Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
9
, No
.
6
,
Decem
ber
201
9,
pp. 4
721
~
4727
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v9
i
6
.
pp
4721
-
47
27
4721
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Bivari
ate m
odified hot
ell
ing’s
2
T
ch
arts usin
g bootstr
ap
dat
a
Fir
as
H
adda
d
1
, Mut
as
em
K.
A
lsm
ad
i
2
, Us
am
a
Ba
da
w
i
3
, T
amer F
ar
ag
4
, Raed
A
lk
ha
s
awneh
5
,
Ibra
him
Alm
ar
as
hde
h
6
,
Wal
aa H
as
s
an
7
1,
5
Depa
rtment
of
Gene
r
al
cour
ses
,
Col
le
ge
of
Applie
d
Studie
s
and Com
m
unit
y
Ser
vic
e
,
Im
am Abdul
rah
m
an
Bin
Faisa
l U
nive
rsit
y
,
Saud
i
Arabi
a
2
,3,4,6,7
Depa
rtmen
t
of
Man
age
m
en
t
Inform
at
ion
S
y
stems
,
Coll
eg
e
o
f
Applie
d
Studies
and
Com
m
unit
y
S
erv
ice,
Im
am Abdu
l
rah
m
an
Bin
Faisa
l U
nive
rsit
y
,
Saud
i
Arabi
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
pr
19
, 201
9
Re
vised
Jun
26
, 201
9
Accepte
d
J
ul
6
, 201
9
The
conv
ent
ion
al
Hotelling’s
2
T
cha
rts
ar
e
evi
d
e
ntly
ine
ff
ic
i
ent
as
it
has
result
ed
in
disor
gani
z
ed
dat
a
wit
h
outl
ie
rs,
and
th
ere
fore
,
thi
s
study
proposed
the
application
o
f
a
novel
al
t
ern
a
ti
ve
robust
Hotelling’s
2
T
cha
rts
ap
proa
ch
.
For
the
robust
sca
le
est
imator
S
n
,
thi
s
appr
o
ac
h
enc
om
passes
th
e
use
o
f
the
Hodges
-
L
e
hm
ann
vec
tor
and
th
e
cov
arianc
e
m
at
rix
in
place
of
the
ari
thmet
ic
m
ea
n
vec
tor
and
the
cova
ria
n
ce
m
at
rix
,
respe
ct
iv
e
l
y
.
The
proposed
cha
rt
w
as
exam
ine
d
per
form
a
nce
wise
.
For
the
purpose
,
sim
ula
te
d
biv
ariate
boo
tstra
p
da
ta
sets
wer
e
used
in
two
condi
t
io
ns,
name
l
y
inde
pend
ent
v
ariabl
es
and
depe
n
dent
var
ia
bl
es.
The
n,
assess
m
ent
was
m
ade
to
the
m
odifie
d
cha
rt
in
t
er
m
s
of
it
s
rob
ustness.
For
the
purpose,
the
li
k
el
ihood
o
f
outl
ie
rs’
de
te
c
t
ion
and
fal
se
a
l
arms
were
com
pute
d.
From
the
outc
om
es
fro
m
the
computat
i
ons
m
ade
,
the
pr
oposed
cha
rts
de
m
onstrat
ed
superior
ity
over
the
conve
nt
ional
ones
for
all
the
ca
ses t
este
d
.
Ke
yw
or
d
s
:
Boo
t
stra
p
Ho
te
ll
ing’s
2
T
ch
arts
Ou
tl
ie
rs
Robust
est
im
ato
rs
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Firas
Hadda
d
,
Coll
ege
of
A
ppli
ed
St
ud
ie
s
a
nd Com
m
un
it
y
Ser
vice
,
Im
a
m
A
bd
ul
ra
hm
an
Bi
n
Fais
al
U
ni
ver
sit
y,
Al
-
D
am
m
a
m
,
Saudi A
ra
bia
.
Em
a
il
:
fsh
ad
da
d@
ia
u.
e
du.sa
1.
INTROD
U
CTION
In
m
anu
factu
r
ing
,
Stat
ist
ic
al
co
ntr
ol
cha
rt
s
ha
ve
bee
n
known
as
t
he
m
os
t
too
l
f
or
m
on
it
or
in
g
the
process
of
pro
du
ct
io
n.
In
m
on
it
or
ing
the
c
har
a
ct
erist
ic
s
of
pro
du
ct
qual
it
y,
in
the
beg
in
ning
,
the
em
plo
ym
e
nt
of
c
ontrol
char
ts
was
fac
il
it
at
ed.
Con
sideri
ng
the
e
xi
ste
nce
of
va
riou
s
c
ha
racteri
sti
cs
of
qu
al
it
y
in
product
qu
al
it
y
determ
inati
on
,
this
app
ro
ac
h
is
insuffici
e
nt
in
te
rm
s
of
pr
act
ic
al
it
y.
No
neth
el
ess,
m
ul
ti
var
ia
te
con
tr
ol
char
ts
(M
VCC)
with
the
capaci
ty
in
identify
ing
the
c
hanges
in
c
ov
a
riance
m
at
rix
Σ
a
nd
the m
ean v
ect
or
μ
in
order t
o
ac
hieve o
ptim
a
l p
er
form
ance o
f
the
pro
du
ct
[
1
,
2
]
.
The
H
otell
ing’
s
2
T
char
t
is
a
m
on
g
the
m
os
t
com
m
on
MVCC
m
et
ho
ds.
[
3
,
4
]
.
W
it
h
the
ca
pa
ci
ty
in
detect
ing
m
ultip
le
outl
ie
rs,
m
ean
s
hifts
an
d
dev
ia
ti
ons
in
t
he
dis
persal
of
con
t
ro
l
distrib
ution
[
5
]
.
The
sta
ti
sti
c
2
i
T
em
plo
ys
the
e
stim
at
or
s
x
a
nd
S
w
hich
are
di
r
ect
ly
i
m
pacted
by
t
he
pr
e
s
en
ce
of
outl
ie
rs
in
t
he
case
of
false
al
arm
s,
resu
lt
in
g
i
n
fa
il
ur
e
in
im
po
sing
c
ontr
ol
in
the
processes
of
producti
on.
The
inc
rea
se
i
n
the
com
plexity
of
the
m
anufa
ct
ur
in
g
of
the
pro
du
ct
s
i
n
a
ddit
ion
t
o
thei
r
char
act
e
risti
cs
that
ge
ner
al
ly
con
ta
in
ou
tl
ie
rs, co
ntri
bu
te
t
o
the
f
ai
l
ur
e
of th
e
ch
a
rt
in per
form
ing
it
s d
esi
gnat
ed
task.
In
orde
r
t
o
ov
erco
m
e
the
im
pact
of
outl
ie
rs
on
t
he
form
e
d
c
on
t
ro
l
cha
rt,
the
ap
plica
ti
on
of
r
obust
est
i
m
at
or
s
would
be
an
a
pp
ropr
ia
te
s
olu
ti
on.
The
se
r
obus
t
est
i
m
at
or
s
sh
ould
be
e
m
plo
ye
d
in
place
of
the
m
ean
vect
or
x
and
the
va
riance
co
var
i
ance
m
a
trix
S
as
in
the
conv
entional
H
otell
ing
’s
2
T
char
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4721
-
4727
4722
Accor
dingly
,
a
char
t
is
c
onsid
ered
r
obus
t
if
i
t
cou
l
d
produc
e
stron
g
reacti
on
to
t
he
cha
nges
to
the
pro
duct
ion
process
,
an
d
t
hi
s
reacti
on
is
c
om
pelle
d
by
th
e
co
ntro
ll
e
d
fal
se
al
arm
s
and
the
prob
a
bili
ti
es
value
s
of
detect
ion
ou
tl
ie
rs
a
re la
r
ge
e
nough an
d t
end
s
to 1
00
%
.
The
bootstra
p
m
et
ho
d
e
nc
om
passes
a
nonp
a
ram
et
ric
tech
ni
qu
e
due
t
o
it
s
inde
pe
ndence
f
ro
m
the
pr
es
um
ption
s
of
data
para
m
et
ric
distribu
ti
on.
N
on
et
he
le
ss,
in
the
m
on
it
ori
ng
of
a
sing
le
proces
s,
this
te
chn
iq
ue
ca
n
gen
e
rate
sin
gle
var
ia
ble
co
ntr
ol
cha
rts.
In
t
hi
s
reg
a
rd,
P
hal
adiga
non
et
al
.
in
[
6
]
m
entioned
the
po
s
sibil
it
y
in
i
nteg
rati
ng
m
ulti
var
ia
te
con
tr
ol
char
ts
with
the
char
ts
of
the
bo
otstr
ap
te
chn
iq
ue
tha
t
hav
e
pro
ven their e
f
fecti
ven
es
s.
Con
si
der
i
ng
th
at
it
is
po
ssi
ble
to
gather
sa
m
ple
that
is
sm
al
l
in
siz
e,
vio
la
ti
on
to
t
he
norm
al
ity
assum
ption
dis
tribu
ti
on
is
po
ssible.
Be
side
s
that,
in
gen
e
r
al
,
est
i
m
at
ion
t
o
the
in
-
co
ntr
ol
sta
te
of
the
c
on
t
ro
l
char
ts
has
to
be
ca
rr
ie
d
ou
t,
but
this
will
hav
e
ad
ve
rse
i
m
pact
on
the
perform
ance
of
the
co
ntr
ol
c
har
t
.
As
ind
ic
at
e
d
in
Mostaje
ran
et
al
.
in
[
7
]
,
non
-
pa
ram
etr
ic
bootstra
p
con
t
ro
l
cha
rts
are
approp
riat
e
for
an
un
i
den
ti
fie
d
distrib
ution
or
w
hen
m
aki
ng
est
i
m
at
ion
on
the
process
par
am
et
ers
from
Ph
ase
I
da
ta
set
or
wh
e
n
it
is im
pr
act
ic
al
to
gathe
r
sam
ple o
f
lar
ge
siz
e.
Fo
r
obse
rv
at
io
n
pu
rpose,
c
ontr
ol
cha
rts
ge
ner
al
ly
re
qu
i
re
norm
al
distribu
ti
on.
N
on
-
pa
ram
et
ric
con
t
ro
l
cha
rts
includi
ng
c
ha
r
ts
of
sig
n
co
nt
ro
l
are
a
ppr
opriat
e
fo
r
non
-
norm
al
distribu
t
ion
s
case
.
For
this
sit
uation,
the
pa
ram
et
ers
of
con
t
ro
l
cha
rt
co
uld
be
c
om
pu
te
d
with
the
use
of
the
al
gorithm
of
no
n
-
para
m
et
ric
bootstra
p.
I
n
the
sit
uation
w
her
e
ass
um
pti
on
s
of
distrib
ut
ion
are
not
re
qu
i
red,
or
i
gin
a
l
ob
ser
vatio
ns
cou
l
d
be
em
plo
ye
d.
Jo
ne
s and
W
il
l
iam
in
[
8
]
are am
on
g
tho
se
w
ho h
a
ve
a
pp
li
ed
bootstra
p
in th
e form
ation
of
the contr
ol
char
ts.
I
n
t
heir
stu
dy,
bootstr
ap
was
desc
rib
ed
as
a
sta
ti
sti
cal
te
chn
i
qu
e
wh
ic
h
em
plo
ys
po
wer
of
c
om
pu
ti
ng
in
place
of
t
he
conven
ti
on
al
par
am
et
ric
as
su
m
ption
.
T
he
propose
d
co
nt
ro
l
cha
rt
was
pr
ese
nted
al
ongs
i
de
the
exte
ns
ive
resu
lt
s
of
co
m
pu
te
r
si
m
ulati
on
,
a
nd
eac
h
c
on
tr
ol
c
ha
rt
was
a
ssess
ed
perform
ance
wise
accor
ding t
o
th
e ave
rag
e
le
ngth
of run.
Niaki
an
d
A
bbasi
in
[
9
]
,
a
novel
bootstra
p
-
ba
sed
m
et
ho
do
l
og
y
f
or
der
i
ving
the
lim
it
s
of
con
t
ro
l
on
the
at
tribu
te
s
was
propose
d
and
f
or
m
ulate
d.
The
us
e
of
th
e
m
et
ho
dolo
gy
al
lows
the
sim
ultaneo
us
c
reat
ion
of
confide
nce
int
erv
al
s
on
t
he
at
tribu
te
s.
T
he
pe
rfo
rm
ance
of
t
he
pro
pose
d
m
e
tho
d
was
the
n
e
xa
m
ined,
in
acco
rd
a
nce
with
the
i
n
-
c
on
t
ro
l
a
nd
out
-
of
-
c
ontrol
a
ve
rag
e
r
un
le
ngth
crit
eria.
T
he
auth
ors
al
so
m
ade
a
si
m
ulati
on
ba
sed
c
om
par
ison
with
a
c
ompara
ble
w
ork
pe
rfor
m
ed
by
Bonfer
r
on
i
a
nd
Sidak,
an
d
the
resu
lt
s
of
t
he
pro
pose
d
m
et
ho
d
a
pp
e
ared
t
o
be
bette
r.
Last
ly
f
or
at
tribu
te
s,
t
he
auth
or
s
m
ade
com
par
ison
be
tween
the bo
otstrap
m
et
ho
d
a
nd t
he
T
2
co
ntr
ol c
ha
rt.
The
a
pp
li
cat
io
n
of a bo
otstra
p
-
base
d
m
ulti
v
ariat
e
T
2
co
ntr
ol ch
a
rt w
as
de
m
on
strat
ed
in
Ph
al
adi
gano
n
et
al
.
in
[
6
]
.
T
hi
s
char
t
can com
petentl
y
m
on
it
or
a
proce
ss
in
data d
ist
rib
ut
ion
that
is non
-
norm
al
or
unknow
n.
W
it
h
the
a
pp
l
ic
at
ion
of
a
sim
ula
ti
on
stu
dy
,
the
auth
ors
evaluated
t
he
perform
ance
of
t
he
co
ntr
ol
char
t
pro
po
se
d
in
th
ei
r
stud
y.
T
he
kernel
densi
ty
est
i
m
at
ion
(K
DE
)
-
base
d
T
2
co
ntro
l
c
har
t
and
the
c
onve
ntion
al
Ho
te
ll
ing
'
s
T
2
con
t
ro
l
c
har
t
wer
e
c
om
par
e
d
in
te
rm
s
of
perform
ance,
a
nd
f
ro
m
the
re
su
lt
s
of
the
sim
ula
ti
on
stud
y,
the p
r
opos
e
d
m
e
tho
d
dem
on
strat
ed
be
tt
er
per
f
or
m
an
ce
as
oppo
se
d
t
o
the
co
nventi
on
al
T
2
c
ontrol
char
t.
As opp
os
e
d
to
the KDE
-
ba
sed
T
2
c
ontrol c
ha
rt, th
e
prop
os
e
d
m
et
ho
d sh
ow
s co
m
par
able
pe
rfor
m
ance.
Gandy
a
nd
K
valøy
in
[
10
]
pro
po
se
d
a
m
et
hod
gro
unde
d
upon
the
bo
otstrap
ping
c
oncept,
w
he
r
e
the
data
wer
e
bootstra
pp
e
d
a
nd
the
n
em
plo
ye
d
in
t
he
est
i
m
ation
of
t
he
in
-
c
on
t
ro
l
sta
te
.
The
us
e
of
this
m
et
ho
d
ap
pea
r
s
to
be
appr
opriat
e
fo
r
div
er
s
e
ty
pes
of
co
ntro
l
cha
rts.
It
is
al
so
app
li
cabl
e
fo
r
c
har
ts
th
at
are
base
d
up
on
re
gr
essi
on
m
od
el
s.
For
no
n
-
p
a
r
a
m
et
ric
bo
otstr
ap,
this
m
et
hod
is
deem
ed
a
s
rob
us
t.
T
he
auth
or
e
m
plo
ye
d
la
rge
sa
m
ple
pr
op
erti
es
of
the
a
dju
stm
ent.
The
adv
a
ntages
of
us
in
g
the
pro
po
s
ed
a
ppro
ac
h
we
re
dem
on
strat
ed
usi
ng a sim
ulatio
n st
udy.
Ed
opka
a
nd
O
gb
ei
de
i
n
[
11
]
,
the
a
utho
rs
e
m
plo
ye
d
a
non
-
pa
ram
et
ric
app
r
oac
h
in
the
a
ssessm
ent
of
the
cum
ulati
ve
su
m
(Cus
um
)
and
t
he
ex
pone
ntial
ly
W
ei
gh
te
d
Mov
i
ng
A
ver
a
ge
(
E
W
M
A)
c
on
t
ro
l
li
m
it
s
fo
r
cert
ai
n
dataset
.
In
t
he
deter
m
inati
on
of
th
e
con
tr
ol
lim
its,
the
aut
hors
e
m
plo
ye
d
the
under
ly
in
g
da
ta
set
conditi
on
al
dis
tribu
ti
on.
In
e
valuati
ng
the
con
t
ro
l
li
m
it
s
and
al
s
o
in
id
entify
ing
t
he
in
-
c
ontrol
a
nd
ou
t
of
con
t
ro
l
of
the
distrib
ution,
th
e
auth
or
s
a
ppli
ed
the
m
et
ho
d
of
bootstra
p.
H
ere,
the
re
was
no
rigid
a
ssu
m
ption,
for
in
sta
nce,
th
e norm
al
ity con
diti
on
for
th
e
sta
ti
sti
cal
p
ro
c
ess contr
ol to
be dis
per
se
d.
In
Mosta
j
era
n
et
al
.
[
1
]
,
the
auth
or
s
dem
on
strat
ed
the
ap
pl
ic
at
ion
of
a
ne
w
bootstra
p
a
lgorit
hm
in
the
c
on
st
ru
ct
i
on
of
H
otell
ing
’s
T
2
c
ontr
ol
cha
rt
.
In
ass
essing
the
pe
r
form
ance
of
t
he
pro
po
s
ed
m
e
tho
d,
the
aut
hors
e
m
plo
ye
d
a
sim
ula
ti
on
stu
dy
.
The
n,
t
he
a
uthors
m
ade
a
com
par
iso
n
be
tween
t
he
re
su
lt
s
of
the
pro
pose
d
m
et
ho
d
a
nd
t
ho
s
e
obta
ine
d
from
the
co
nv
e
ntio
nal
H
ot
el
li
ng
’s
T
2
c
on
t
ro
l
c
har
t
a
nd
al
so
the
resu
lt
s
of
bootstrap
re
porte
d
by
Ph
al
adiga
no
n
with
the
app
li
cat
ion
of
in
-
co
ntr
ol
and
ou
t
-
of
-
con
t
ro
l
aver
a
ge ru
n
le
ng
t
hs
res
pecti
ve
ly
r
epr
e
sente
d by
ARL0 an
d ARL1
,.
In
M
os
ta
j
e
ran
et
al
.
[
7
]
,
the
auth
or
s
pr
e
se
nted
the
us
e
of
non
‐
par
am
etr
ic
bootstra
p
m
ul
ti
var
ia
te
con
t
ro
l
c
ha
rts
|
S|,
W,
a
nd
G,
and
this
m
et
ho
d
is
gr
ou
nd
e
d
upon
the
us
e
of
bootstra
pp
e
d
data
in
the
est
i
m
at
ion
of
t
he
in
‐
c
on
t
r
ol
sta
te
.
I
n
this
stud
y,
the
a
ut
hors
s
uccee
ded
in
obta
ini
ng
s
at
isfact
or
y
perf
or
m
ance
of
bootstrap
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Biv
ar
iate
modi
fi
ed
hote
ll
ing
’
s
T
2
c
ha
rts
u
si
ng
bootstra
p d
ata
(
Firas
Ha
ddad
)
4723
con
t
ro
l
c
har
ts.
Com
par
ison
was
al
so
m
ade
betwee
n
the
perform
ance
of
the
pro
pose
d
cha
rts
an
d
t
hat
of
the S
hewha
rt
‐
ty
pe
co
ntr
ol c
ha
rt
s.
Ba
sed
on
H
otell
ing
’s
T
2
sta
ti
sti
c,
Mostajeran
et
al
.
i
n
[
12
]
dem
on
s
trat
ed
th
e
a
pp
li
cat
ion
of
a
bootstra
p
m
ulti
var
ia
te
con
tr
ol
char
t
a
nd
c
om
par
ed
it
with
a
H
otell
ing
’
s
T
2
par
am
et
ric
m
ulti
var
ia
te
con
t
ro
l
char
t,
a
m
ulti
v
ariat
e
sign
co
nt
ro
l
char
t,
a
nd
a
m
ulti
var
ia
te
W
il
c
oxon
co
ntro
l
cha
rt.
A
sim
ula
ti
on
stud
y
was
e
m
plo
ye
d for t
he pur
po
se
.
This
stu
dy
at
tem
pts
to
im
pr
ov
e
the
perf
orm
ance
of
H
ot
el
li
ng
’s
2
T
cha
rt
and
the
refor
e
,
a
ne
w
m
et
ho
d
is
pr
opose
d.
I
n
pa
rtic
ular,
m
od
ific
at
ion
on
the
s
ensiti
viti
es
to
wards
outl
ie
rs
is
to
be
car
ried
ou
t.
Fu
rt
her,
in
the
con
str
uctio
n
of
the
new
m
et
hodo
l
og
y,
t
his
stud
y
ap
plies
the
rob
us
t
est
im
at
or
of
locat
i
on
as
fo
ll
ows:
the
Hod
ge
s
-
Lehm
ann
est
im
at
or
an
d
the
c
ov
ariance
m
at
rix
of
the
r
obus
t
scal
e
est
im
a
tor
.
Me
anwhil
e, in
resam
pling
the
d
at
a
from
the n
orm
al
l
y dist
ribu
te
d data, t
he m
et
ho
d o
f boot
strap
is
em
plo
ye
d.
Accor
dingly
,
t
he
c
oncept
of
Hod
ges
-
Lehm
ann
est
im
at
or
and
the
pro
per
t
ie
s
of
t
he
scal
e
est
im
a
tor
of
will
be
highli
gh
te
d
in
the
ne
xt
sect
ion
(S
ec
ti
on
2).
T
his
is
fo
ll
owe
d
by
the
desc
riptio
n
of
the
c
onstr
uc
ti
on
of
the
H
otell
ing
’s
2
T
char
ts.
T
he
n,
t
he
e
nsuin
g
sect
ion
(S
ect
io
n
4)
will
descr
i
be
t
he
fin
dings
of
sim
ulati
on
in
a su
m
m
ary fo
r
m
. Th
e fin
al
se
ct
ion
c
on
cl
ude
s the
pa
per
.
2.
ROBUST
LO
CA
TI
ON A
N
D
S
C
ALE ES
TIMAT
ORS
This
pap
e
r
de
m
on
strat
es
the
ap
plica
ti
on
of
a
novel
r
obus
t
locat
ion
est
im
at
or
a
nd
th
ree
rob
us
t
scal
e
est
i
m
at
or
s.
Asi
de
from
al
lowin
g
easy
im
ple
m
entat
ion
in
t
he
cal
culat
io
n
and
co
ns
tr
uction
of
th
e
H
ote
ll
ing
’
s
2
T
char
t,
these
m
et
ho
ds
a
ppe
ar
to
be
a
ppr
opriat
e
te
ch
nical
ly
wh
en
de
al
ing
with
m
ul
ti
var
ia
te
da
ta
.
The follo
wing
sect
ion
highli
ghts t
he
prope
rtie
s
of eac
h
est
i
m
at
or
.
2.1.
R
obust
lo
cat
i
on
es
tima
t
or: h
od
ge
s
-
le
h
man
n
est
im
at
or
The
locat
io
n
e
stim
ation
f
or
a
sa
m
ple
con
ta
i
ning
n
obser
va
ti
on
s
wa
s
first
introd
uced
i
n
Hod
ges
an
d
Lehm
ann
(
1963)
.
This
est
im
at
or
ta
kes
a
m
edian
of
the
a
ver
a
ges
of
the
)
1
(
2
1
n
n
po
te
ntial
obs
erv
at
io
n
pairs. As
pr
ov
i
ded b
y
B
row
n and Kil
dea
(1
978)
,
the esti
m
a
tor
is
de
fine
d
a
s foll
ow
s:
“A
si
m
ple
Hodg
e
s
-
Le
hm
ann
est
i
m
a
tor
for
that
j
j
Y
X
fo
r
j
=
1,
2,
…
,
n
w
here
j
Y
are
i.i
.d
rando
m
vecto
r’
s
sym
m
et
ric
about
zero,
with
de
ns
it
y
functi
on
G
a
nd
c
on
ti
nuous
bounde
d
densi
ty
g.
The
H
-
L
est
i
m
at
or
of
θ
is
the
m
edian
of
n
j
i
X
X
j
i
,
1
,
2
and
an
as
ym
pto
ti
cal
ly
e
qu
i
valent
est
im
at
or
n
ˆ
is
the m
edian
of
n
j
i
X
X
j
i
,
1
,
2
.”
The
si
gn
ific
a
nc
e
of
pro
pe
rtie
s
of
this
l
oc
at
ion
est
im
at
o
r
ha
s
29%
br
eakdo
wn,
sym
m
et
ric
about
the p
a
ram
et
er θ,
a
bout
0.955 a
sy
m
pto
ti
c relat
ive eff
ic
ie
ncy
and it
r
e
qu
ir
es
O
(
2
n
) o
per
at
io
n at
m
ini
m
u
m
.
2.2.
R
obust
sc
ale estim
ator
:
n
S
In
Ro
us
see
uw
and Cr
oux
[
13
]
,
the e
stim
at
or
n
S
f
or
t
he
sam
ple
n
x
,
.
.
.
,
x
1
was
define
d
a
s foll
ow
s:
|}
|
{
j
i
j
i
n
x
x
m
ed
m
ed
c
S
f
or
j
i
n
j
i
;
,
.
.
.
,
2
,
1
,
(1)
Wh
e
re:
1
9
2
6
.
1
c
de
note
s
a
c
orrecti
on
facto
r
i
n
m
aking
S
n
un
biased
f
or
predete
rm
i
ned
sam
ples.
F
or
S
n
,
it
s
pr
im
ary
pr
oper
ti
es
are
as
fo
ll
ow
s:
car
ries
50%
m
axi
m
u
m
br
ea
kdow
n,
58
%
eff
ic
ie
nt
at
norm
al
distribu
ti
on,
lim
it
ed
functi
on
of
i
nf
lue
nce
,
an
d
enc
om
passes
an
a
ff
i
ne
e
qu
i
var
ia
nce
est
i
m
at
or
.
Acc
ordin
gly,
the
work
by
Rou
sse
eu
w
a
nd Cr
oux
[
13
]
presente
d
m
or
e
sp
eci
fics
reg
a
r
ding
S
n
.
3.
CONSTR
U
C
TION
OF TH
E ROB
US
T
H
OTE
LL
ING
’
S
2
T
CHARTS
The
pr
opos
e
d
robust
H
otell
ing’s
2
T
char
ts
hav
e
sim
ple
con
st
ru
ct
io
n.
T
he
locat
io
n
m
easur
e
of
Hod
ges
-
Lehm
ann
e
stim
at
or
is
e
m
plo
ye
d
in
place
of
the
pa
ram
et
ric
m
ean
vecto
r,
wh
il
e
the
va
riance
cov
a
riance
m
atr
ic
es, that is
,
n
S
is em
plo
ye
d
in
place o
f
t
he v
a
riance c
ovaria
nc
e m
a
trix
S
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4721
-
4727
4724
Give
n
ip
i
x
x
,...,
1
for
n
i
,..,
2
,
1
entai
ls
an
n
x
p
m
at
rix
wh
e
re
n
denotes
the
siz
e
of
the
bootst
rap
ind
ivi
du
al
ob
serv
at
io
ns,
w
hile
p
=
2
de
no
te
s
the
a
m
ou
nt
of
qual
it
y
char
act
erist
ic
s.
Acc
ordin
gly,
the cal
culat
io
n of t
he H
otell
ing
’s
2
T
char
ts
f
ollow
s
the
steps
bel
ow
:
1.
Fo
r
eac
h
c
olum
n
within the
n
x
p
m
at
rix,
c
om
pu
te
the
Hodg
e
s
-
Le
hm
ann estim
at
or
.
2.
The
n,
t
he
r
obust
v
aria
nce
c
ov
ariance m
at
rices are c
om
pu
te
d, f
ollo
ws
the
st
eps
as
d
e
scribe
d belo
w:
Con
si
der
i
ng
t
he
sym
m
et
ric
char
act
e
risti
c
of
va
riance
cov
a
riance
m
at
rix
of
,
the
m
ai
n
diag
on
a
l
enco
m
passes
t
he
m
at
rix
of
sam
ple
var
ia
nc
e
co
var
ia
nc
e
sign
i
fied
by
=
2
wh
e
re
j=
1
a
nd
2,
as
dem
on
strat
ed
i
n
[
14
-
18
]
.
For
oth
e
r
el
e
m
ents
of
this
m
a
trix,
they
enco
m
pass
the
cov
a
rian
ce
between
ea
ch
pair of
tw
o var
ia
bles inclu
ding
g
j
X
X
,
w
ho
se
c
om
pu
ta
ti
on
f
ollow
s
the ste
ps
belo
w:
a.
Ca
lc
ulate
(
)
,
(
)
,
=
1
,
2
;
=
1
,
2
≠
b.
Fo
r
r
a
nks
)
X
,
(X
g
j
c
or
r
betw
een
j
X
an
d
g
X
, calc
ulate
the s
pea
r
m
an
co
rr
el
at
io
n
[
19
]
).
c.
Fo
r
the
scale
e
stim
at
or
n
S
,
re
pea
t st
eps (i
-
ii)
.
The
com
pu
ta
ti
on
of
sam
ple
cov
a
riance
bet
ween
t
he
va
riables
j
X
an
d
g
X
f
or
2
×
2
var
ia
nc
e
cov
a
riance
m
atr
ix
of
is base
d on the
f
or
m
ulas sho
wn b
el
ow:
)
,
(
g
j
n
X
X
S
=
)
(
j
n
X
S
)
(
g
n
X
S
)
X
,
(X
g
j
c
or
r
(2)
3.
Finall
y, the
ne
w
c
har
ts
of the
prop
os
ed
Hote
ll
ing
2
are fo
rm
ed usin
g
t
he
e
quat
ion bel
ow
:
)
(
)
(
)
(
1
n
_
2
HL
X
S
HL
X
X
T
i
n
T
i
i
S
HL
(
3)
Evaluate
d
was
m
ade
to
the
pro
posed
rob
us
t
Ho
te
ll
ing’s
2
T
ch
art
with
the
a
ppli
cat
ion
of
si
m
ula
te
d
dataset
s in 5
000
rep
li
cat
ions.
As for th
e sim
ulati
on
,
it
foll
ows th
e sett
ings
as foll
ows:
a.
T
he ge
ner
al
li
ke
li
ho
od
of f
al
s
e ala
rm
is estab
li
sh
e
d
at
α =
0.05,
b.
T
he n
um
ber
of
v
a
riables e
nc
om
passes
p
=
2, an
d,
c.
The
siz
es
of sa
m
ple
n
= 20, 3
0,
40, 5
0
a
nd 100.
Me
anwhil
e, th
e cha
rt is f
or
m
ed
a
nd assesse
d
in
tw
o ph
a
se
s as foll
ows:
a.
Ph
ase
I
pro
duces
5000
da
ta
set
s
from
N
p
(
0
,
I
p
)
in
t
w
o
ci
rc
um
st
ances,
that
is
,
C
ase
A
inclu
de
s
ind
e
pende
nt
va
riables,
w
hile
Ca
se
B
co
nta
ins
de
pe
ndent
var
ia
bles.
F
urt
her,
the
est
i
m
a
tors
of
H
odge
s
and
Le
hm
ann
(
HL
)
a
nd
the
r
obus
t
scal
e
c
ov
a
riance
m
at
rix
f
or
for
t
he
c
onven
ti
onal
a
nd
r
obus
t
c
ha
rts
are calc
ulate
d.
b.
Ph
ase
I
I
inclu
des
the
creati
on
of
fr
es
h
obs
erv
at
io
n
f
or
ea
ch
dataset
in
orde
r
to
al
low
the
pe
rfor
m
ance
of assessm
ent.
The
pe
rfo
rm
ances
of
the
ne
w
rob
us
t
char
t
is
evaluate
d
co
nc
ern
i
ng
it
s
false
al
ar
m
s
and
it
s
li
kelihood
of
detect
ing
ou
tl
ie
rs,
and
su
c
h
perform
ances
are
eq
uiv
al
e
nt
to
the
f
racti
on
of
t
he
am
ou
nt
of
values
of
r
obus
t
sta
ti
sti
cs
fo
r
new
obser
vations
w
hich
ar
e
gr
e
at
er
t
han
the
uppe
r
c
on
t
ro
l
li
m
it
(
UCL)
to
t
he
a
m
ou
nt
of r
e
plica
ti
on
s
(50
00).
For all
processes
of c
om
pu
ta
ti
on
, th
e
y are e
xecu
te
d wit
h
MA
TL
A
B versi
on
2015
.
4.
RESU
LT
S
The
outc
om
es
gen
e
rated
by
the
co
nventional
Ho
te
ll
ing
’s
2
T
and
t
he
m
od
ifie
d
robu
st
Ho
te
ll
ing’s
2
T
ch
arts,
c
orres
pondin
gly
la
beled
as
̅
−
2
an
d
−
2
are
s
how
n
in
Table
s
1
-
2.
F
or
Ca
s
e
A
wh
ic
h
co
ntain
s
ind
e
pe
nd
e
nt
var
ia
bles
are
,
the
res
ults
dem
on
strat
e
the
supe
rio
rity
of
perform
a
nce
of
the
m
od
ifie
d
H
otell
ing
’s
2
T
chart
ov
er
t
he
tra
diti
on
al
H
otell
ing
’s
2
T
char
t
pa
rtic
ularly
with
re
sp
ect
to
fals
e
al
arm
s.
Ad
diti
on
al
ly
,
acco
rd
i
ng
to
t
he
outl
ie
rs’
detect
ion
,
com
par
able
r
esult
is
identifia
ble.
In
this
r
egard,
the m
od
ifie
d H
otell
ing
’s
2
T
chart
f
ully
supe
rse
des
t
he
c
onve
nt
ion
al
H
otell
in
g’
s
2
T
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Biv
ar
iate
modi
fi
ed
hote
ll
ing
’
s
T
2
c
ha
rts
u
si
ng
bootstra
p d
ata
(
Firas
Ha
ddad
)
4725
Table
1.
False
al
arm
r
at
es
and outl
ie
rs’
detec
ti
ng
pro
bab
il
it
y for the
co
nve
ntion
al
a
nd t
he
m
od
ifie
d
ho
te
ll
ing
‘s
T
2
co
nt
ro
l c
har
ts,
wh
ere:
p=
2
a
nd α
=0.05,
ε
de
no
te
s
the
per
ce
ntage
of
ou
tl
ie
rs
a
nd
sev
e
ral v
al
ues
of no
n
-
ce
ntrali
ty
p
aram
et
ers
3
a
nd 5 in
ca
se
A (case
with i
nd
e
pe
nd
e
nt
vari
ables)
n
µ
̅
−
2
−
2
Cas
e(A)
20
0
(0,0
)
(3.4
)
(3.0
4
)
0
.1
(3,3
)
(2.5
4
)
4
9
.7
(6.1
8
)
70
(5,5
)
(3.4
8
)
94
(5.0
2
)
9
8
.5
0
.2
(3,3
)
(2.7
4
)
4
.22
(4.1
4
)
4
0
.74
(5,5
)
(1.4
2
)
2
9
.66
(3.0
6
)
8
4
.48
30
0
(0,0
)
(2.1
6
)
(5.7
8
)
0
.1
(3,3
)
(1.6
6
)
4
2
.54
(2.6
4
)
8
7
.8
(5,5
)
(2.0
4
)
9
2
.02
(2.6
)
9
9
.96
0
.2
(3,3
)
(0.5
)
2
.08
(0.9
4
)
6
5
.5
(5,5
)
(0.2
6
)
1
5
.24
(0.7
8
)
96
40
0
(0,0
)
(2.8
4
)
(1.8
6
)
0
.1
(3,3
)
(1.6
6
)
4
0
.62
(0.4
6
)
5
7
.8
(5,5
)
(1.0
2
)
9
7
.3
(0.4
6
)
9
8
.84
0
.2
(3,3
)
(0.5
2
)
0
.82
(0.1
8
)
2
8
.9
(5,5
)
(0.1
2
)
1
6
.1
(0.8
0
)
8
4
.16
50
0
(0,0
)
(5.2
6
)
(7.8
4
)
0
.1
(3,3
)
(1.9
4
)
6
0
.06
(2.2
6
)
8
6
.26
(5,5
)
1
.02
9
9
.6
2
.18
9
9
.98
0
.2
(3,3
)
(0.5
4
)
4
.86
(1.0
4
)
6
7
.24
(5,5
)
(0.1
2
)
5
4
.7
0
.9
9
8
.1
100
0
(0,0
)
(12
.06
)
(16
.44
)
0
.1
(3,3
)
(1.0
4
)
7
6
.4
(8.7
)
9
6
.48
(5,5
)
(0.1
4
)
100
(8.5
8
)
100
0
.2
(3,3
)
(2.8
8
)
4
.3
(4.7
4
)
8
0
.8
(5,5
)
(0.0
8
)
8
7
.72
(4.5
6
)
9
9
.86
As
al
s
o
ca
n
be
obse
rv
e
d,
the
m
od
ifie
d
H
ote
ll
ing
’s
2
T
char
t
s
hows
im
pr
ov
e
d
rates
of
fals
e
al
arm
s
with
the
inc
rea
se
of
the
siz
es
of
sam
ples
(
n
)
.
Fu
rt
her
m
or
e,
for
the
al
te
rn
at
ive
char
t,
t
he
pro
ba
bili
ti
es
rat
es
for
ou
tl
ie
rs
’
detect
ion
inc
rea
se
w
it
h
the
increas
e
of
sam
ple
si
ze.
Howe
ver,
f
or
the
c
on
tr
ol
char
t
of
the
m
od
i
fied
Ho
te
ll
ing‘s
2
T
,
th
e
changes
of
th
e
rates
val
ues
of
t
he
outl
ie
rs’
detect
ion
pro
ba
bili
ty
app
ears
to
be
sm
al
le
r
as
oppose
d
to
th
e
changes
de
m
on
strat
ed
by
t
he
cha
rts
of
the
co
nv
e
ntio
nal
H
otell
ing
‘
s
2
T
especial
ly
wh
e
n
the
outl
ie
rs’
pe
rcen
ta
ge
incr
eases
from
0.
1
to
0.2
notwit
hst
and
i
ng
t
he
s
hifted
m
ean
an
d
the
siz
e
of
s
a
m
ple.
As
ca
n
be
c
on
strue
d
f
ro
m
the
gen
e
rated
re
su
lt
,
the
m
od
if
ie
d
cha
rt
is
m
or
e
rob
us
t
in
r
eact
ing
to
c
ha
ng
e
s
in
the pr
ocess of
pro
du
ct
io
n
.
Fo
r
Ca
se
B
t
ha
t
con
ta
in
s
de
pende
nt
va
riab
le
s
as
sho
wn
in
Ta
ble
2,
t
he
rates
of
false
al
arm
s
and
tho
se
of
outl
ie
rs’
detect
ion
of
the
r
obus
t
char
ts
a
pp
ea
r
to
be
s
up
e
ri
or
c
om
par
ed
t
o
the
e
xact
ra
te
s
in
the
co
nv
e
ntio
na
l
char
t
w
he
n
there
a
re
outl
ie
r
s
no
t
withstan
di
ng
t
he
n,
and
.
N
otably,
the
f
al
se
al
ar
m
s
rates
decr
ease
s
with
the
increase
of
the
sam
ple
siz
e
(
n
).
Also
,
the
pr
ob
a
bi
li
ty
detect
ion
rates
app
ea
r
to
be
increasin
g nea
r
ly
1
00%.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
2
01
9
:
4721
-
4727
4726
Table
2
.
Ra
te
s
of f
al
se
al
arm
and pr
ob
a
bili
ty of
detect
ing
outl
ie
rs
f
or the
trad
it
io
nal and t
he
m
od
ifie
d
ho
te
ll
ing
‘s
T
2
co
nt
ro
l c
har
ts
w
he
n p=2 an
d
α
=
0.05,
ε
is t
he perc
entage
of
ou
tl
ie
rs
a
nd se
ver
al
v
al
ue
s
of no
n
-
ce
ntrali
ty
p
aram
et
ers
3
a
nd 5 in ca
se
of
dep
e
ndent
var
ia
bles
case
(
B
)
n
µ
̅
−
2
−
2
Cas
e(B)
20
0
(0,0
)
(0.0
8
)
(22
.2)
0
.1
(5,5
)
(0.5
)
88
(8.2
6
)
9
8
.78
0
.2
(5,5
)
(0.4
2
)
2
2
.7
(4.9
4
)
8
8
.1
30
0
(0,0
)
(0.0
6
)
(1.3
4
)
0
.1
(5,5
)
(0.2
4
)
7
6
.7
(0.6
)
9
8
.36
0
.2
(5,5
)
(0.1
4
)
8
.54
(0.2
6
)
8
5
.96
40
0
(0,0
)
(0)
(0.5
)
0
.1
(5,5
)
(0.0
2
)
9
0
.5
(0)
8
7
.36
0
.2
(5,5
)
(0)
8
.94
(0.0
)
3
9
.26
50
0
(0,0
)
(0)
(0.3
6
)
0
.1
(5,5
)
(0.0
4
)
9
5
.78
(0.0
6
)
9
6
.18
0
.2
(5,5
)
(0)
2
8
.02
(0.1
8
)
8
0
.16
100
0
(0,0
)
(0)
(5.1
2
)
0
.1
(5,5
)
(0.0
2
)
9
9
.88
(1.7
6
)
9
9
.98
0
.2
(5,5
)
(0)
7
1
.58
(0.5
8
)
9
8
.42
5.
EMPI
RICAL
CASE
We
us
e
d
the
exam
ple
fr
om
Vargas,
Qu
ee
nsber
ry
data
set
s
in
order
to
c
om
par
e
and
e
va
luate
resu
lt
s
of
t
he
perfor
m
ance
of
bot
h
the
c
onve
nti
on
al
a
nd
m
odifie
d
co
ntr
ol
c
har
ts.
Thei
r
da
ta
com
pr
ise
s
of
tw
o
char
act
e
risti
cs,
rand
om
var
ia
bles,
nam
el
y
1
X
and
2
X
on
30
dif
fer
e
nt
pr
oducts
ta
ken
f
ro
m
the
pro
duct
io
n
process
.
In
V
arg
as
,
Q
ueen
s
berry
data
set
’s
two
va
riabl
es
wer
e
us
e
d.
The
ob
se
r
vations
of
both
r
andom
var
ia
bles
are
sh
ow
n
in
Tabl
e
3
(App
e
ndix
)
.
The
ta
ble
al
so
shows
the
values
of
the
new
H
otell
ing
’s
T
2
sta
ti
sti
cs alon
g
with t
he
c
onve
ntion
al
T
2
sta
ti
sti
cs.
We
cal
c
ulate
d
the
UC
L
us
in
g
the
sim
ulati
on
f
or
the
r
obus
t
and
the
co
nven
ti
on
al
T
2
c
har
ts
to
be
8.0
3
and
6.461
9
res
pecti
vely
.
W
e
set
the
value
of
al
l
UCL
for
the
r
obus
t
cha
rts
and
the
c
onve
ntion
al
f
or
α
=0.0
5.
This
case
has
false
al
ar
m
p
roba
bili
ty
wit
h
30
obser
vations.
The
fina
l
resu
lt
s
sh
ow
that
in
the
c
ase
of
conve
ntion
al
c
har
t,
the
pro
du
ct
ion
process
is
not
in
co
ntr
ol
at
tw
o
obse
rv
at
io
ns
,
the
s
econd
a
nd
tw
e
ntiet
h
ob
s
er
vations,
wh
e
reas t
he pr
ocess
is
out
of
con
t
ro
l
only
on
seco
nd
ob
se
r
va
ti
on
in
case
of
robust c
har
ts.
6.
CONCL
US
I
O
N
AND DIS
C
US
SI
ON
The
m
od
ifie
d
rob
us
t
al
te
rn
at
ives
H
otell
ing‘s
2
char
t
dem
on
strat
es
s
up
e
ri
or
it
y
in
pe
rform
ance
as
oppose
d
to
the
conve
ntio
nal
Ho
te
ll
ing‘s
2
ch
art
par
ti
c
ularly
con
ce
r
ning
fa
lse
al
arm
s.
Al
so
,
as
oppose
d
t
o
the
c
onve
ntio
na
l
H
otell
ing
‘
s
2
char
t,
the
m
odifie
d
rob
us
t
al
t
ern
at
ives
H
otell
ing
‘s
2
char
t
a
pp
ea
r
s
bette
r
a
t
ou
tl
ie
rs dete
ct
ion.
REFERE
NCE
S
[1]
A.
Mos
ta
je
r
an,
N.
Ir
anpa
n
ah,
and
R
.
Nooro
ss
ana
,
"A
New
Bootstra
p
Bas
ed
Algori
thm
for
Hotelling’s
T2
Multi
var
i
ate
Co
ntrol
Ch
art
,
"
Jou
rnal
of
S
ci
en
ce
s,
Islamic Re
pub
lic
of
Iran,
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Ap
pendix
Table
3
.
T
he
two va
riables
X
1
an
d
X
2
of
vargas
da
ta
set with t
he values
of T
2 s
ta
ti
sti
cs u
sing
the con
ven
ti
onal
a
nd the
wi
nsorize
d
MOM
e
stim
at
or
Prod
u
ct No
1
X
2
X
2
0
T
T
2
HL
-
Sn
1
0
.56
7
6
0
.55
8
0
.80
7
0
.76
3
2
0
.53
8
5
6
.30
3
1
2
.97
5
2
2
.03
4
3
0
.53
5
9
.52
4
0
.13
7
3
0
.33
1
4
0
.56
2
6
1
.10
2
1
.83
7
5
2
.20
8
5
0
.48
3
5
9
.83
4
1
.56
9
7
1
.74
2
6
0
.52
5
6
0
.22
8
0
.33
0
.35
1
7
0
.55
6
6
0
.75
6
0
.97
7
1
.08
3
8
0
.58
6
5
9
.82
3
0
.90
4
0
.95
5
9
0
.54
7
6
0
.15
3
0
0
.12
6
9
0
.07
2
10
0
.53
1
6
0
.64
0
.80
1
0
.96
8
7
11
0
.58
1
5
9
.78
5
0
.71
9
2
0
.78
5
12
0
.58
5
5
9
.67
5
0
.91
0
1
.06
7
6
13
0
.54
6
0
.48
9
0
.48
3
0
.52
14
0
.45
8
6
1
.06
7
5
.24
1
3
6
.58
5
15
0
.55
4
5
9
.78
8
0
.07
3
0
.11
16
0
.46
9
5
8
.64
3
.53
5
7
4
.63
6
5
17
0
.47
1
5
9
.57
4
2
.26
9
6
2
.53
9
18
0
.45
7
5
9
.71
8
3
.24
4
2
3
.54
9
7
19
0
.56
5
6
0
.90
1
1
.39
8
1
.56
2
9
20
0
.66
4
6
0
.18
6
.83
2
6
6
.90
6
21
0
.6
6
0
.49
3
1
.89
7
8
1
.76
7
22
0
.58
6
5
8
.37
3
.35
6
4
5
.66
7
23
0
.56
7
6
0
.21
6
0
.42
7
5
4
6
0
.33
2
24
0
.49
6
6
0
.21
4
1
.18
3
8
1
.34
3
25
0
.48
5
5
9
.5
1
.49
6
8
1
.75
3
7
26
0
.57
3
6
0
.05
2
0
.48
4
3
2
0
.41
3
7
6
27
0
.52
5
9
.50
1
0
.28
9
8
9
0
.50
28
0
.55
6
5
8
.47
6
2
.06
3
5
3
.86
1
9
29
0
.53
9
5
8
.66
6
1
.38
5
9
6
2
.69
3
30
0
.55
4
6
0
.23
9
0
.24
0
4
3
0
.16
9
7
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