DFR

IFR

CFR

DFR


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Nature of the life data


V IN F a ile d /S e rv ic e d

C o m p o n e n t

F a ilu re /S e rv ic eM ile a g e

X 0 0 9 B a tte ry 4 5 0 0 0X 0 1 8 F u e l p u m p 9 1 6 8 0X 0 2 1 B ra k e p a d s 7 8 4 7 0X 0 0 6 F ro n t w ip e rs 7 7 3 5 0X 0 2 8 H e a d la m p 4 0 0 7X 0 1 5 C lu tc h d is k s 1 5 0 4 0 0X 0 3 1 F ro n t w ip e rs 5 1 4 2 0X 0 0 3 Ig n . S w itc h 3 9 6 1X 0 1 3 B a tte ry 1 6 8 9 0X 0 0 7 F ro n t s tru ts 2 7 1 6 0X 0 2 6 B a tte ry 7 2 2 8 0X 0 3 1 B a tte ry 1 3 1 9 0 0X 0 2 7 D o o r lo c k 7 2 9 8X 0 1 7 F u e l p u m p 4 7 3 4X 0 2 3 B a tte ry 1 7 2 0 0X 0 2 5 B a tte ry 7 4 5 4X 0 1 4 H e a d la m p 2 3 0 6 0X 0 2 9 F ro n t s tru ts 1 0 1 9 0X 0 1 6 B a tte ry 6 9 0 4 0X 0 1 9 B a tte ry 5 2 4 8X 0 0 8 B ra k e p a d s 4 0 0 6 0X 0 1 2 B ra k e p a d s 6 1 9 6 0X 0 1 2 C lu tc h d is c s 1 0 5 7 0 0X 0 0 5 B a tte ry 4 9 3 9 0X 0 2 0 H e a d la m p 2 8 6 9 0X 0 1 1 F ro n t s tru ts 4 5 6 7 0X 0 2 5 B a tte ry 4 6 5 8 0X 0 2 2 D o o r lo c k 3 7 1 0 0X 0 1 0 C lu tc h d is k s 5 3 0 0 0X 0 0 2 B a tte ry 3 8 7 0 0X 0 2 4 F ro n t w ip e rs 6 0 5 4X 0 0 1 C lu tc h d is k s 6 9 6 3 0X 0 0 4 B ra k e p a d s 1 0 6 3 0 0X 0 3 0 F ro n t w ip e rs 6 7 0 0 0

D a ta A n a ly s is

C o m p lic a tio n s :

3 ) fa ilu re /c e n s o r in g

o n th e s a m e V IN

4 ) m u ltip le fa ilu re s


5 ) m u ltip le c e n s o r in g


2 ) v a ry in g ra te s o f

m ile a g e

a c c u m u la tio n

1 ) s ta g g e re d v e h ic le

s ta r t t im e

Censoring – Case study


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sr. no Failure_Mode Total1 Battery 102 Br_pads 33 clutch_disk 44 Door_Lock 25 Fr_strut 36 Fr_wiper 37 fuel_Pump 28 Head_lamp 39 Ignition_switch 1


Method of analysis- depends upon size and nature of data -Non parametric -Parametric


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Example-1: Six proto types on test are monitored at 0, 500 and 1000 hrs. Each proto has two failure modes. Data is as shown in figure 1.


500 hrs 1000 hrs 0 hrs

FM1

FM2

FM2

FM1

FM1

RUNOUT (survived)

Predict Hazard h(ti ), Cum Hazard H(t) and Reliability R(t) wrt FM-1

figure1: Six components on test: two potential failure modes


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Censoring

Typically, when test or field data are analyzed, some parts can be found unfailed, and

the only knowledge about their failure times is that these times are beyond (i.e., to

the right on the time axis of) the observation time. These data are said to be right

censored.

A failure time know only to be before (i.e., to the left on the time axis of) a given time

is said to be left censored. For example, a part is found to have already failed at the

time of its first examination.

Legend:

observation time

right censored observation

left censored observation

starting time

unknown failure time


Right censoring and left censoring are special cases of interval censoring,

i.e., when a part is found Unfailed at the beginning of the observation period and

is found failed at the end of the observation period.

Most typical in engineering applications is the case of right censoring,

which may occur due to stopping a test at a predetermined run time,

breaking down of a test facility or

part failing due to a competing failure mode


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non parametric method: Based on data no statistical model



FM1

FM2

FM2

FM1

FM1

RUNOUT (survived)

figure1: Six components on test: two potential failure modes

Time (hrs) 0 500 1000

Number of parts at risk 6 6 2

Number of failures due to FM1 0 2 1

Number of failures due to FM2

0 0 2


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the hazard rate: h(t) =

number of part failures at a point in time

number of parts at risk at that time


Nonparametric Hazard Analysis (wrt FM1):


FM1

FM2

FM2

FM1

FM1

RUNOUT (censored)

Hazard h(ti ) 0 2/6 1/2

Cum Hazard H(t)=S h(ti ) 0 2/6 5/6

Reliability R(t)=exp{-H(ti )} 1 0.72 0.43

Six components on test: two

potential failure modes


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Example-2: seven proto types on test are monitored at 0, 250, 500,750 and 1000 hrs. Each proto has two failure modes. Data is as shown in figure 2.

What is reliability of the product at 1500 hrs?


Predict reliability of the product at 1500 hrs

X

X

X

O

survived

O

X : Failure mode 1 O: Failure mode 2

Figure 2: seven components on test: two potential failure modes

Component-1

Component-2

Component-4

Component-3

Component-5

Component-6

Component-7

Component-8

Removed from the test

Hrs 0 250 400 500 750 1000 1500


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0 250 400 500 750 1000 1500number of

components at risk 8 8 6 5 4 3 2

number of componets failed due to FM1 0 2 0 1 0 0 0


number of components removed

from test0 0 1 0 0 0 0

Time in Hrs


0 250 400 500 750 1000 1500h1(t): hazard_rate of

FM10 0.333 0 0.25 0 0 0

H1(t): cum

hazard_function of

FM1

0 0.333 0.333 0.583 0.583 0.583 0.583

R1(t): Reliability

function due to FM11 0.7165 0.7165 0.5580 0.5580 0.5580 0.5580

Time in Hrs

h1(t)= (row 2)/ (row 1)

H1(t)=Σ h1(u) u≤ t

R1(t)= Exp(-H(t))

0 250 400 500 750 1000 1500number of





from test0 0 1 0 0 0 0

Time in Hrs

Reliability due to FM1


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Reliability due to FM2

0 250 400 500 750 1000 1500number of





from test0 0 1 0 0 0 0

Time in Hrs

0 250 400 500 750 1000 1500h2(t): hazard_rate of

FM20 0 0 0 0.250 0.333333 0

H2(t): cum_hazard_

function of FM20 0 0 0 0.250 0.583 0.583

R2(t): Relibilty

function due to FM21 1 1 1 0.7165 0.4346 0.4346

Time in Hrs


Component reliability would be: R1(t) * R2(t)

0 250 400 500 750 1000 1500R1(t): Reliability

function due to FM11 0.7788 0.7788 0.6376 0.6376 0.6376 0.6376

R2(t): Relibilty

function due to FM21 1 1 1 0.7165 0.4346 0.4346

Reliability of the

component1 0.7788 0.7788 0.6376 0.4569 0.2771 0.2771

Time in Hrs


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If root cause analysis of FM1 is done successfully and it is removed What would be improved reliability?

No new testing at this stage: Assume that component will not fail due to FM1: Revise the risk set


0 250 400 500 750 1000 1500number of

components at risk8 8 7 6 5 4 2

h2(t): hazard_rate of

FM20 0 0 0 0.2 0.25 0

H2(t): cum

hazard_function of

FM2

0 0 0 0 0.2 0.45 0.45

R(t) due to FM2 only 1 1 1 1 0.8187 0.6376 0.6376

Time in Hrs

0 250 400 500 750 1000 1500number of





from test0 0 1 0 0 0 0

Time in Hrs


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Limitations of non parametric methods

No extrapolations Less precision

Alternative: Parametric models for distribution function


Distributions commonly used to model the life- variables

1. Exponential

2. Weibull

3. Ln normal

Exponential distribution is a special case of weibull distribution


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Density function, f (t )

Life Variable, T

b =0.5

b =1b =3

b =2

Reliability function, R (t )

0

1

Life Variable, T

b =0.5b =1

b =3b =2

Hazard function, h (t )

Life Variable, T

b =0.5b =1

b =3

b =2

Cumulative hazard function,

H (t )

Life Variable, T

b =0.5

b =1

b =3

b =2

Parametric Analysis:

Weibull Distribution

))/t(exp(tb)t(f bbb 1

})/(exp{)( bttR

scale parameter

b shape parameter

b>1: IFR

b=1: CFR

b<1: DFR

1 bbtb)t(h b)/t()t(H


Run MINITAB file


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Parametric Analysis: Linearizing Weibull

As an example, consider the equation of Weibull unreliability function:

After rearranging and taking double log of both sides, we obtain the equation of a straight line (Y = Ax + B):

where the slope is the estimate of the Weibull shape parameter

and the intercept is the estimate of the Weibull scale parameter

})/t(exp{)t(R)t(F b 11

BxAY

))ln(b()tln()b())t(Rln(ln(

Ab̂

)A/Bexp(ˆ


Use soft wear to estimate the parameters of weibull distribution

step 1: estimate R(t) for each t. step 2: use (t, R(t)) pairs to estimate parameters of the weibull distribution


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Reliability organization

Mind set

Engineering + statistics Stat


Organization: Go back to slide # 4


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IDENTIFY DESIGN VALIDATE

VERIFY

ANALYSE

MONITOR AND CONTROL

CONCEPT DESIGN & DEVELOPMENT

MANUFACTURING AND FIELD

RELIABILITY MANAGEMENT


Reliability engineer

Marketing + Customer service

Engineering + Manufacturing+ Assembly


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Reliability Block Diagrams for System Reliability

A complex system is made up of sub-systems and components.

• Each component/subsystem has its own reliability that can be

modeled using various distributions

• We can use reliability block diagrams to estimate system

reliability

2.


The combined reliability of blocks in series equals the

product of reliabilities of each block.

monitor R1= 0.9379

cpu R2 = 0.9979

mouse R3 = 0.9998

Series system: Personal computer

Rs = 0.9379 * 0.9979 * 0.9998 = 0.9357


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If reliability of PC has to be 0.9999 at mission time t

One way to select the component is

monitor R1= 0.999967

cpu R2 = 0.999967

mouse R3 = 0.999967

Rs = 0.99967 * 0.999967 * 0.999967 = 0.9999


If reliability of PC has to be 0.9990 and

best available supplier of CPU provides CPU with

reliability 0.999999, then,

monitor and mouse with reliabilities 0.99901,

are acceptable to achieve system reliability

0.999.


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The combined unreliability (1- reliability) of blocks in

parallel equals the product of unreliability of each block.


Parallel System

A document sorting machine requires a small light source

that is used to detect the presence of a document.

In order to increase Reliability two light sources are used.

Reliability diagram is

Light source 0.977

Light source 0.977

In this case the reliability would be

Rs = 1- (0.023 * 0.023) = 0.999


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Combination Series And Parallel Systems

The important thing to remember in a combined system is to solve the reliability of the parallel system First, Then use it in series to solve the series system reliability.

Example: Input Output

Formula: R2,3 parallel = 1 – U2 x U3 System = R1 x R2,3 x R4

= 1 – (0.10 x 0.10) = 0.95 x 0.99 x 0.99 = 1 – 0.10 = 0.93 = 0.99

R1 =0.95

R3 = 0.9

R2 = 0.9

R4 = 0.99


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