Analisa Kegagalan.pdf

8/10/2019 Analisa Kegagalan.pdf

1/7

COMPONENT

LIFE 19

useful

ife, it is

nor

true for

other mortality

distributions

and, herefore,

he

oper-

ationofdivisionperformedinobtainingEq.(3.9)isnecessaryingeneral.

EXAMPLE

3-1

(a)

If

a

device

has a failure

rate

of 0.5

X

l$-s

failures/h

:

5

x

104

failures/h

:

o.Svo

1000

h,

what

s its

reliability

or

an operating

eriod

of

100

h? If there

are 10,000

tems n the

test,

how

many fairures

are expected

n

r00

h?

R0)

-

R(100)

*

s-0.ixto-r)


2/7

SERIES

AND

PARATLEL

SYSTEMS

3I

FIGURE

+2

r:I

F_:l

schematic

vstem

ith

unirs

n

series.

-1:n1

F---t-J-1iJ-

4.2

SERIES

SYSTEMS

Assuming

n components-

n-

Fls.

4-2

are ndependent

and

the

system

will

survive

for

operating

ime

r

[wirh

R(0)

:

l]

if,

andtnly

if,

each

on" of

th"

componenrs

surviveso time l, then he systemeliability s

Frorn

Eq.

2-12)

Rr(r):.*p[-

I i^,fOo,f

R-(')

expf-,i

Il^,od,]

exp

{-/Jf

I

r,1,11ar}

-

@-ta)

For

useful

ife

with

all

failure

ates ,s)

constanl

'

R" ,G):expi- ( i^ , ) , ]

G-tb)

i= 1

Thus the eflective ailure rate of a system ormed from nonredundant ompo-

nents

s equal

o

the

sum

of the

failure

rates

of

the

ndividual

components.

The

components

eed

not

be

identical.

The

mortality

of

a

series

ystem

s

m""(t)':

-i,

(^,,0).*p

{-

f:Li,r,(,)]d"}

G-2)

The

MTTF

of a

series

ystem

s

',":

Io-

*o

{-

I:f,,2,^,r"1]a'})a,

4-3)

and

s

dependent

n

the

ailure

ates

of the

ndividual

components.

EXAMPLE 4-1

A

system

consists

of

four

independent

omponents

n

series,

each

having

a reliabil ity

of

0.970.

what

is

the

reliabirity

f ihe

system?

n"-

It

R;(r;

(0.970)1

0.885

i- I

If,the.system

omplexity

s

increased

o

that

it

contains

eight

ofthese

components,

what

s

the

new

eliability?

8

,.c,"

=

fl

R;(r)

:

(0.970)s

0.78j


3/7

3:

L\-TRoDucrtoN

To

RELL{BIltrt,

L\

DEsIcN

Ii

rhe

more

complex

system

s

required

o

have

he

same

eliabirity

as

the

simprer

-;:\::il

i.e.,

0.885,

what

must

he

reliability

of

each

component

.t,

*

'

R;

:

(0.8tJ)ri8

0.985

ll l l

Reliabil ity

s

always

quar

o

or

less

han

unity.

In

addition,

t

is

clear

ar

upon

muldprying

omponent

eliabirities,

he

reriability

of

a

comprex

eries

-'.'s;em

wi*

decrease

apidry

with

many

componenrs.

Ii;

,yrt;;':onsists

of

-

io

independent

omponents

n

series (eaci

compo".",

1"'"irg"a reliability

: 99percent),he ystemeriabiriryi1 e

""rylii"p...."i"'fr,h

400

uch

::ironents

in

series,_

he

reliability

decreases

o

r.g

percent.

we

concrude

-:::

components

hich

11e

used

n

large

nurnr..,

in

series

n

complex

sljstems

-:sr

have

extren,ely

mall

ailure

rates.

The

MTBF

for

a

series

s)'stem

n

usefur

ife

can

be

carcurated

y

con-

": : : ; : ig

the

individuar

vtrBFs

into

failure

ates,

adding

h.r.

; ; ; ; ;

a sysrem

'

-::re

ate

and

converting

his

o

u

,yrr.rn

tnlfnf.

r'-i l ' lPLE

4-2

An

airborn6-erectronic

ystem.has

radar,

a

computer,

nd

an

i&*'r'

:1

unit

with

MTBFs

of

g3,

167,

and500

h,

respectively.

Find

the

system

,uflif

and

he

reliability

or

a

5_l

op.'."ri"g1;;..

Unil

Equiva.lent

ailure

rate

MTBF,fi

feilurell000

h

Radar

Computer

Auxiliary

R, l

r2

167

6

500

2

rotrl

=

20

System

UTBF

=

1000/29

=

56 6

.t

3,

g

urfrxrnlr

"i

:-:

nission

rfl*ifllllLlllt{h

:-

::dar,

R

:

gl%

: rmputer,

R:97f ;

"_:x i l iary,

:99%

R"r"(5)

r5t '"0

=gO%

iltl

#r i t r

f \ERGLZE-DE-ENERGIZE

,r .

lllllln**

r::':

in

Eq. (4-lb).is

the

system

perating

ime.

As

written,

here

s

an

"*'n,*flru':

ssumption

hat.a[

.orponant,

in

ttr.

,yrt.rn

operate

co'tinuously

fo r

lllllnru

:-"::

s)stem

operaiing

perioo.

i.

r."y

ri,uations,

however,

not

all

com_

1',,,ffi:

f'll'..t:,tli:

manner'.

.:.t1er,

irev

will

a"'

"nuiji)

iiun.tioninn

,l,lr**'

:;J)

part

of

the

ime

and

will

be'de_ine,rg'i'7Jf"","""i.1),il:.r.Tt:f

illllltnr

r:B*

This

can

be

treatect

n

various

wavs.


4/7

3

txtnooucttoN

To RErrABrLrry

tN

DESIGN

A

question

always

arises, .e.,

is

it

better to leave

a

system

on

all the

time

or

to

switch

it

on and

oft'when

needed?

The

answer

depends

on the

ratio

of the probability

of

surviving

the hours

in the_unneeded

nergized

condition

to

the

probability

of

surviving on-off

switching

cycles.

In

adiition,

there

is

-

a

question^of_

conomy,

since he

cost

of

euergy

consumed

during

unnecessdry

.ooperation

is important.

At least

equally

important

is

the

fact

i-trat

energizei

components

are

subje:t

to

wearout

or

gradual

degradation

(including

exceeding

tolerance

imits).

These

processes

re

neady

nlnexistent

in

the

d-e-energized

condition.

E(AMPLE

4-3

consider

a communication

system

consisting

of a transmitter,

t

teceiver,

and

an encoder.

Fairure

of one

causes

ystem

airure.

During

g

h

d

communication

he

units

operate for

various

periods.

Determine

the

reliability

br

maintaining

ommunications

ithout

ailure

or

g

h.

Operrting

Feilure

ate,

Unir

priod,

h

feilures/h

R;

Transmitter

6

Receiver

I

Encoder

4

0.0267

0.00125

0.015

0.16

r

0.01

0.05

total = 0.23

0.85

0.99

0.94

R"y"

=

- rt

:

{o-23

:

0.79

=

79 perCent

PARALLEL

SYSTEMS

{

i

iAssume-that

he

n

components

n

Fig. 4-3

are ndependent

and

the

system

wil

."::-

for

operating

ime

r; if any

one of the

components

survives (or

the

sys-

hn

fzil5

only

if

all

the

components

ail),

then

the

unreliabilitv

is

O"dr)

Rsdr)=l-QsAt)

:

l

-IQ{t)Qdt)

.

= l - { i l - f i ( /Xl

Q'Q)Qdt)

Q"-r(r\Q"Q)

'

Q"-,{t)Q"G)l

-Rdu. . . i l -R,(dl

-t

Q'Q):

|

-

-

R;(r)l

(4-5)

e

is an

imp-lied

ssumption

hat all

units

are

operating

simultaneously.)

The

mortality

of

the

parallel

system

s

msdt):

Ir*{D n,tl

- R{r)t

(4-7\

the

product

is taken

over

all

factors

from

I

to n,

except

when

:

;.


5/7

26 trrroD$crtox

to

tELIArrLrry

Er

DEsrcl{

vived

up

to

age

T,

i.e.,

/l r

R"..,.(4r)

-

(.*o

{-

}[-*r

-

"-]])

d-:(ry7',d

{i,^r-l(Lr")t;

P:Tr$"

the

alidiry

f

(a)

Es.

3-l),

il

rq.6-rro)-

wnat

s

be

rliabih-ty

f

an

enginewitha

ailnrerate

f

Hlilg;t

foran

Operatinginnof

100 ?

000

?

10,000

?

(3-re)

where

he

terms

rerate

o

early

rife

[b1sd

on

the approximation

or

rdr]

arthough

the

weibull

distribution

caq

be usedJ,

usefur

ife,

and

wearout

fire

ftasea-

on

tt

e

normal

distribution

arthough

he weibull

can

be

used),

eading

rom

hft

to right.

If

f

>5fc,

thcn

R"

is

essentially

q*al

ro

unity.

lt

T+iStr;_n"y

1r."

Table

3-l),

then

.R.

s

essentially

quaf

o

unity.

So

far,

we

bave

discussed

asic

(nathematical)

theory

and

we

have

dever-

oped

general

expressions-

The

discrssion

has

been

in

ir.*,

oi"l*poo"nt,

or

devicts-

There

has

beea

an

impricit

assumptioa

of

appricarion

o

..doti""l,,

items

in

a

populdion,

an

items

being

*loaded;

and

operatea

o

tt

*

uu*e

.rrun-

ner'

There

is

no

necessity{or

sucfr

an

assumptioa-

in"

tn*ory

"nJ

"quution,

pply

equally

weil

(arthough

comprexity

ncreases)

ts

we

go

from

parts throughcompooeots,units, devices,subassemblies,

ssemtdies"

"iryur".or,'u"A

*yrr"*,

to

*super-systemso'

of great

complexity.

once

correct

varues

or

failure

rats

or reliabilities

(or

good

estiruates

of

these

values)

of

components

n

systems

are

available,

o

J"

p"Ju*,

"""",

alculations

of

slsterrreliabilities

even

when

the

systems

are

the

*ori

**prr*

combinatio-ns

f

-components

onceivable.

The

exactness

"r

trr.'r.ruo-lroo",

ljj^1"r{"::

rhe

probability

carcuratiocs

(these

are quite

exact}

but

on

the

exactness

f

the

data

on which

the

calculations

are

based.

Reliability

calcurations

are

a

necessary

and

integral

part

of

the

design

of

a

syste*'

once

a

device

or

system

has

been

designJ

*b

FrJ;;;n',ri.r.o,

however,

elativetylittle

can

be

done

about

ts

reliability.

PROBLEMS

'-t

H,r?T*:Y:d^lT,,t:hY.[ty:*

approximated

ysubtractingthe

xponat

,, rom

Hll;,JL:i'_ig1."n-n.-'.ry ##,#i;;;;;:"ffi

*il":,,:-haf

lf

?#

hich

this

is valid

for

4,

5, and

6

decimal plaes.

3-2

3-3

-t-+'

ffiFfltr,":t:,fl*q.:";1ry5rr

is

9:0om2a:.

whar

s he

aitun

ate,

he

MTTF,

he

TBF,

nd

he

etiabitity

oian

oeerating-**

"ro.i'i6i'#'ilr=fr?Fj

t-5

Determine

the

nunrbs

of renlrffir .-,inr *.:-;J

^-

^-

-,,

lig:^1'"tg1"9:lp$J*iffi

',i*,1..lJil.liJ

'oTo'*o*r"*

n

operation.

wo

undred

"t,,*.;&;ffi;

;fi,T.lr1ffiJff1#"#flT:


6/7

GIO ,IPONENT

f,TFE tI

fo-r75ftlhof

usefulife

duringtheyear;aad&ercrcatrfegffi

opede6pm

S,0mb

$,I)0 h

of aga

C.onpany

polcy

dictates

}at

no eneiBe

e ogEtr

ed lr

tte

wrout

period.

b=lxl0{Arr

l"=txl0t/t i r

4:=50 lr

Is

=

50.000 hr

Is

=

6i'009

hr

,

Agr.br+

A

givea

component

has

an

MTBF

of

106h-

(a)

What

is the

reliability

for

an operating

period

of

I0 h?

(6)

\ytratisthereliabilityforanopemringgriedoft0hhr5unitsinscries?

Forl0inseries?

(c)

what

is

the

reliability

for

a single

com@ent

for an

@eritirg

perilcl

of

t00 h sLaiog from

an

age of

1000

h? Frorn

ar agc

of

ffi h? rvlpr

inherent

assrrrption

did

yoa

make?

(d)

what

is

the

reliability

for

a

coaponent srHch

stara

qerating

at ao

age of

2ts h ia

useful

Iife?

What

assumption

did

you

rcake?

(e)

Draw

corrclusions

from

comprisons

of

*re above

cakllations-

(a) Brimaie the reliability and failure rale of a test sarrde

of

200 iresrs from a

conponent

population

if8

fail

during

tle first

hour.

(b)

If

failing

items

are

replaced,

estimate

rdiabilities srd

failure

ates

when

t*o npre

fail

during

the

second

hour,

fve

rnore

f*il during the

&ird

hour, fqr

more fail

during the

fourth

and

fifth

hours,

and

eiglrt fail

during

the

sixth

through

telrth

hour.

{c)

Estimatereliabilitiesandfailureratesforthedatahpart(r)ifnmeofthefaileditemsare

replaced

''

d)

Compare

the

results

aad

draw

corrcIusisrs. W'hat

diference.

if any, would

ttrere be in the

I

results

fthese

were

early

or

useful life tests?

-18

--';An

eng'm

slraft

has a

failure

rate

of0.5

X

l0-r/h- Thcseslr

used

lrith

rfte

shaft lave a failure

''

rateof2.5Xl0-?h.

tfagivencompnytus3000engir*swiththescssaftsandsealsandeach

'

engine

operates

350

days

per year

it

useful

life,

estiEEtc t$e

number

ofshafs and

scals that

ynust.

be replaced

annualll

J-9

A sanple

of t50

componenG

is subjectd

to testing

{prcsmably

in

rncfid life)-

Tker failures

are

foundat

theend

ofilO0

h; fourmorpattheend

of8fl) h:trryo

moreattheendoll200h:

four

more

a1

he

end of

1800 h;

and

nc furths

failures are

fornd when

tbe tst is terminated at

25m .

(a)

Btimate

the

MTBF

if failed

componants

are replaced *hen

found-

(6)

Esrimate

the

MTBF

if

no

rephcernents

are made.

-

(c)

What

is the

most

conservative

estinnte

you

could m&e

using,rhese

data?

J-.10

.Two

t}'pes

of components

with

ideaticat

eletrical

characteristics

have

different

&ilure rates:

.

The

failure

rate

of

componeot

I is f,r(r)

=

constant

:

I

ZJl000

h; for

g

it

is

Mr)

:

10-6r

where

r

is in

hours.

which

of

the

t*-o

corwoflents is ns

reliable for a

rua of l& 1fi0, t000,

t0,0m

h?

3-ll

The

failure

rate

for

a

certain ype

of

components

Xr)

=

trot where

o)

0 and k cons&ut-

-

Find

its

reliability,

mortality,

and,MTTF.

Repeat

or

Xr)

= l.orr/r.

II2

The

failure

ate

or

a

certain rype

of

cornpneot t rtr)

-

a

+

bt wkrc

c) 0

ard

6

>

0

are

constatrl

Find

reliability,

rprtality,

and MTTF.

3'13

A

girea

tem

has

a

random

ahure

ate of l0-r failurdh-

Wearout

r uormally dstributed

with

a

mcan

Iy)

of

1500

h aad

s $andard&ciation

of ljO

lL

I

I

I

I

F

i

3

T6

3-V


7/7

fi rxrrooucnoN To

RELIABETTY

N DESIGN

Hminatingp" by

substitution,

.e.,

p,

:

(l

-

p,

-P')

and

collecting

erms'

Q

:

2P,'+

4P"'

-

4Po3

Put

-

P,r

t

p, and

poare

mall,

he last

three

erms

can

be neglected'

hen

A=2p,2

*

4p.r

Tbe mprovement actor s

._0forsingle

_

p,*p"

-

Q

for

quad

2p,2

*

4p'2

fr

p, : p,

:

0.01,Gr

:

33.33

+10 SOLUTION

TO

4.6

Aquest ionwasaskedwhether therel iabi t i tyblockdiagramforFig.4-4should

be

shown

as series

or

parallel.

The

proper

answer

depends

on

the

definition

or criterion

of adequate

erformance

of

the

system.

If the

two

va-lves

re

nor-

mally

shut

but

are

Jxpected

o

opeo

on

command

o

Provide

low,

this

is a series

system

n ierms of ,itiubitity' If, however, he two valvesare normally open

butareexpectedtoshutoncommandtostopf low,thisisaparal lelsystem

in

termsof reliability.

ilil

IRO B LE

I}I

S

l-1 A system onsists

f 100

units

n

series,

ach

unit

having

a

reliability

of 0'99'

what

is the

reliabilityofrhesyste;?

Whaifractionofsuchsysternswillperformsatisfactorilv?

{-2

An

old-fashioned

trinf

of Christmas

ree

ights

has

10

bulbs

connected

n series'

Wlrat

must

the

reliabilityor.".r,

iuli

t"

if,n"t.

is

to

be

a

90

percent

hance

f

the string

ighting

after

one

ysrr

ofstorage?

*3Anunmannedmissiledesignedforspaceexplorationhas1000componenlsinseries.Ifthe

missions requiredo havJa reliabitiiyof 90percent ndeach omponent as hesame elia'

bility,

what

must

be he reliability

of each

omponent?

-4-4

A

given

component

as

a constant

ailure

ate

of

0'0050

ailure/h'

Determine:

(a)

Reliability

of

oneunit

for

an

operating

ime

of

300

h'

(6)

Reliability.

f

two units

n

series

or

an

operating

ime

of

150

t'

-.

(c)

Reliability

f

three nits

n series

or

an

cperating

ime

of 100

h'*

(a)

nenaUitity

f

four

unis

in

series

or

an

operating

ime

of

75

h'

*

J-J

A system as

'

nont.OrnOu"i

"ontponents

thiir

fa.ilure

ates

ri

areconstant'

but

(possibly) ll

different. Find

the

,.iiubiti,y,

mortality,

and

MfiF

of

the

system. specialize

or

the

case

when

all

tr; are eQual.

rr

G5

Find

the MTBF

or the

system

f

five components

n

series

ave

constant

aiiure

ates

of

1'4'

1.7,1.g,1.2, nd

1.6

ail'rres

er

1000

, respectively'

:

+7

An

equipment

as585

components,

s

istec

below.

It

is specified

hat

the

equipment

must

have

a reliability

of

"i

t.utiSSpercent

for

an

18-h

mission

ime.

Does he

equipment

meet

this

specification?

fso,

how

well?

Analisa Kegagalan.pdf

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