Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 2
,
A
p
r
il
201
4, p
p
.
19
3
~
19
9
I
S
SN
: 208
8-8
7
0
8
1
93
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Reliability and Cost Model of
P.M. in A Component of an
Electrical Distribution System
Considering Ageing Mechan
ism
S
Afsh
ar
*, M Fotuhi
Firuz
a
bad
**
* Depart
em
ent o
f
El
ectr
i
c
a
l
a
nd
Com
puter Engin
eering
,
Is
l
a
m
i
c
Azad Unive
r
s
i
t
y
S
c
ien
c
e
and
Res
earch
Bran
ch,
T
e
hran,
Iran
** Departement
of Electr
i
cal
Eng
i
neer
i
ng, Sharif
University
of
Technolog
y
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 28, 2013
Rev
i
sed
Jan 26, 201
4
Accepte
d
Fe
b 8, 2014
Applica
tion of
Reliab
ili
t
y
Cen
t
ered Ma
inten
a
nc
e (RCM) in
a s
y
stem
results
in a d
ecrease in
component failure ra
tes and
as such improvement in
th
e
s
y
stem
reli
abil
it
y. One of the m
a
jor
subjects of the RCM is focused on the
Online and
Offline Preventive M
a
intenance (OPM and FPM whi
c
h together
will be deno
ted
b
y
OFPM) of th
e com
ponents w
h
ich r
e
pair
ing th
e com
ponen
t
needs or doesn’
t
need to stop
the mission carr
y
ing ou
t b
y
it.
The RCM is
clas
s
i
fi
ed as
a pr
event
i
ve m
a
in
te
nanc
e policy
and
has significan
t contributio
n
in practical ap
plications. However, l
itt
le res
e
arch has
been
devoted to
modeling the o
n
line
and offline Preven
t
i
ve Mainten
a
nce
.
T
h
is
resear
ch
assumes that th
e component failure r
a
te
will be improved
if
th
e OFPM is
performed for a long period
of time
as a part of an RC
M program.
Application of an OFPM program could
cause the component set at
least
to
“as bad as o
l
d
state but cann
ot re
ach
the “as good as new
”
state. Th
e
em
phasis of this research is to
m
ode
l the OFPM for critical com
ponents or
an
y
equipment
with critical
f
a
ilure in
a s
y
stem.
Th
e proposed m
odel is bas
e
d
on the
concept o
f
PM and improvement fact
or of
reli
abi
lit
y
in
a system
wi
t
h
critical components which th
eir
failur
e
cou
l
d cause a f
a
ilur
e
in
the s
y
stem
(first-order
cut-
sets).
Keyword:
Im
perfect
M
a
i
n
t
e
na
nce
Prev
en
tiv
e Main
ten
a
n
ce
(PM)
Reliab
ilit
yCen
tered
Main
ten
a
n
c
e (RCM)
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
S Afs
h
ar,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Islamic Azad
Uni
v
ersity scie
nce a
n
d r
e
s
e
arc
h
b
r
an
ch
,
T
e
hr
a
n
,
Ir
an
1.
INTRODUCTION
It h
a
s
b
e
en
sho
w
n
th
at
p
r
even
tiv
e m
a
in
ten
a
n
ce will d
e
fi
n
itely en
h
a
n
c
e th
e wo
rk
ing
co
nd
itio
n or
r
e
du
ce th
e failu
r
e
of
a
syste
m
(o
r
a co
m
p
on
en
t)
[
1
], [2
].
Based
on the
working c
ondition of a
com
ponent
being restored
aft
e
r perform
i
ng
m
a
intenance
activ
ities, th
e
m
a
in
ten
a
n
c
e can
b
e
Classified
in
to
t
h
ree catego
r
ies: Perfect main
ten
a
nce,
Min
i
ma
l
maintenance, a
n
d Im
perfect
maintenance
[3].
Perfect
m
a
intenance
m
eans a
ll actions
perform
ed to
re
store the c
o
m
pone
nt worki
n
g c
o
ndition t
o
as
good as
new.
Minim
a
l
m
a
intenance
m
eans the actions
pe
rform
e
d to rest
ore t
h
e c
o
m
ponent t
o
the C
o
ndition
ri
g
h
t
bef
o
re t
h
e act
i
ons
, w
h
i
c
h i
s
oft
e
n
cal
l
e
d as bad
as ol
d st
at
e. Im
perfect
m
a
i
n
t
e
nanc
e rest
ores t
h
e
com
pone
nt worki
ng c
o
ndition to
som
e
whe
r
e betwee
n as
go
od as
ne
w a
n
d as
ba
d as
Ol
d.
Perfect m
a
in
tenance
m
a
y
be reason
abl
e
fo
r sy
st
em
s wi
t
h
onl
y
one c
o
m
pone
n
t
and t
h
e m
i
nim
a
l
m
a
i
n
t
e
nan
ce seem
s rat
i
onal
f
o
r
failure
be
ha
vior of system
s whe
n
only one or
few
c
o
mpone
n
ts
is re
placed by
a ne
w one
. Thus, perfect
m
a
i
n
t
e
nance a
nd m
i
nim
a
l
m
a
i
n
t
e
nanc
e are
o
f
t
e
n
fo
u
nd
ve
r
y
l
i
m
i
t
e
d uses
i
n
p
r
act
i
cal
ap
pl
i
cat
i
ons.
N
o
r
m
al
ly
,
th
e failu
re
rate u
n
d
e
r i
m
p
e
rfect
m
a
in
ten
a
n
ce is so
m
e
wh
er
e between as
good as ne
w and a
s
bad as
old.
On the
othe
r hand, m
a
intenance ca
n also
be class
i
fied in
t
o
co
rrectiv
e m
a
in
tenan
ce an
d preven
tiv
e m
a
in
ten
a
n
c
e
according t
o
the status
of a c
o
m
ponent
before m
a
intenance
is perform
ed [2].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
19
3 – 1
9
9
19
4
Co
rrectiv
e m
a
in
ten
a
n
c
e (C
M) is an
y m
a
in
ten
a
n
c
e
w
h
en
a
co
mp
on
e
n
t is
f
a
ile
d
and
p
r
ev
en
tive
m
a
i
n
t
e
nance (
P
M
)
i
s
t
h
e
m
a
i
n
t
e
nanc
e act
ions
whe
n
a co
m
ponent
i
s
op
erat
i
ng o
r
can
cont
i
n
ue i
t
s
m
i
ssi
on.
The
o
u
t
a
ge a
n
d a
g
i
n
g
pr
o
b
l
e
m
s
of a com
p
o
n
ent
ca
n
b
e
r
e
du
ced thr
oug
h pr
ev
en
tiv
e
m
a
in
ten
a
n
ce [4
].
Practitio
n
e
rs introd
u
ce t
h
e Reliab
ility Cen
t
ered
Ma
in
ten
a
n
c
e (RCM) to
imp
r
ov
e Co
m
p
onen
t
ou
tag
e
s
effect a
n
d com
ponent a
v
ailability. The
m
a
jor effort
of t
h
e
OPM
program
foc
u
s
e
s on t
h
e
pre
v
entive
main
ten
a
n
ce
(PM).
An
im
p
o
r
tan
t
PM activ
ity o
f
t
h
e
OPM prog
ram
is th
e
On
line an
d offlin
e Prev
en
tiv
e
Main
ten
a
n
ce
(OFPM
). Th
ese
m
a
in
ten
a
n
ce activ
ities are in
te
n
d
e
d
to pro
l
on
g
t
h
e
u
s
efu
l
life of a co
m
p
o
n
en
t. It
sh
ou
l
d
b
e
no
ted
th
at th
e reliab
ility co
u
l
d
b
e
i
m
p
r
ov
ed th
rou
g
h
t
h
e OFPM
activ
ities fo
r
eq
u
i
p
m
en
t o
f
wh
ich
syste
m
failu
re
is critical.
In
th
is p
a
p
e
r, th
e effect on
syste
m
reliab
i
l
ity
a
nd the cost issue are studie
d w
h
en
ap
p
l
ying
th
e O
F
PM
act
i
v
i
t
y
. The c
once
p
t
of
p
r
ev
ent
i
v
e m
a
i
n
t
e
nance
has
bee
n
di
scuss
e
d
by
m
a
ny
researc
h
ers
[1
,
2,
4,
5
,
6,
7]
.
They proposed that the effect
ive age
of a s
y
ste
m
is reduc
ed by a cer
tain units of tim
e
after each im
perfec
t
m
a
i
n
t
e
nance [8
,
9
,
10]
.
C
a
nfi
e
l
d
[1]
ha
s pre
s
ent
e
d t
h
e
effect
of i
m
perfect
PM
on
ha
zard
f
unct
i
o
n
o
f
w
h
i
c
h t
h
e
ha
zard
rat
e
at
age is rest
ore
d
to the hazard rate at a younge
r age
,
while the hazard level
rem
a
ins unc
ha
nge
d.
The c
oncept of
i
m
p
r
ov
em
en
t facto
r
is propo
sed
b
y
Malik
[9] an
d Lie an
d
Ch
un
[7
], wh
ich
is sim
ilar to
th
e id
ea
p
r
esen
t
e
d
b
y
Naka
ga
wa [
1
2
]
, t
h
at
i
s
, t
h
e
po
st
-m
ai
nt
enan
c
e
ag
e
of
a s
y
s
t
e
m
is
r
e
d
u
c
ed
f
r
o
m
t
to
t
and t
h
e
pre
-
main
ten
a
n
ce
reliab
ility o
f
th
e
syste
m
)
(
t
r
has
be
com
e
)
(
t
r
A similar conce
p
t
has
been prese
n
ted in [5, 15,
1
6
]
, in
wh
ich
i
t
is assu
m
e
d
that m
a
in
ten
a
n
c
e will rest
o
r
e the syste
m
to
a
b
e
tter co
nd
ition
(bu
t
n
o
t
t
o
t
h
e as-
g
ood
-as
n
e
w st
ate). Th
e
d
e
gree o
f
im
p
r
o
v
e
m
e
n
t
o
f
a sy
stem’s reliab
ility is
a rand
o
m
v
a
riab
le wh
ich
d
e
p
e
n
d
s
on the c
o
m
ponent’s a
g
e.
The m
e
t
hod s
t
at
ed i
n
t
h
e a
b
o
v
e st
udi
es
has
been
di
sc
usse
d by
P
h
a
m
and
Wan
g
[1
2]
an
d i
s
desi
g
n
at
ed
as “
t
he i
m
provem
e
nt
fact
or
m
e
t
h
od”
. T
h
e
re
sea
r
ch areas
of t
h
e im
perf
ect prev
en
tiv
e m
a
in
te
n
a
n
ce
have
bee
n
f
o
c
u
se
d o
n
t
h
e i
s
sues
of
opt
i
m
al
PM
or re
pl
ac
em
ent
pol
i
c
i
e
s, i
n
cl
u
d
i
n
g sch
e
dul
i
n
g m
odel
s
an
d
alg
o
rith
m
s
b
y
min
i
mizin
g
th
e av
erag
e co
st
-rate (co
s
t/tim
e)
o
f
a system
[1
-7
,
10
,
13
,
15
,
16
].
The
de
gr
ee of
m
a
i
n
t
e
nance
can be
m
easur
ed by
ei
t
h
er
t
h
e fre
que
ncy
of
PM
or
t
h
e avera
g
e
t
i
m
e
in
terv
al b
e
tween
PM
in
terv
en
tio
ns
[1
-2
, 4
,
5
,
7
-
16
].
In
thi
s
researc
h
, eac
h com
p
one
n
t in
a
d
i
stribu
tio
n syste
m
i
s
t
r
eat
ed as a sy
st
em
wi
t
h
m
a
ny
com
pone
nt
s
.
It
i
s
al
so di
f
f
i
c
ul
t
t
o
m
easure
t
h
e deg
r
ee o
f
m
a
i
n
t
e
nance f
o
r t
h
e
OFPM
i
n
a s
h
ort
pe
ri
o
d
o
f
t
i
m
e. Thus
, t
h
i
s
pape
r u
s
es t
h
e
t
o
t
a
l
cum
u
l
a
ti
ve t
i
m
e
done
by
t
h
e OFPM
act
i
v
i
t
y
fo
r a c
o
m
pone
nt
at
age
t
as a
m
easure
fo
r t
h
e de
gree
o
f
m
a
i
n
t
e
nanc
e.
Th
e
reliab
ility
is co
m
p
ared fo
r th
e co
m
p
o
n
en
t th
at is
with
an
d withou
t
i
m
p
l
e
m
en
tin
g
th
e OFPM
.
Si
nce t
h
e
O
F
P
M
no
rm
al
ly
does
not
i
n
cl
u
d
e
pa
rt
s re
pl
ace
men
t
, it is assu
m
e
d
th
at th
e
sh
ap
e
o
f
t
h
e
failu
re
di
st
ri
b
u
t
i
on i
s
not
cha
n
ged
b
u
t
t
h
e effect
i
v
e age of a co
m
ponent
i
s
re
duce
d
by
u
n
i
t
s
of t
i
m
e
i
f
OFPM
i
s
per
f
o
r
m
e
d.
It h
a
s
b
e
en
sho
w
n
th
at
p
r
even
tiv
e m
a
in
ten
a
n
ce will d
e
fi
n
itely en
h
a
n
c
e th
e wo
rk
ing
co
nd
itio
n or
r
e
du
ce th
e failu
r
e
of
a
syste
m
(o
r
a co
m
p
on
en
t)
[
1
], [2
].
Based
on the
working c
ondition of a
com
ponent
being restored
aft
e
r perform
i
ng
m
a
intenance
activ
ities, th
e
m
a
in
ten
a
n
c
e can
b
e
Classified
in
to
t
h
ree catego
r
ies: Perfect main
ten
a
nce,
Min
i
ma
l
maintenance, a
n
d Im
perfect
maintenance
[3].
Perfect
m
a
intenance
m
eans a
ll actions
perform
ed to
re
store the c
o
m
pone
nt worki
n
g c
o
ndition t
o
as
good as
new.
Minim
a
l
m
a
intenance
m
eans the actions
pe
rform
e
d to rest
ore t
h
e c
o
m
ponent t
o
the C
o
ndition
ri
g
h
t
bef
o
re t
h
e act
i
ons
, w
h
i
c
h i
s
oft
e
n
cal
l
e
d as bad
as ol
d st
at
e. Im
perfect
m
a
i
n
t
e
nanc
e rest
ores t
h
e
com
pone
nt worki
ng c
o
ndition to
som
e
whe
r
e betwee
n as
go
od as
ne
w a
n
d as
ba
d as
Ol
d.
Perfect m
a
in
tenance
m
a
y
be reason
abl
e
fo
r sy
st
em
s wi
t
h
onl
y
one c
o
m
pone
n
t
and t
h
e m
i
nim
a
l
m
a
i
n
t
e
nan
ce seem
s rat
i
onal
f
o
r
failure
be
ha
vior of system
s whe
n
only one or
few
c
o
mpone
n
ts
is re
placed by
a ne
w one
. Thus, perfect
m
a
i
n
t
e
nance a
nd m
i
nim
a
l
m
a
i
n
t
e
nanc
e are
o
f
t
e
n
fo
u
nd
ve
r
y
l
i
m
i
t
e
d uses
i
n
p
r
act
i
cal
ap
pl
i
cat
i
ons.
N
o
r
m
al
ly
,
th
e failu
re
rate u
n
d
e
r i
m
p
e
rfect
m
a
in
ten
a
n
ce is so
m
e
wh
er
e between as
good as ne
w and a
s
bad as
old.
On the
othe
r hand, m
a
intenance ca
n also
be class
i
fied in
t
o
co
rrectiv
e m
a
in
tenan
ce an
d preven
tiv
e m
a
in
ten
a
n
c
e
according t
o
the status
of a c
o
m
ponent
before m
a
intenance
is perform
ed [2].
Co
rrectiv
e m
a
in
ten
a
n
c
e (C
M) is an
y m
a
in
ten
a
n
c
e
w
h
en
a
co
mp
on
e
n
t is
f
a
ile
d
and
p
r
ev
en
tive
m
a
i
n
t
e
nance (
P
M
)
i
s
t
h
e
m
a
i
n
t
e
nanc
e act
ions
whe
n
a co
m
ponent
i
s
op
erat
i
ng o
r
can
cont
i
n
ue i
t
s
m
i
ssi
on.
The
o
u
t
a
ge a
n
d a
g
i
n
g
pr
o
b
l
e
m
s
of a com
p
o
n
ent
ca
n
b
e
r
e
du
ced thr
oug
h pr
ev
en
tiv
e
m
a
in
ten
a
n
ce [4
].
Practitio
n
e
rs introd
u
ce t
h
e Reliab
ility Cen
t
ered
Ma
in
ten
a
n
c
e (RCM) to
imp
r
ov
e Co
m
p
onen
t
ou
tag
e
s
effect a
n
d com
ponent a
v
ailability. The
m
a
jor effort
of t
h
e
OPM
program
foc
u
s
e
s on t
h
e
pre
v
entive
main
ten
a
n
ce
(PM).
An
im
p
o
r
tan
t
PM activ
ity o
f
t
h
e
OPM prog
ram
is th
e
On
line an
d offlin
e Prev
en
tiv
e
Main
ten
a
n
ce
(OFPM
). Th
ese
m
a
in
ten
a
n
ce activ
ities are in
te
n
d
e
d
to pro
l
on
g
t
h
e
u
s
efu
l
life of a co
m
p
o
n
en
t. It
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Relia
b
ility a
nd Co
st Mod
e
l o
f
P.M. in
A Compon
en
t
o
f
a
n
Electrica
l Distrib
u
tion
S
y
stem… (S
. Afsha
r
)
19
5
sh
ou
l
d
b
e
no
ted
th
at th
e reliab
ility co
u
l
d
b
e
i
m
p
r
ov
ed th
rou
g
h
t
h
e OFPM
activ
ities fo
r
eq
u
i
p
m
en
t o
f
wh
ich
syste
m
failu
re
is critical.
In
th
is p
a
p
e
r, th
e effect on
syste
m
reliab
i
l
ity
a
nd the cost issue are studie
d w
h
en
ap
p
l
ying
th
e O
F
PM
act
i
v
i
t
y
. The c
once
p
t
of
p
r
ev
ent
i
v
e m
a
i
n
t
e
nance
has
bee
n
di
scuss
e
d
by
m
a
ny
researc
h
ers
[1
,
2,
4,
5
,
6,
7]
.
They proposed that the effect
ive age
of a s
y
ste
m
is reduc
ed by a cer
tain units of tim
e
after each im
perfec
t
m
a
i
n
t
e
nance [8
,
9
,
10]
.
C
a
nfi
e
l
d
[1]
ha
s pre
s
ent
e
d t
h
e
effect
of i
m
perfect
PM
on
ha
zard
f
unct
i
o
n
o
f
w
h
i
c
h t
h
e
ha
zard
rat
e
at
age is rest
ore
d
to the hazard rate at a younge
r age
,
while the hazard level
rem
a
ins unc
ha
nge
d.
The c
oncept of
i
m
p
r
ov
em
en
t facto
r
is propo
sed
b
y
Malik
[9] an
d Lie an
d
Ch
un
[7
], wh
ich
is sim
ilar to
th
e id
ea
p
r
esen
t
e
d
b
y
Naka
ga
wa [
1
2
]
, t
h
at
i
s
, t
h
e
po
st
-m
ai
nt
enan
c
e
ag
e
of
a s
y
s
t
e
m
is
r
e
d
u
c
ed
f
r
o
m
t
to
t
and t
h
e
pre
-
main
ten
a
n
ce reliab
ility
o
f
th
e
syste
m
)
(
t
r
has be
com
e
)
(
t
r
A sim
i
lar concept
has
b
een
pre
s
ente
d in [5,
15,
1
6
]
, in
wh
ich
i
t
is assu
m
e
d
that m
a
in
ten
a
n
c
e will rest
o
r
e the syste
m
to
a
b
e
tter co
nd
ition
(bu
t
n
o
t
t
o
t
h
e as-
g
ood
-as
n
e
w st
ate). Th
e
d
e
gree o
f
im
p
r
o
v
e
m
e
n
t
o
f
a sy
stem’s reliab
ility is
a rand
o
m
v
a
riab
le wh
ich
d
e
p
e
n
d
s
on the c
o
m
ponent’s a
g
e.
The m
e
t
hod s
t
at
ed i
n
t
h
e a
b
o
v
e st
udi
es
has
been
di
sc
usse
d by
P
h
a
m
and
Wan
g
[1
2]
an
d i
s
desi
g
n
at
ed
as “
t
he i
m
provem
e
nt
fact
or
m
e
t
h
od”
. T
h
e
re
sea
r
ch areas
of t
h
e im
perf
ect prev
en
tiv
e m
a
in
te
n
a
n
ce
have
bee
n
f
o
c
u
se
d o
n
t
h
e i
s
sues
of
opt
i
m
al
PM
or re
pl
ac
em
ent
pol
i
c
i
e
s, i
n
cl
u
d
i
n
g sch
e
dul
i
n
g m
odel
s
an
d
alg
o
rith
m
s
b
y
min
i
mizin
g
th
e av
erag
e co
st
-rate (co
s
t/tim
e)
o
f
a system
[1
-7
,
10
,
13
,
15
,
16
].
The
de
gr
ee of
m
a
i
n
t
e
nance
can be
m
easur
ed by
ei
t
h
er
t
h
e fre
que
ncy
of
PM
or
t
h
e avera
g
e
t
i
m
e
in
terv
al b
e
tween
PM
in
terv
en
tio
ns
[1
-2
, 4
,
5
,
7
-
16
].
In
thi
s
researc
h
, eac
h com
p
one
n
t in
a
d
i
stribu
tio
n syste
m
i
s
t
r
eat
ed as a sy
st
em
wi
t
h
m
a
ny
com
pone
nt
s
.
It
i
s
al
so di
f
f
i
c
ul
t
t
o
m
easure
t
h
e deg
r
ee o
f
m
a
i
n
t
e
nance f
o
r t
h
e
OFPM
i
n
a s
h
ort
pe
ri
o
d
o
f
t
i
m
e. Thus
, t
h
i
s
pape
r u
s
es t
h
e
t
o
t
a
l
cum
u
l
a
ti
ve t
i
m
e
done
by
t
h
e OFPM
act
i
v
i
t
y
fo
r a c
o
m
pone
nt
at
age
t
as a
m
easure
fo
r t
h
e de
gree
o
f
m
a
i
n
t
e
nanc
e.
Th
e
reliab
ility
is co
m
p
ared fo
r th
e co
m
p
o
n
en
t th
at is
with
an
d withou
t
i
m
p
l
e
m
en
tin
g
th
e OFPM
.
Si
nce t
h
e
O
F
P
M
no
rm
al
ly
does
not
i
n
cl
u
d
e
pa
rt
s re
pl
ace
men
t
, it is assu
m
e
d
th
at th
e
sh
ap
e
o
f
t
h
e
failu
re
di
st
ri
b
u
t
i
on i
s
not
cha
n
ged
b
u
t
t
h
e effect
i
v
e age of a co
m
ponent
i
s
re
duce
d
by
u
n
i
t
s
of t
i
m
e
i
f
OFPM
i
s
per
f
o
r
m
e
d.
2.
ASS
U
MPTIO
N
S A
N
D
C
O
NSI
D
ER
ATI
O
NS
The c
h
aracte
r
istics associated wit
h
the
OFPM are
sh
ort main
ten
a
n
ce
i
n
terv
als, sh
ort
m
a
in
ten
a
n
c
e
ti
m
e
in
o
n
lin
e PM an
d
littl
e i
m
p
r
o
v
e
m
e
n
t
o
f
th
e reliabilit
y. As a resu
lt, it is n
ece
ssary to
d
e
fi
ne th
e
assu
m
p
tio
n
s
b
a
sed
on
th
e abov
e ch
aracteristics to
d
e
v
e
lop
a m
o
d
e
l. Th
e assu
m
p
tio
n
s
to th
e m
o
d
e
l are:
1
.
In
practice, th
e OFPM is ex
ecu
ted
in
sh
ort in
te
rvals and the fre
quency
may
be fi
xed, f
o
r i
n
st
a
n
ce,
o
n
c
e a
week or two ti
m
e
s a week
.
Sin
ce it is
k
nown th
at
th
e reliab
ility o
f
t
h
e system
will
b
e
sligh
tly i
m
p
r
ov
ed
due
to e
x
ec
uting the
OFPM for a c
o
m
pone
nt, this resea
r
c
h
will foc
u
s
on t
h
e total c
u
m
u
lative tim
e
spent in the
OFPM acti
v
ity fo
r a lon
g
p
e
ri
o
d
of tim
e.
2. Si
nce t
h
e O
FPM
i
s
perf
o
r
m
e
d by
t
h
e i
n
-l
i
n
e o
p
erat
ors
,
the m
a
intenance
cost of the OFPM is
co
nsid
erab
ly lower th
an
th
at
of an
y o
t
h
e
r
k
i
nd
s
o
f
m
a
in
ten
a
n
ce.
3
.
Th
e in
crease of th
e to
tal cum
u
la
tiv
e ti
m
e
sp
en
t
in
t
h
e
o
fflin
e prev
en
tiv
e m
a
in
ten
a
n
c
e activ
ity will
redu
ce t
h
e av
ailab
l
e ti
m
e
in
p
r
od
u
c
tion
and so in
crease
t
h
e pr
odu
ctio
n l
o
ss co
st. Bu
t
pr
odu
ctio
n lo
ss
co
st in
o
n
lin
e prev
en
ti
v
e
m
a
in
ten
a
n
c
e is clo
s
e t
o
zero.
4
.
Si
n
ce th
e OFPM in
vo
lv
es o
n
l
y m
i
n
o
r
m
a
in
ten
a
n
c
e witho
u
t
an
y rep
l
acemen
t
o
r
rep
a
ir
activ
ity, it
is
assum
e
d t
h
at
t
h
ey
o
n
l
y
p
o
s
t
po
ne t
h
e
fai
l
ure
occ
u
r
r
e
n
c
e
b
u
t
kee
p
i
n
g
t
h
e s
h
ape
o
f
com
pone
nt
’s
fai
l
u
re
d
i
str
i
bu
tio
n.
5. S
u
ppose that the degre
e
of im
provem
ent for
the com
ponent’s
reliability is
m
.
The
n
, m
is a
fun
c
tion
of
b
o
t
h
th
e t
o
tal cum
u
la
tiv
e ti
m
e
(
p
t
) spe
n
t
i
n
t
h
e
OFPM
a
n
d t
h
e age
of t
h
e c
o
m
pone
nt
(t
’
)
,
i
.
e.,
m (
p
t
, t’). For
practical applications, the m
(
p
t
, t
’) f
unct
i
on c
a
n be
obt
ai
ne
d
from
t
h
e hi
st
ori
cal
dat
a
o
f
a
com
pone
nt
.
3.
MAT
H
EM
AT
ICAL
M
O
DE
LING
Accord
ing
to
Assu
m
p
tio
n
s
4, th
e failu
re pro
b
a
b
ility
d
e
n
s
ity fu
n
c
tion
(pdf) of a co
m
p
o
n
en
t with
and
wi
t
h
o
u
t
i
m
pl
em
ent
i
ng t
h
e
O
FPM
are
s
h
o
w
n i
n
Fi
gu
re
1,
whe
r
e
)
(
1
t
f
a
n
d
)
(
0
t
f
are respecti
v
ely
the failure
pd
f o
f
a com
p
one
nt
wi
t
h
an
d
wi
t
h
o
u
t
im
pl
em
ent
i
ng t
h
e O
FPM
. It
can be
seen fr
om
Fi
gure 1 t
h
at
t
h
e f
a
i
l
u
re
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
19
3 – 1
9
9
19
6
den
s
i
t
y
of a
c
o
m
ponent
wi
t
h
t
h
e
OFPM
at
a
g
e t
’
i
s
t
h
e
sa
m
e
as t
h
e
fai
l
u
re
densi
t
y
o
f
t
h
e c
o
m
pone
nt
wi
t
h
o
u
t
executing t
h
e
OFPM at
age
t”.
Fi
g
u
re
1
.
P
d
f
of
a c
o
m
pone
n
t
wi
t
h
a
n
d
wi
t
h
out
OF
PM
A
p
pl
i
cat
i
o
n
Figure
2. Reliability functio
n
of a c
o
m
pone
nt with a
n
d without
OF
PM Application
Th
is m
ean
s that th
e co
m
p
onen
t
with th
e
OFPM p
l
an
is t’-t” (say
) un
its
o
f
tim
e yo
u
nger th
an
t
h
e
com
pone
nt
wi
t
h
o
u
t
i
t
.
Th
us,
can be t
r
eat
ed as t
h
e i
m
provem
e
nt
of a
g
i
ng.
I
n
ot
her
wo
rd
s, t
h
e
OF
P
M
activ
ity d
e
lays th
e failure
o
c
cu
rren
ce b
y
u
n
i
t
s
o
f
t
i
m
e
.
I
t
c
a
n
be
proved that the m
ean
of
)
(
1
t
f
, say
1
m
, is
also
greater tha
n
the
m
ean of
)
(
1
t
f
,
1
m
by
u
n
its o
f
ti
me.
Ass
u
m
e
that
)
(
R
is th
e
d
i
fferen
ce of th
e reliab
i
lity at t’ b
e
tween
)
(
1
t
f
and
)
(
0
t
f
. Let
)
(
'
0
t
R
be
th
e reliab
ility
o
f
th
e co
m
p
onen
t
with
ou
t execu
tin
g
th
e
OFPM an
d
)
(
'
1
t
R
be the reliability of the com
pone
nt
wi
t
h
t
h
e O
F
P
M
act
i
v
i
t
y
as sho
w
n i
n
Fi
g
u
r
e
2. As
sum
e
t
h
at
t
h
e t
o
t
a
l
cum
u
l
a
t
i
v
e t
i
m
e
of c
o
m
pone
nt
spe
n
t
i
n
th
e
OFPM activ
ity at ag
e t’ is
p
t
. T
h
en
,
base
d
on
t
h
e
co
nce
p
t
o
f
t
h
e
Im
prov
em
ent
Fact
o
r
m
e
t
hod,
t
h
e
d
e
gree
o
f
im
p
r
o
v
e
m
e
n
t
for th
e co
m
p
on
en
t
’
s
reliab
ilit
y at ag
e t’ is
)
(
p
t
D
, where:
)
(
)
(
)
(
)
(
'
0
'
1
t
R
t
R
R
t
D
p
(1
)
From
Figure
2,
)
(
'
0
t
R
and
)
(
'
1
t
R
are the
integrated a
r
e
a
of
)
(
'
0
t
f
and
)
(
'
1
t
f
after t’, resp
ectiv
ely.
Whe
r
e;
)
(
1
)
(
'
0
'
0
t
f
t
R
An
d
)
(
1
)
(
'
0
'
0
t
f
t
R
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Relia
b
ility a
nd Co
st Mod
e
l o
f
P.M. in
A Compon
en
t
o
f
a
n
Electrica
l Distrib
u
tion
S
y
stem… (S
. Afsha
r
)
19
7
Sin
ce th
e to
tal cu
m
u
lativ
e ti
me,
p
t
, of a c
o
m
ponent s
p
ent in
perf
orm
i
ng the
OFPM activity will not
d
i
rectly equ
a
l to
th
e im
p
r
ove
m
e
n
t
o
f
ag
ing
fro
m
th
e OFPM, th
e
relatio
n
b
e
tween
p
t
and
need t
o
be
obt
ai
ne
d.
I
n
re
al
wo
rl
d,
)
(
p
t
D
i
s
u
n
k
n
o
w
n a
n
d i
s
di
ffi
c
u
l
t
t
o
be
m
easured
.
Ho
weve
r,
)
(
'
0
t
f
can be obt
ai
ne
d
fr
om
t
h
e equi
p
m
ent
ven
d
o
rs
a
n
d
)
(
'
1
t
f
can
be a
n
al
y
zed f
r
om
t
h
e
m
a
i
n
t
e
nance
hi
st
ory
dat
a
o
f
t
h
e com
pone
nt
.
Th
us, t
h
e
val
u
e of
for t
h
e co
m
ponent
at
ag
e t
’
can be cal
cul
a
t
e
d an
d t
h
e val
u
e o
f
)
(
p
t
D
can the
n
be o
b
t
a
i
n
e
d
.
B
a
sed o
n
Fi
g
u
re
1, i
t
can
be f
o
un
d t
h
at
whe
n
t
’
i
n
cr
eases, t
h
e
de
g
r
ee o
f
i
m
prov
em
ent
of
com
pone
nt’s
reliability will becom
e
slow
down due
to t
h
e
value
of
b
e
i
n
g fix
e
d
.
Th
u
s
, i
n
add
itio
n to
p
t
, the
com
pone
nt age, and t’, is anot
her
factor t
o
affect the degree
of im
provem
e
nt of c
o
m
ponent’s
reliability.
There
f
ore,
)
(
p
t
D
can be m
odi
fi
ed
t
o
be
)
,
(
'
t
t
D
p
. Similar
l
y,
)
(
R
becom
e
s
)
,
(
'
t
R
and
)
,
(
'
t
t
D
p
will be
)
,
(
'
t
R
, t
h
at
i
s
,
Eq
uat
i
on
(
1
)
can
be
m
odi
fi
ed as:
)
,
(
)
,
(
'
'
t
R
t
t
D
p
(2
)
4.
CA
SE ST
UD
Y
For
an e
x
am
pl
e we ca
n co
ns
i
d
er t
h
e
di
st
ri
b
u
t
i
on
sy
st
em
sho
w
n i
n
fi
g
u
r
e
4 w
h
i
c
h i
s
a
part
of a
n
ur
ba
n el
ect
ri
c
po
we
r
di
st
ri
b
u
t
i
on
sy
st
em
i
n
S
w
ede
n
t
h
e t
o
t
a
l
sy
st
em
consi
s
t
o
f
:
Med
i
u
m
v
o
ltage un
d
e
rg
ro
und
cab
les an
d ov
er
h
e
ad
lin
es (11 and
2
0
kV)
:
51
5,
5
k
m
to
tall
y.
Po
wer t
r
an
sf
or
m
e
rs fr
om
sub
s
t
a
t
i
ons
havi
ng
2
0
/
0
,
4
k
V
a
n
d
1
1
/
0
,
4
k
V
vol
t
a
ge:
6
3
7
t
o
t
a
l
l
y
.
M
e
di
um
vol
t
a
g
e
b
r
eake
r
s (1
1 kV
an
d 2
0
kV
)
are 5
3
8
i
n
n
u
m
ber
M
e
di
um
vol
t
a
g
e
swi
t
c
hes
(
1
1
kV
an
d
2
0
kV
)
are
1
3
5
0
i
n
nu
m
b
er.
Fi
gu
re
3.
A
pa
r
t
of
t
e
st
di
st
ri
b
u
t
i
o
n
sy
st
em
For th
e C
3
3
tran
sform
e
r wh
ich
is a
first
o
r
d
e
r cu
t-set; we can
g
e
n
e
rate a cu
m
u
lativ
e wei
b
u
ll
d
i
stribu
tio
n fun
c
tio
n as sho
w
n
in fi
g
u
re
4
u
s
in
g
statistical d
a
ta for th
e co
mp
on
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
19
3 – 1
9
9
19
8
Fig
u
re
4
.
Cu
mu
lativ
e pro
b
a
b
i
lity o
f
failure
weibu
ll Distribu
tio
n fun
c
tio
n
Using
wei
b
u
l
l
cu
m
u
lativ
e p
r
ob
ab
ility o
f
failu
re Mo
d
e
l
co
nstan
t
s presen
ted
in
fi
g
u
re 4
)
,
(
'
t
t
C
p
Fun
c
tio
n is illu
strated b
y
app
l
yin
g
45
.
0
d
C
,
180
r
C
,
0000073
.
0
,
725
.
1
,
0005
.
0
,
05
.
1
,
and
0005
.
0
w
h
en
t’
=
21
00
un
its of
ti
m
e
an
d
is sho
w
n
i
n
Figur
e 5. By ap
p
l
ying
t’
=
21
00
, it can
b
e
fo
und
th
at
th
e op
tim
a
l
to
tal cu
m
u
lativ
e ti
m
e
o
f
th
e OFPM
)
(
*
p
t
i
s
9
7
.
3
2
uni
t
s
of t
i
m
e;
t
h
e de
gree
o
f
i
m
provem
e
nt
i
n
reliab
ility
)
,
(
'
t
t
D
p
is 0.
12
0
8
; the
di
ffe
rence
o
f
failure
rate
Δ
i
s
0.
00
0
2
67;
t
h
e di
f
f
ere
n
ce of
e
xpect
e
d
num
be
r
of
failu
re
)
(
i
s
0.
34
1;
a
n
d
t
h
e
sa
ved
co
st
P i
s
10.342. From
the above
exam
ple,
It can b
e
no
ted
th
at t
h
e im
p
r
ov
em
en
t in
reliab
ility an
d
red
u
c
tion
i
n
co
st
are si
g
n
i
ficant wh
en
t
h
e
OFPM
i
s
ap
pl
i
e
d. It
i
s
al
so s
h
o
w
n t
h
at
t
h
e
effect
o
f
t
h
e O
FPM
st
ro
n
g
l
y
depe
n
d
s o
n
t
h
e
com
pone
nt
’s f
a
i
l
u
re
d
i
str
i
bu
tio
n.
Fig
u
r
e
5 sh
ows an
ex
am
p
l
e of
C
(
,
t’) fun
c
tio
n at
45
.
0
d
C
,
180
r
C
,
0000073
.
0
,
725
.
1
,
0005
.
0
,
05
.
1
, a
n
d
0005
.
0
Fig
u
re
5
.
Co
st
fun
c
tion
at t’=2
100
u
n
its
o
f
time fo
r offlin
e
PM wh
en
=0
.00
000
73
and
725
.
1
We can
also
fou
n
d
th
at th
e
o
p
ti
m
a
l to
tal cu
mu
lativ
e ti
m
e
o
f
th
e OFPM
(
*
)
is 9
7
.
32
un
its o
f
tim
e,
th
e d
e
gree
o
f
i
m
p
r
o
v
e
m
e
n
t
in
reliab
ility is
calcu
lated
as
D (
, t’
) =
0
.
1
2
0
8
,
the
di
ffe
re
nce
of
failu
re
rate
)
(
h
i
s
0.
00
0
2
6
7
, t
h
e di
ffe
rence
f
expecte
d
num
b
er of failure
)
(
i
s
0.
34
1, a
n
d t
h
e co
st
save
d
i
s
as P =
1
0
.342
. It can
b
e
seen
fro
m
t
h
is ex
am
p
l
e th
at th
e d
e
g
r
ee of i
m
p
r
ov
em
en
t in
reliab
ility
is
m
o
re sig
n
i
fican
t
th
an
th
e red
u
c
tion
i
n
co
st
wh
en
the OFPM is app
lied
.
It can
al
so be
shown t
h
at the ef
fect of t
h
e OFPM s
t
rongly
depe
n
d
s
o
n
t
h
e
com
pone
nt
’s
f
a
i
l
u
re
di
st
ri
b
u
t
i
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Relia
b
ility a
nd Co
st Mod
e
l o
f
P.M. in
A Compon
en
t
o
f
a
n
Electrica
l Distrib
u
tion
S
y
stem… (S
. Afsha
r
)
19
9
5.
C
O
N
C
L
U
S
ION
A
N
D
SUMM
ARY
Based
on
th
e co
n
c
ep
ts of the Prev
en
tiv
e
Main
ten
a
n
ce an
d
th
e Im
p
r
o
v
e
m
en
t Facto
r
Meth
od
, th
e
OFPM
m
o
d
e
l i
s
co
ndu
cted
with
sev
e
ral assum
p
t
i
o
n
s
b
e
i
n
g
mad
e
. B
o
th the to
tal cu
m
u
lativ
e tim
e
and t
h
e
age
of the c
o
mpone
n
t (t’) a
r
e
incorp
orat
e
d
i
n
t
h
e
pr
o
pose
d
m
odel
.
An
op
ti
m
u
m
t
o
tal cu
m
u
lativ
e ti
m
e
) can
be
obt
ai
ne
d
by
t
h
e n
u
m
e
ri
cal
anal
y
s
i
s
m
e
t
hod
wi
t
h
t
h
e
consideration
of the effects of the cost and c
o
m
pone
nt
reliability. An exa
m
ple has been
give
n and shown that
t
h
e p
r
o
p
o
se
d
OFPM
m
odel
m
i
ght
be a
n
a
p
pr
oac
h
o
f
c
h
o
o
s
i
ng m
a
i
n
t
e
nan
ce p
o
l
i
c
y
for
c
r
i
t
i
cal
com
pon
ent
s
i
n
a syste
m
.
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NC
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os
t optim
iza
t
i
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a
in
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EEE
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[2]
Chaudhuri D an
d KC Sahu. “Preventiv
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inten
a
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EEE
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Reliab
ility
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ility
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EE
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and T D
o
w
n
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w
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r
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a
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e m
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inte
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h
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a
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A
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eli
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E
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y
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b
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ptim
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inten
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e
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W
a
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a
kagaw
a
T
.
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M
ean tim
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ilure w
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e
n
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a
int
e
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ce”
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r
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i
a
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ilit
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[13]
M
a
rtorel
l S
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A
S
a
nchez
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S
e
rradel
l
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A
ge-
d
ependen
t
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i
ab
ilit
y m
odel
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idering
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t
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a
intenan
ce
a
n
d
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ng and
system Safety
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999; 64: 19-31.
[14]
Nakagawa
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i
c
i
e
s w
h
en preven
ti
ve m
a
int
e
nanc
e
is
im
perfe
ct”
.
IEEE Transactions on Reliability
.
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[15]
Wa
ng H a
nd H Pha
m
.
“Opt
i
m
a
l
a
g
e
-
de
pe
nde
nt
pre
v
e
n
t
i
v
e
ma
i
n
t
e
na
nc
e pol
ic
ie
s wi
t
h
i
m
pe
rfec
t
ma
i
n
te
na
nce”.
International Jo
urnal of
Reliabil
ity, Quality and
Safety Eng
i
neering
. 1996; 3(2): 1
19-135.
[16]
Mitchell J Mondro. “Approxima
tion of Mean
Tim
e
between Failures W
h
en
a Sy
stem
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o
d
ic Maintenan
c
e”.
IEEE Transactio
ns
on Reliability
. 2002; 51(2)
: 16
6-167.
BIOGRAP
HI
ES OF
AUTH
ORS
S
a
eed
Afs
h
ar,
was Born in 1973 in Tehr
an, I
r
an. He r
eceived the B.S. d
e
gr
ee in Contro
l
Engineering fro
m
Tehran University
, Iran
,
in
1996,
and the M.S. d
e
grees in
Electrical
Engineering fro
m
Tehran University
, Iran
,
in 19
99. He is now a PHD student in Islam
i
c Azad
uni
ve
rsi
t
y
Sci
e
nc
e
a
nd Re
sea
r
ch Bra
n
c
h
,
Te
hra
n
,
Ira
n
.
H
i
s work of i
n
te
re
st
i
s
Re
l
i
a
b
i
lity
Center
ed Main
tenancre, Prev
entive Maintenan
c
e
a
nd Reliab
ility
s
t
ud
y
of
Electrical distr
i
bution
s
y
st
ems
M
a
hmud F
o
tu
hi F
i
r
u
z
a
ba
d,
w
a
s born in Ir
an. H
e
r
eci
eved
B.S
c
.
and M
.
S
c
. D
e
gre
e
s in
Electrical ngineering from
Sharif
University
of
Technolog
y
and
Tehran
University
in 1986
and
1989 respectiv
ely
and M.Sc. and
Ph.D. Degrees in El
ectrical
Engineering from
the University
o
f
Saskatchewan in 1993 and 199
7 respectiv
ely
.
Dr.
Fotuhi-Firuzabad worked as a postdoctoral
fellow in the Departm
e
nt of Electrical Engin
eer
in
g, University
of Saskatchewan fr
om
Jan. 1998
to Sept. 2000 and from
Sept. 2001 to Sept. 20
02 wh
ere he co
nducted res
earch in the area of
pow
er sy
st
em
reliabi
lit
y.
H
e
w
o
rked as an assist
ant professor in the sam
e
departm
e
nt from
Sept.
2000 to Sept. 2
001. Presently
he is an associat
e prof
essor and Head of the
Departm
e
nt of
Electrical
Engin
eering
,
Sharif University
of T
echnolog
y
,
and Tehran, Iran
.
Dr. Fotuhi-Firuzabad
is also
a m
e
m
b
er
.
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