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2670
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g t
a
b
l
e
,
i
nd
i
c
a
t
i
n
g
m
o
r
e
o
r
l
e
s
s
e
ve
nt
s
,
f
o
r
m
i
ni
m
i
z
i
n
g
s
t
at
e
s
p
ace
w
a
s
e
m
p
l
o
y
ed
b
y
[5
]
.
C
h
an
K
W
et
.
al
,
[6
]
de
v
e
l
ope
d
a
n
onl
i
n
e
a
l
g
or
i
t
hm
o
f
s
y
s
te
m
in
s
ta
b
ilit
y
s
t
u
d
ie
s
f
o
r
c
o
n
s
id
er
ab
l
e a
m
o
u
n
t
o
f
r
ed
u
ct
i
o
n
i
n
s
t
at
e s
p
ace
w
i
t
h
d
y
n
a
m
i
c s
ec
u
r
i
t
y
c
o
nt
i
n
ge
nc
y
s
c
r
e
e
ni
ng.
S
i
n
g
ul
a
r
va
l
ue
a
na
l
ys
i
s
o
f
l
o
a
d
f
l
o
w
j
a
c
o
b
i
a
n
w
a
s
us
e
d
f
o
r
r
a
nki
n
g t
he
c
o
nt
i
n
ge
nc
i
e
s
w
i
t
h r
e
ga
r
d
t
o
v
o
l
t
ag
e
co
l
l
ap
s
e t
o
r
ed
u
ce t
h
e s
t
a
t
e s
p
ace e
f
f
ect
i
v
el
y
[7
]
.
I
d
ea o
f
i
n
t
e
g
r
at
i
n
g
o
p
er
at
o
r
s
ex
p
er
i
en
ce i
n
co
n
t
i
n
g
e
n
c
y
s
el
ect
i
o
n
f
o
r
d
ecr
eas
i
n
g
t
h
e
s
t
at
e
s
p
ace
w
as
p
r
o
p
o
s
ed
[8
]
.
A
r
t
i
f
i
ci
al
n
e
u
r
al
n
et
w
o
r
k
s
w
er
e a
l
s
o
e
xp
l
o
r
e
d
f
o
r
c
o
nt
i
nge
nc
y
r
a
n
ki
n
g.
F
uz
z
y
l
o
gi
c
b
a
s
e
d
M
W
r
a
nki
ng
f
o
r
c
o
nt
i
nge
nc
y
s
e
l
e
c
t
i
o
n
w
a
s
e
xp
l
o
r
e
d
[9
]
.
H
e
J
et
.
al
,
[
10
]
t
oo
k a
n a
d
va
nt
a
ge
o
f
c
o
m
b
i
ni
ng
s
t
a
t
e
e
nu
m
e
r
a
t
i
o
n a
nd
M
o
nt
e
C
a
r
l
o
s
i
m
ul
a
t
i
o
ns
,
b
y
ex
er
ci
s
i
n
g
s
t
at
e
s
p
ace
p
ar
t
i
t
i
on
i
ng
m
e
t
h
od.
F
u
r
t
h
e
r
,
f
e
e
d
f
o
r
w
a
r
d n
e
u
r
a
l
n
e
t
w
or
k
w
a
s
e
m
p
l
o
y
e
d
f
or
on
l
i
ne
c
o
nt
i
n
ge
nc
y
s
c
r
e
e
ni
ng
[
11]
.
S
u
p
p
o
r
t
v
ect
o
r
m
ac
h
i
n
e
s
al
o
n
g
w
i
t
h
s
cal
ar
p
er
f
o
r
m
a
n
ce i
n
d
i
ces
w
er
e ex
p
l
o
i
t
ed
t
o
r
a
nk c
o
nt
i
nge
nc
i
e
s
a
c
c
o
r
d
i
ng t
o
t
he
s
e
ve
r
i
t
y
[
12]
.
A
li M
a
n
s
o
u
r
i e
t.
a
l,
[
13]
in
v
e
s
tig
a
te
d
th
e
i
m
p
a
c
t o
f
d
i
r
ect
l
o
ad
co
n
t
r
o
l
o
n
n
o
d
al
r
el
i
ab
i
l
i
t
y
o
f
a
d
er
eg
u
l
at
ed
p
o
w
er
s
y
s
t
e
m
.
S
aeed
A
f
s
h
ar
et
.
al
,
ex
cer
s
i
s
ed
p
r
ev
en
t
i
v
e
m
a
i
n
te
n
a
n
c
e
f
o
r
e
le
c
tr
ic
a
l d
is
t
r
ib
u
tio
n
s
y
s
te
m
d
e
lib
e
r
a
tin
g
a
g
e
in
g
[
14]
.
E
ar
l
i
er
r
es
ear
ch
w
as
c
en
t
er
ed
o
n
co
m
p
u
t
at
i
o
n
o
f
d
et
er
m
i
n
i
s
t
i
c p
er
f
o
r
m
an
ce
i
n
d
i
ce
s
a
n
d
d
ev
el
o
p
m
e
n
t
o
f
A
N
N
b
a
s
e
d
m
a
n
ip
u
la
tin
g
te
c
h
n
iq
u
e
s
f
o
r
th
o
s
e
i
n
d
ic
e
s
.
B
u
t,
c
o
n
tin
g
e
n
c
y
b
y
d
e
f
in
itio
n
h
a
s
a
g
r
e
a
t d
e
g
r
e
e
o
f
u
n
c
e
r
ta
i
n
t
y
i
m
b
ib
e
d
i
n
it.
P
r
e
v
io
u
s
m
e
th
o
d
s
e
m
p
lo
y
e
d
d
e
te
r
m
in
i
s
tic
in
d
i
c
e
s
w
h
i
c
h d
o
e
s
no
t
gua
r
a
nt
e
e
r
a
n
do
m
n
e
s
s
i
n
c
o
m
p
u
t
a
t
i
on
,
w
hi
c
h
w
a
s
t
h
e
m
a
j
or
pr
obl
e
m
n
e
v
e
r
be
e
n
a
ddr
e
s
s
e
d.
P
r
o
pos
e
d P
r
oba
bi
l
i
s
t
i
c
i
n
d
ex
o
r
P
r
o
b
ab
i
l
i
s
t
i
c P
er
f
o
r
m
an
ce I
n
d
ex
(
P
P
I
)
i
n
t
eg
r
at
es
r
an
d
o
m
n
e
s
s
i
n
t
h
e p
r
o
ces
s
o
f
i
t
s
co
m
p
u
t
at
i
o
n
.
I
n
t
h
e c
u
r
r
en
t
r
es
ear
ch
i
nv
e
s
t
i
g
a
t
i
on
s
P
P
I
m
e
t
h
od i
s
pr
opos
e
d,
w
hi
c
h
m
a
y
be
pr
a
c
t
i
c
a
l
f
or
c
on
t
i
n
g
e
n
c
y
s
c
r
e
e
n
i
ng
of
po
w
e
r
s
y
s
t
e
m
.
2.
C
O
M
P
O
S
I
TE P
O
W
ER
S
Y
S
TEM
R
ELI
A
B
IL
I
TY
EV
A
L
U
A
TI
O
N
T
h
er
e w
er
e t
w
o
co
n
v
en
t
i
o
n
al
m
et
h
o
d
s
a
v
ai
l
ab
l
e f
o
r
cal
c
u
l
at
i
n
g
t
h
e r
el
i
ab
i
l
i
t
y
o
f
co
m
p
o
s
i
t
e p
o
w
er
s
ys
t
e
m:
a.
M
o
n
te
C
a
r
lo
S
i
m
u
la
tio
n
T
e
c
h
n
iq
u
e
s
b.
A
n
al
y
t
i
cal
M
et
h
o
d
s
M
o
n
te
C
a
r
lo
m
e
th
o
d
s
o
f
s
i
m
u
la
tio
n
c
o
m
p
u
te
d
t
h
e
r
e
lia
b
ilit
y
i
n
d
ic
e
s
b
y
c
o
n
s
id
e
r
in
g
r
a
n
d
o
m
ch
ar
act
er
i
s
t
i
c
o
f
t
h
e
s
y
s
t
e
m
.
T
h
es
e
m
et
h
o
d
s
co
n
s
i
d
er
ed
t
h
e p
r
o
b
l
e
m
a
s
a
s
eq
u
e
n
ce
o
f
ex
p
er
i
m
e
n
t
s
.
I
n
an
al
y
t
i
cal
m
et
h
o
d
s
,
a
m
at
h
e
m
at
i
cal
m
o
d
el
w
as
b
ei
n
g
u
s
ed
t
o
ch
ar
act
e
r
iz
e
th
e
s
y
s
te
m
a
n
d
r
e
lia
b
ilit
y
i
n
d
ic
e
s
w
er
e co
m
p
u
t
ed
f
r
o
m
t
h
e
m
o
d
el
.
I
n
t
h
e cu
r
r
e
n
t
r
es
ear
ch
p
ap
er
,
s
t
at
e s
p
ace en
u
m
er
at
i
o
n
ap
p
r
o
ach
i
s
ad
o
p
t
ed
.
A
na
l
yt
i
c
a
l
m
e
t
ho
d
s
a
nd
M
o
nt
e
C
a
r
l
o
m
e
t
ho
d
s
w
e
r
e
ha
vi
ng
o
w
n a
d
va
nt
a
ge
s
a
nd
d
i
s
a
d
va
nt
a
ge
s
a
s
d
i
s
c
us
s
e
d
i
n
[
15]
,
[
16
]
.
C
o
m
p
u
ta
tio
n
a
l
t
i
m
e r
eq
u
i
r
ed
f
o
r
o
b
t
ai
n
i
n
g
i
n
d
i
ces
w
as
r
e
l
at
i
v
el
y
l
es
s
er
i
n
an
al
y
t
i
ca
l
t
ech
n
i
q
u
es
.
P
ar
t
i
cu
l
ar
s
i
m
p
l
i
f
y
i
n
g
as
s
u
m
p
t
i
o
n
s
m
a
y
b
e n
eed
ed
w
h
en
t
h
e s
y
s
t
e
m
b
eca
m
e co
m
p
l
e
x
an
d
l
ar
g
e.
A
l
s
o
,
s
i
m
u
la
t
io
n
m
e
th
o
d
s
m
a
y
n
e
e
d
lo
n
g
ti
m
e
f
o
r
th
e
c
o
m
p
u
ta
tio
n
.
2
.1
.
St
a
t
e
s
pa
c
e en
u
m
era
t
i
o
n
m
et
h
o
d
S
et
o
f
al
l
p
o
s
s
i
b
l
e
o
u
t
co
m
e
s
o
f
a
r
an
d
o
m
p
h
e
n
o
m
e
n
o
n
ca
n
b
e
d
es
i
g
n
at
ed
a
s
s
t
at
e
s
p
ac
e.
I
n
o
t
h
er
w
or
ds
,
c
o
m
bi
n
a
t
i
on of
i
n
di
v
i
du
a
l
s
t
a
t
e
s
o
f
v
a
r
i
ou
s
c
o
m
pone
n
t
s
l
i
k
e
g
e
n
e
r
a
t
or
s
,
t
r
a
ns
m
i
s
s
i
on
l
i
n
e
s
,
a
n
d l
oa
d
m
a
y
b
e t
er
m
ed
as
s
t
at
e o
f
a p
o
w
e
r
s
y
s
t
e
m
.
T
h
e s
t
at
e s
p
ace o
f
a p
o
w
er
s
y
s
t
e
m
i
s
r
ep
r
es
en
t
ed
as
v
ect
o
r
X
.
X
={x
1
, x
2
,
…,
x
n
}
(1
)
w
h
er
e,
x
1
, x
2
,
…,
x
n
ar
e s
t
at
es
o
f
i
n
d
i
v
i
d
u
a
l
co
m
p
o
n
e
n
t
s
l
i
k
e g
en
er
at
o
r
s
an
d
t
r
an
s
m
i
s
s
i
o
n
l
i
n
es
A
s
y
s
t
e
m
s
t
at
e i
n
s
t
at
e
s
p
ace en
u
m
er
at
i
o
n
m
et
h
o
d
m
a
y
b
e
d
e
s
ig
n
a
te
d
b
y
p
r
e
s
e
n
t s
ta
te
a
n
d
tr
a
n
s
itio
n
t
h
at
ca
n
o
ccu
r
b
et
w
ee
n
s
t
at
e
s
.
S
y
s
t
e
m
s
t
at
e i
n
d
i
cat
es
t
h
e
p
r
es
en
t
w
o
r
k
i
n
g
co
n
d
i
t
i
o
n
o
f
w
o
r
k
i
n
g
,
f
ai
l
ed
,
m
a
i
nt
e
na
nc
e
,
et
c.
C
h
a
n
g
e i
n
s
t
at
e
m
a
y
ca
u
s
e t
h
e t
r
an
s
i
t
i
o
n
f
r
o
m
o
n
e s
t
at
e
t
o
an
o
t
h
er
.
S
u
ch
p
o
s
s
i
b
l
e
co
m
b
i
n
at
i
o
n o
f
a
l
l
s
t
a
t
e
s
m
a
ke
up
t
he
s
ys
t
e
m
s
t
at
e
s
pac
e
.
I
d
eal
l
y
,
f
o
r
p
r
eci
s
e as
s
es
s
m
e
n
t
o
f
p
o
w
er
s
y
s
t
e
m
r
el
i
ab
i
l
i
t
y
,
e
n
t
i
r
e
co
n
t
i
n
g
en
c
y
s
t
at
es
o
f
al
l
o
r
d
er
s
n
eed
s
t
o
b
e co
n
s
i
d
er
ed
.
B
u
t
i
t
m
i
g
h
t
b
e p
r
act
i
cal
l
y
i
m
p
o
s
s
i
b
l
e t
as
k
f
o
r
as
s
es
s
i
n
g
al
l
co
n
t
i
n
g
en
c
i
es
.
F
o
r
ex
a
m
p
l
e
,
RBT
S
-
6
b
us
t
e
s
t
s
ys
t
e
m
w
i
t
h 1
1
ge
ne
r
a
t
o
r
s
a
nd
9
t
r
an
s
m
i
s
s
i
o
n
l
i
n
es
,
t
o
t
al
n
u
m
b
er
o
f
s
t
at
es
n
eed
ed
ar
e 2
20
(
i
.
e
.
10,
4
8,
5
76)
f
o
r
t
h
e as
s
es
s
m
e
n
t
.
T
o m
i
n
i
m
i
z
e
t
h
e
e
f
f
or
t
of
a
t
e
di
ou
s
t
a
s
k
,
num
e
r
ou
s
a
ppr
oxi
m
a
t
i
o
n
s
a
n
d
m
e
t
h
ods
w
e
r
e
de
v
e
l
ope
d.
T
r
unc
a
t
i
o
n
o
f
S
ta
te
-
S
p
ace (
T
S
S
)
w
as
p
r
o
p
o
s
ed
i
n
t
h
e ear
l
i
er
r
es
ear
ch
t
o
d
ecr
eas
e t
h
e co
m
p
u
t
at
i
o
n
al
b
u
r
d
en
[
17]
.
I
n
th
e
T
S
S
m
e
t
h
o
d
,
s
ta
te
s
w
it
h
in
s
ig
n
i
f
ic
a
n
t p
r
o
b
a
b
iliti
e
s
w
e
r
e
e
x
cl
u
d
ed
i
n
s
t
at
e
en
u
m
er
at
i
o
n
p
r
o
ced
u
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
P
r
obabi
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m
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2663
F
u
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ie
d
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p
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c
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s
id
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r
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th
a
t t
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p
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b
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s
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tin
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a
la
r
g
e
n
um
be
r
of
ov
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r
l
a
ppi
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f
a
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u
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s
a
n
d l
o
w
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r
num
be
r
of
f
a
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l
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r
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s
.
I
t
w
a
s
c
on
t
e
m
pl
a
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d t
h
a
t
pr
oba
bi
l
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t
i
e
s
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s
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s
w
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r
l
a
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p
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f
a
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ur
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s
m
a
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e
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e
g
lig
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le
w
h
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n
c
o
m
p
a
r
e
d
w
ith
p
r
o
b
a
b
ilitie
s
w
it
h
lo
w
e
r
n
u
m
b
e
r
o
f
f
a
il
u
r
e
s
[1
]
.
I
t
w
a
s
o
b
se
r
v
e
d a
g
r
e
a
t
r
e
du
c
t
i
on
i
n
t
h
e
num
be
r
o
f
s
t
a
t
e
s
t
o be
a
s
s
e
s
s
e
d a
n
d pos
s
i
bi
l
i
t
y
f
or
a
s
s
e
s
s
m
e
n
t
i
n
l
ar
g
e
v
ar
i
et
y
o
f
s
y
s
t
e
m
s
w
i
t
h
t
h
e
ai
d
o
f
s
u
i
t
ab
l
e
co
m
p
u
t
er
p
r
o
g
r
am
[
17]
.
E
ar
l
i
er
,
co
n
v
en
t
i
o
n
al
m
et
h
o
d
s
o
f
c
on
t
i
ng
e
n
c
y
r
a
n
k
i
ng
us
e
d t
h
e
c
on
c
e
pt
of
P
e
r
f
or
m
a
n
c
e
I
n
de
x (
P
I
)
a
s
de
s
c
r
i
be
d i
n
E
q
ua
t
i
o
n
2
.
PI
=
∑
P
flo
w
l
P
l
m
ax
2
n
n
l
=
1
(2
)
w
h
er
e,
=
t
he
M
W
f
l
o
w
o
n l
i
ne
‘
l
’
=
m
a
x
i
mu
m
f
l
o
w
o
n
l
i
n
e
’
l’
O
n
ce p
o
w
er
f
l
o
w
s
w
er
e
u
n
d
er
t
h
e
l
i
m
i
t
(
r
at
ed
l
i
n
e cap
ac
i
t
y
)
,
t
h
en
l
ar
g
er
v
al
u
e
s
o
f
‘
n
’
l
ead
s
t
o
s
m
al
l
er
v
al
u
e f
o
r
P
I
.
P
I
m
ay
b
e g
r
eat
er
w
h
e
n
o
n
e o
r
m
o
r
e l
i
n
e
s
ar
e o
v
er
l
o
ad
ed
i
n
t
h
e p
o
w
er
s
y
s
t
e
m
.
C
o
nt
i
n
ge
nc
i
e
s
w
e
r
e
r
a
n
ke
d
b
a
s
e
d
o
n t
he
m
a
g
ni
t
ud
e
o
f
t
he
P
I
va
l
ue
s
.
C
o
nt
i
n
ge
nc
i
e
s
b
e
l
o
w
t
he
t
hr
e
s
ho
l
d
w
e
r
e
di
s
c
a
r
de
d du
e
t
o
in
s
ig
n
i
f
ic
a
n
t
co
n
t
r
i
b
u
t
i
o
n
f
o
r
r
el
i
ab
i
l
i
t
y
.
H
o
w
e
v
er
,
t
h
e ear
l
i
er
co
n
cep
t
o
f
p
er
f
o
r
m
an
ce
i
n
d
e
x
s
u
f
f
er
s
cer
t
ai
n
s
h
o
r
t
co
m
i
n
g
s
.
T
h
e r
eal
p
o
w
er
v
al
u
es
u
s
ed
f
o
r
co
m
p
u
t
at
i
o
n
o
f
P
I
w
er
e ab
s
o
l
u
t
el
y
d
et
er
m
i
n
is
tic
.
T
h
er
e w
a
s
n
o
u
n
cer
t
ai
n
t
y
i
n
ear
l
i
er
co
m
p
u
t
at
i
o
n
s
.
A
l
s
o
,
t
h
e co
m
p
u
t
at
i
o
n
o
f
P
I
w
a
s
d
ep
en
d
en
t
o
n
e
x
p
o
n
en
t
s
el
ect
i
o
n
.
S
m
al
l
er
v
a
l
u
e
s
o
f
e
x
p
o
n
en
t
ca
u
s
ed
t
h
e
m
a
s
k
i
n
g
e
f
f
ect
.
G
r
eat
er
t
h
e v
al
u
e o
f
ex
p
o
n
en
t
l
es
s
er
w
as
t
h
e
ch
an
ce o
f
m
i
s
cl
as
s
i
f
i
cat
i
o
n
o
f
s
t
at
es
an
d
t
h
at
w
as
co
n
s
i
d
er
ed
as
m
as
k
i
n
g
e
f
f
ec
t
[4
]
.
I
n a
dd
i
t
i
o
n,
l
a
r
ge
r
va
l
ue
of
e
x
pon
e
n
t
g
i
v
e
s
r
i
s
e
t
o n
o
nl
i
n
e
a
r
i
t
y
.
A
c
c
or
di
n
gl
y
,
f
or
m
e
r
r
e
s
e
a
r
c
h
i
n
v
e
s
t
i
g
a
t
i
ons
di
s
c
l
os
e
d t
h
a
t
opt
i
m
um
i
nt
e
ge
r
s
e
l
e
c
t
i
o
n
f
o
r
e
xp
o
ne
n
t
w
i
l
l
hi
g
hl
y
i
n
f
l
ue
nc
e
t
he
P
I
c
a
l
c
ul
a
t
i
o
n a
nd
f
u
r
th
e
r
a
f
f
e
c
ts
th
e
c
o
nt
i
n
ge
nc
y
r
a
nki
n
g
[
18]
.
3.
P
R
OP
OS
E
D
M
E
T
HOD
OL
OG
Y
I
n
t
h
e cu
r
r
en
t
r
es
ear
ch
i
n
v
e
s
t
i
g
at
i
o
n
s
,
a n
e
w
i
n
d
ex
i
s
p
r
o
p
o
s
ed
t
h
at
o
v
er
co
m
es
af
o
r
e
m
en
t
i
o
n
ed
s
ho
r
t
c
o
m
i
n
gs
.
T
ho
u
gh
t
he
c
o
m
p
ut
a
t
i
o
na
l
pr
oc
e
du
r
e
i
s
l
a
bor
i
ou
s
v
i
s
-
à
-
v
i
s
c
onv
e
nt
i
on
a
l
P
e
r
f
or
m
a
n
c
e
I
n
de
x
(
P
I
)
,
t
h
e
r
a
nk
i
ng
of
c
on
t
i
ng
e
n
c
i
e
s
i
s
qu
i
t
e
pr
o
m
i
s
i
ng
.
T
h
e
pr
opos
e
d i
n
de
x
i
s
de
s
i
g
n
a
t
e
d a
s
P
r
oba
bi
l
i
s
t
i
c
P
er
f
o
r
m
a
n
ce I
n
d
ex
(
P
P
I
)
a
nd
i
s
d
e
f
i
ne
d
i
n e
q
ua
t
i
o
n 3
.
PPI
=
∑
=
1
=
1
(3
)
w
h
er
e:
W
=
R
eal
n
o
n
-
n
e
g
at
i
v
e
w
ei
g
h
t
i
n
g
f
act
o
r
Y
=O
r
d
er
o
f
t
h
e ex
p
o
n
en
t
N
=
N
o.
of
bu
s
e
s
n
=N
o
.
o
f
co
n
t
i
n
g
en
c
i
es
L
kj
=MW
cu
r
t
ai
l
ed
at
k
th
bu
s
f
or
j
th
c
o
nt
i
n
ge
nc
y
F
j
=F
r
eq
u
en
c
y
o
f
f
ai
l
u
r
e f
o
r
j
th
c
o
nt
i
n
ge
nc
y
V
a
l
ue
o
f
t
he
w
e
i
ght
i
ng
f
a
c
t
or
(
W
)
m
a
y
be
t
a
k
e
n
a
s
1.
O
r
de
r
of
e
x
pon
e
n
t
(
Y
)
h
a
s
t
o be
opt
i
m
a
l
l
y
s
e
l
e
c
t
e
d
.
L
o
w
e
r
o
r
hi
g
he
r
va
l
ue
s
f
o
r
Y
m
a
y
r
e
s
ul
t
i
n
m
a
s
ki
n
g a
nd
no
n
l
i
ne
a
r
i
t
y
p
r
o
b
l
e
m
s
i
n r
a
n
ki
ng t
he
co
n
t
i
n
g
e
n
ci
es
,
r
es
p
ect
i
v
el
y
.
T
h
e p
r
o
ced
u
r
e f
o
r
co
m
p
u
t
at
i
o
n
o
f
P
P
I
i
s
i
l
l
u
s
t
r
at
e
d
in
th
e
f
o
llo
w
i
n
g
s
e
c
tio
n
.
I
t
w
a
s
p
r
o
p
o
s
ed
t
o
car
r
y
o
u
t
r
e
s
ear
ch
s
t
ud
i
e
s
i
n a
s
ys
t
e
m
a
t
i
c
m
a
nne
r
a
s
s
ho
w
n
i
n
F
i
gur
e
1
.
I
n
itia
ll
y
it w
a
s
p
l
an
n
ed
t
o
g
at
h
er
t
h
e r
el
i
ab
i
l
i
t
y
d
at
a,
co
m
p
o
n
en
t
f
ai
l
u
r
e r
at
e,
r
ep
ai
r
r
at
e f
o
r
t
h
e t
e
s
t
p
o
w
er
s
y
s
t
e
m
n
et
w
o
r
k
.
H
en
ce
f
o
r
t
h
,
g
e
n
e
r
a
to
r
a
n
d
tr
a
n
s
m
i
s
s
io
n
a
v
a
ila
b
ilitie
s
w
e
r
e
c
a
lc
u
la
te
d
[1
]
.
F
u
r
th
e
r
,
s
ta
te
p
r
o
b
a
b
ilitie
s
a
n
d
s
ta
te
f
r
eq
u
en
c
i
es
w
er
e co
m
p
u
t
ed
a
n
d
av
ai
l
ab
l
e cap
aci
t
y
(
C
av
)
w
a
s
cal
c
u
l
at
ed
f
o
r
d
i
f
f
er
e
n
t
s
t
at
es
.
F
i
n
al
l
y
,
P
P
I
i
s
d
et
er
m
i
n
ed
an
d
co
n
t
i
n
g
e
n
ci
es
w
er
e s
cr
ee
n
ed
f
o
r
co
m
p
o
s
i
t
e p
o
w
er
s
y
s
t
e
m
.
4.
C
O
M
P
U
TA
TIO
N
O
F
P
R
O
B
A
B
I
LI
S
TIC
P
ER
F
O
R
M
ANCE
IN
D
EX
I
n
th
is
s
e
c
tio
n
,
th
e
p
r
o
c
e
s
s
o
f
P
P
I
c
a
lc
u
la
tio
n
is
illu
s
tr
a
te
d
b
y
c
o
n
s
id
e
r
in
g
a
s
m
a
ll 3
b
u
s
R
o
y
B
illin
to
n
T
e
s
t S
y
s
te
m
(
R
B
T
S
)
[1
]
. T
ab
l
e 1
s
h
o
w
s
s
u
m
m
ar
y
o
f
g
en
er
at
i
o
n
d
at
a an
d
T
ab
l
e 2
s
h
o
w
s
s
u
m
m
ar
y
o
f
tr
a
n
s
m
i
s
s
io
n
d
a
ta
f
o
r
R
o
y
B
illin
to
n
T
e
s
t S
y
s
te
m
(
R
B
T
S
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
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5
Start
Read System Reliability Data
,
Component Failure Rate
,
Repair Rate
Calculate Generator
,
Transmission line availabilities using
Compute State Probabilities P
1
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P
2
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…
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For j
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Lmax
Report Loss of
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Zero Load
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Update Lkj Values
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0001
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1
Non
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Most Critical
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Update PPI
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Moderately
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Yes
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Yes
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I
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8708
In
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p.
95
6
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96
4,
199
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
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[
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.
,
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-
lin
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d
y
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m
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r
i
t
y
co
n
t
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n
g
en
cy
s
cr
ee
n
i
n
g
an
d
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an
k
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n
g
,
” I
E
E
P
r
o
c.
G
en
er
.
T
r
an
s
m
.
D
i
s
t
r
i
b.
,
v
o
l
.
14
4,
no.
2,
p
p.
13
2
–
138
,
19
97
.
[
7]
A
.
B
e
r
i
z
z
i
,
Y
.
G
.
Z
e
ng
,
P
.
M
a
r
a
nni
n
o,
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.
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a
c
c
a
r
i
ni
,
a
nd
P
.
A
.
S
c
a
r
pe
l
l
i
ni
,
“
A
s
e
c
ond
or
de
r
m
e
t
hod f
or
c
ont
i
ng
e
nc
y
s
e
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e
r
i
t
y
a
s
s
e
s
s
m
e
nt
w
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e
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pe
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t
t
o v
ol
t
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g
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ol
l
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ps
e
,
”
I
E
E
E
T
r
a
ns
.
P
ow
e
r
S
y
s
t
.
,
v
ol
.
15,
n
o.
1,
pp.
81
–
8
7,
20
00
.
[
8]
E
.
B
. E
v
a
n
g
e
l
i
s
t
a
, A
. B
i
a
n
c
o
, J
.
A
.
G
o
m
e
s
, J
. C
. F
. G
u
i
m
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e
s
,
A
.
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. d
a
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a
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l
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a
, “
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u
t
o
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a
t
i
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ont
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nc
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nt
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r
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t
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o a
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n s
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he
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d out
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g
e
,
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i
n
P
ow
e
r
T
e
c
h P
r
oc
e
e
di
ng
s
,
200
1
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E
E
P
o
r
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o
, 2
0
0
1
, v
o
l
. 3
, p
. 6
–
pp
.
[
9]
A
.
O
zd
e
m
i
r
an
d
C
.
S
i
ng
h,
“
F
uz
z
y
D
e
c
i
s
i
on M
a
k
i
ng
A
g
a
i
ns
t
M
a
s
k
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ng
P
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bl
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m
i
n M
W
C
ont
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ng
e
nc
y
R
a
nk
i
ng
,
”
I
E
E
E
P
o
w
e
r
E
n
g
. R
e
v
., v
o
l
. 2
2
,
n
o
. 2
, p
p
.
5
5
–
56
,
2
00
2.
[
1
0]
J
. H
e
, Y
. S
u
n
, D
. S
. K
i
r
s
c
h
e
n
,
C
. S
i
n
g
h
, a
n
d
L
. C
h
e
n
g
, “
S
t
a
t
e
-
s
pa
c
e
pa
r
t
i
t
i
o
ni
ng
m
e
t
hod f
or
c
o
m
pos
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t
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pow
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sy
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t
e
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r
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l
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l
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t
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s
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e
s
s
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e
nt
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I
E
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e
ne
r
.
T
r
a
ns
m
.
D
i
s
t
r
i
b.
,
v
ol
.
4,
no.
7,
p
p.
78
0
–
79
2,
20
10.
[
1
1]
K
.
V
e
r
m
a
a
nd K
.
R
.
N
i
a
z
i
,
“
S
u
pe
r
v
i
s
e
d l
e
a
r
ni
ng
a
ppr
oa
c
h t
o o
nl
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n
e
c
ont
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ng
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nc
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s
c
r
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ni
ng
a
nd r
a
nk
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ng
i
n
pow
e
r
s
y
s
t
e
m
s
,”
I
n
t
. J
. E
l
e
c
t
r
.
P
o
w
e
r
E
n
e
r
g
y
S
y
s
t
., v
o
l
.
38,
n
o.
1,
pp.
9
7
–
104
,
2
01
2.
[
1
2]
Y
.
J
i
a,
P
.
W
an
g
,
X
.
H
an
,
J
.
T
i
an
,
an
d
C
.
S
i
n
g
h
,
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f
as
t
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s
cr
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ech
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e f
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t
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m
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a
bi
l
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t
y
e
v
a
l
ua
t
i
on,
”
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E
E
E
T
r
a
n
s
.
P
ow
e
r
S
y
s
t
.
,
v
ol
.
28,
n
o.
4,
pp.
412
7
–
4
13
3,
20
13
.
[
1
3]
A.
M
a
n
s
o
u
r
i
,
A.
Aa
z
a
m
i,
A
.
O
m
id
ia
n
,
E.
M
o
h
a
m
a
d
ia
n
,
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n
d
R
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A
a
z
a
m
i,
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Ev
a
lu
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nt
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l
e
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t
r
.
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om
put
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ng
.
,
v
ol
.
3,
no
.
2
,
p
.
2
54
,
2
01
3.
[
1
4]
S
.
A
f
s
ha
r
a
nd M
.
F
.
F
i
r
uz
a
ba
d,
“
R
e
l
i
a
bi
l
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t
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nd C
os
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ode
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n A
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om
pone
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ons
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A
g
e
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ng
M
e
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ha
ni
s
m
,
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nt
.
J
.
E
l
e
c
t
r
.
C
om
put
.
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ng
.
,
v
ol
.
4,
no
.
2
,
p
.
1
93
,
2
01
4.
[
1
5]
R
.
B
i
l
l
i
nt
on a
nd L
.
W
e
n
y
ua
n,
“
H
y
br
i
d a
ppr
oa
c
h f
or
r
e
l
i
a
bi
l
i
t
y
e
va
l
ua
t
i
on of
c
om
pos
i
t
e
g
e
ne
r
a
t
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on a
n
d
t
r
an
s
m
i
s
s
i
on s
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t
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m
s
us
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ng
M
ont
e
-
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r
l
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s
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ul
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t
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on a
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nu
m
e
r
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t
i
on t
e
c
hn
i
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ue
,
”
i
n
I
E
E
P
r
oc
e
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di
ng
s
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(
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e
ne
r
a
t
i
on,
T
r
a
ns
m
i
s
s
i
on a
nd D
i
s
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r
i
but
i
on)
,
1
99
1,
v
o
l
.
13
8,
pp.
2
3
3
–
24
1.
[
1
6]
Y
.
L
i
u a
nd C
.
S
i
ng
h,
“
R
e
l
i
a
bi
l
i
t
y
e
v
a
l
ua
t
i
on of
c
o
m
pos
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t
e
pow
e
r
s
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s
t
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m
s
us
i
ng
M
a
r
k
o
v c
u
t
-
s
et
m
et
h
o
d
,
” I
E
E
E
T
r
a
ns
.
P
ow
e
r
S
y
s
t
.
,
v
ol
.
25
,
n
o.
2,
pp.
7
77
–
7
85,
2
01
0.
[
1
7]
K
.
V
e
nk
a
t
a
s
a
t
he
e
s
h B
a
bu,
V
.
M
a
dhus
ud
ha
n,
a
n
d
V
.
G
a
ne
s
h,
“
T
S
S
ba
s
e
d c
om
pos
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t
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p
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s
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t
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l
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t
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on c
o
ns
i
de
r
i
ng
de
m
a
nd r
e
s
pons
e
,
”
I
nt
.
J
.
L
a
t
e
s
t
T
e
c
hnol
.
E
ng
.
M
a
n
a
g
.
A
p
p
l
. S
c
i
.
I
J
L
T
E
M
A
S
,
v
o
l
. 6
, n
o
.
6,
p
p.
15
0
–
15
4,
J
un
.
2
01
7.
[
1
8]
B
.
P
.
S
on
i
,
A
.
S
a
x
e
na
,
a
nd V
.
G
upt
a
,
“
A
l
e
a
s
t
s
qua
r
e
s
uppor
t
v
e
c
t
or
m
a
c
hi
ne
-
ba
s
e
d a
ppr
oa
c
h f
or
c
ont
i
ng
e
nc
y
c
l
a
s
s
i
f
i
c
a
t
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on a
nd
r
a
nk
i
ng
i
n
a
l
a
r
g
e
pow
e
r
s
y
s
t
e
m
,
”
C
og
e
nt
E
ng
.
,
v
ol
.
3,
n
o.
1,
p.
11
37
20
1,
20
16.
[
1
9]
V
.
S
an
k
ar
,
“S
y
s
t
e
m
R
el
i
ab
i
l
i
t
y
C
o
n
cep
t
s
,
” H
i
m
al
a
y
a P
u
b
l
.
H
o
u
s
e,
2
0
1
5
.
[
2
0]
L
.
B
a
m
an
d
W
.
J
e
w
el
l
,
“P
o
w
er
s
y
s
t
e
m
an
al
y
s
i
s
s
o
f
t
w
ar
e
t
o
o
l
s
,
” i
n
P
o
w
er
E
n
g
i
n
eer
i
n
g
S
o
ci
et
y
G
e
n
er
al
M
eet
i
n
g
,
200
5.
I
E
E
E
,
2
00
5,
pp.
1
39
–
1
44.
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