TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3634 ~ 36
4
1
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5116
3634
Re
cei
v
ed
No
vem
ber 1
1
, 2013; Re
vi
sed
De
cem
ber 1
3
,
2013; Accep
t
ed Jan
uary 2
,
2014
Resear
ch on Software Fault Distribution for Web
Application
Wanjiang Ha
n*
1
, Lixin Jiang
2
, Sun Yi
1
, Li
Y
e
3
, Han
Xiao
3
, Weijian Li
3
, Liu Chi
3
1
School of Softw
a
r
e En
gin
eer
i
ng, Beij
ing U
n
i
v
ersit
y
of Posts
and T
e
lecom
m
unic
a
tion, Be
ijin
g, Chi
na
2
Departme
n
t of Emergenc
y R
e
spo
n
se, Ch
in
a Ea
rthqu
ake
Net
w
orks C
ent
er, Beiji
ng, Chi
na
3
I
nternati
ona
l Schoo
l, Beiji
ng
Universit
y
of
P
o
st and T
e
leco
mmunicati
on B
e
iji
ng, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: han
w
a
nj
ia
ng
@bu
p
t.edu.cn
A
b
st
r
a
ct
T
h
is pa
per stu
d
ies
multip
le s
o
ftw
are fault di
stri
butio
n
mod
e
l, then
exten
d
s
the id
eas
of
softw
are
fault esti
mati
o
n
bas
ed
on th
e an
alysis
of a
larg
e nu
mber
of proj
ect fault
data. It prese
n
ts the esti
mat
i
o
n
mo
de
l of softw
are fau
l
ts distr
i
buti
on for W
e
b App
licat
i
on,
w
h
ich refers t
o
the G-O mo
del
and
Ray
l
ei
gh
mo
de
l. T
h
is p
aper fits the
fault pre
d
ictio
n
mo
d
e
l a
n
d
show
s the steps to deter
mi
ne th
e rel
e
van
t
para
m
eters. F
i
rstly, estimati
n
g
the pro
bab
ili
ty of fi
nding a
fault accord
in
g to similar pr
oject dat
a. T
h
e
n
estimatin
g
the
total nu
mber o
f
faul
ts. Softw
a
r
e fault esti
mat
i
on
mo
de
l has
certain d
i
rectiv
e sign
ifica
n
ce t
o
the pr
edicti
o
n
an
d p
l
an
ni
ng
proj
ects.Expe
r
iments sh
ow
that the
mod
e
l
has
gr
eat
p
o
tentia
l to
pre
d
ict
softw
are fault.
Ke
y
w
ords
:
fault,
fault predict
ion
mo
del, test
data, W
eb ap
pl
icatio
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Software faul
t predictio
n is a very important
rese
arch
topic in software engi
nee
ring. It is
based on the
fault record in histori
c
al d
a
ta to predict
the faults in
the future. It
help
s
softwa
r
e
proje
c
t pla
n
n
i
ng an
d p
r
o
c
ess ma
nage
ment. At the sam
e
time,
it provide
s
d
e
ci
sion
su
pp
ort.
Software
faul
t pre
d
ictio
n
t
e
ch
nolo
g
y de
veloped
from
the l
a
st
ce
ntury 7
0's.
In t
h
is
pe
riod,
m
any
fault predi
ctio
n model
s a
r
e
appea
re
d. Its pu
rpo
s
e i
s
to count p
o
ssible faults in
softwa
r
e. It can
help dete
r
min
e
wheth
e
r th
e system
ca
n
be laun
ch
ed
and be
used
. Faults in so
ftware p
r
od
ucts
can
not
meet
the n
eed
s
of users i
n
som
e
ext
ent. Eve
r
y software d
e
velopme
n
t team m
u
st
kn
o
w
how to p
r
op
e
r
ly deal with t
he faults of t
he softw
are, whi
c
h is
relat
ed to the fun
damental
qua
lity
softwa
r
e dev
elopme
n
t.
Software te
sti
ng is
a very i
m
porta
nt peri
od of
the
software life cy
cl
e, esp
e
ci
ally in We
b
Applicatio
n. F
r
om te
sting
we ca
n o
b
tain
fault
data. Th
roug
h
studyin
g and
an
alyzi
ng the
s
e
dat
a,
we ca
n estim
a
te
faults,
th
en we
can effectively
improve the
proje
c
t pla
nnin
g
a
nd eve
n
p
r
e
d
ict
the prod
uct relea
s
e time.
In the pro
c
e
s
s of software
testing, fault
m
anag
eme
n
t is a very imp
o
rtant task, which
are
activities to
e
n
su
re fa
ults t
o
be
tra
c
ked
and m
ana
ge
d in th
e
software life
cy
cle.
In ge
neral, f
ault
tracking
an
d
manag
eme
n
t need
s to
a
c
hieve the foll
owin
g two
ob
jectives:
one
is to e
n
sure that
each defici
e
n
c
y wa
s foun
d to be solv
ed, the ot
her is colle
cting
fault data, reco
gni
zing a
n
d
preventin
g fa
ults in th
e fut
u
re. F
o
r fa
ult manag
eme
n
t, many pe
ople
only thin
k of
how to
corre
c
t
the faults.
Ho
wever,
effecti
v
e prev
enting
faults ba
se
d
on fault
analy
s
is
a
r
e
ea
sy t
o
be
ign
o
red.
In
fact, in a project develo
p
m
ent, colle
ctin
g and a
nalyzing fault data
is very impo
rtant. From t
h
e
fault data,
we can
get
a l
o
t of related
data a
bout
software
q
ualit
y. For
examp
l
e, studyin
g t
he
fault tren
d
cu
rves to d
e
termine
wheth
e
r or not th
e e
n
d of te
st p
r
o
c
ess i
s
comm
only u
s
ed
an
d is
an effe
ctive way. Fault
da
ta com
m
on
st
atistical
char
t
s
in
clud
e faul
t trend
s, fault
distrib
u
tion, f
ault
timely processing
statistics and etc.
Therefore, i
n
the a
c
tual p
r
oje
c
t, the curve
of int
r
o
duci
ng p
r
od
u
c
ts i
s
very i
m
porta
nt
index. Study the prope
rti
e
s of t
hese curve
s
, whi
c
h has a
cert
ain sig
n
ifican
ce for lau
n
ching
proje
c
ts a
nd prod
uct
s
. Unt
il now, no co
mmon mo
d
e
l
for all project has been reporte
d.Thro
ugh
the study of variou
s
kind
s
of
fault model
s, This p
ape
r sho
w
s a fa
ul
t estimating
model ba
se
d
o
n
Web ap
plication software.
It plays a cert
ain
role fo
r the predi
ction a
nd plan
ning p
r
oje
c
ts.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Software F
a
u
l
t Distributio
n for We
b Appli
c
ation (Wa
n
ji
ang Han)
3635
2.
Related Softw
a
r
e Fa
ult Distribu
tion
Model
Software fa
ul
t estimating t
e
ch
nolo
g
y mainly incl
ude
s the
static
predi
ction
te
chn
o
logy
and dyn
a
mic predi
ction t
e
ch
nolo
g
y. The stati
c
p
r
e
d
iction te
ch
n
o
logy in
cludi
ng Akiyam
a
[1]
quantitative model, Hal
s
t
ead [2] mod
e
l, Lipow [3]
model, Takaha
shi [4] model, Akiya
m
a
faultden
sity model [5],
Boehm
CO
QUALM
O
m
odel [6
-8], Bayesian
m
odel [9], Ca
pture
-
Re
captu
r
e
m
odel [1
0] an
d
etc. T
h
e
dyn
a
mic mod
e
l i
s
time
relatio
n
mo
del, thi
s
kin
d
of
mod
e
l is
empiri
cal research an
d statistical technolo
g
y to
find software
faults with
the distribu
tion
relation
shi
p
betwe
en
so
me sta
g
e
s
b
a
se
d on tim
e
. The mai
n
dynami
c
m
odel
s in
clud
e
the
Rayleig
h
mo
del, expon
en
tial model a
nd S cu
rve
model. Thi
s
pa
per
mai
n
ly studie
s
t
he
relation
shi
p
model b
e
twe
en software
faults an
d time du
ring th
e test pe
riod
. Therefo
r
e,
this
se
ction mainl
y
describe
s
three m
odel
s.
2.1.
Ra
y
l
eigh Distribution Mo
del
Rayleig
h
mo
del [11] i
s
a
comm
on
relia
bility m
odel. I
t
can fo
re
ca
st the fault di
stribution
durin
g software life
cycle.
This
kind
of model i
s
ba
sed on
the WeiBull statistical distri
bu
tion.
WeiBull di
stri
buted reliabili
ty analysis is widely us
ed
in different field. The pro
bability den
si
ty
function of
WeiBull di
stri
buted t
ag en
d is gradu
all
y
converge to
0, but never eq
ual to 0
.
The
experts of T
r
achte
nbe
rg [
12] and
IBM
[13] have
re
searche
d
o
n
t
he
softwa
r
e
proje
c
t fault
s
and
they found
th
at the di
stri
b
u
tion a
c
cords with
Ra
ylei
g
h
di
stributio
n
model
[14].
The
pro
babili
ty
distrib
u
tion
d
ensity fun
c
tio
n
of Rayleig
h
mod
e
l is
2
)
/
(
2
e
)
c
/
t
(
K
2
f(t)
c
t
, the
c
u
mulativ
e
distrib
u
tion fu
nction i
s
)
e
1
(
K
F(t)
2
)
/
(
c
t
,where K is
the total faults
. T
s
t
ands
for time, c
is an
con
s
ta
nt and
m
t
2
c
, where
m
t
is the time wh
en
f(t)
reach
ed maxim
u
m, and
K
/
)
F(t
m
approximat
ely equal to 0.4. Therefo
r
e, we c
an estim
a
te the total numbe
r of faults at
a ce
rtain time
as well a
s
the sp
ecific
Ra
yleigh
dist
rib
u
tion pa
rame
ter. Thu
s
we
can
simplify th
e
cou
n
ting p
r
o
c
ess. It is easy to control t
he qualit
y of
the enterpri
s
e perfo
rma
n
ce goal by u
s
i
ng
R
a
yleigh model. It is
necess
ar
y to take meas
ur
e
s
to corre
c
t it whe
n
the p
r
oce
s
s ap
pea
red
abno
rmal.
2.2.
Exponen
t
ial Distribu
ted
Model
The exp
one
n
t
ial distri
bute
d
mod
e
l i
s
desi
gne
d for the te
st pe
riod. The
exp
onential
distrib
u
ted m
odel i
s
also called reliabilit
y growth
mod
e
l whi
c
h in
clu
des fa
ult co
u
n
ting mod
e
l a
n
d
failure inte
rval time mode
l. The fault proba
b
ility dist
ribution fu
ncti
on (PDF) of
the expone
ntial
distrib
u
ted m
odel is
)
(
K
f(t)
t
e
, and the cumul
a
tive distribu
tion function
(CDF) i
s
)
1
(
)
(
t
e
K
t
F
, wh
ere
t re
pre
s
ent
s time
, k
rep
r
e
s
ent
s total
numb
e
r of
faults a
nd
λ
, a
shape
param
eter, represents th
e probability of finding a defect. The exponential di
stribut
ed
model
is the
simple
st
but
one
of the
mo
st imp
o
rt
ant
model
s
over t
he
reliabl
e m
odel
s a
nd it
is the
fundame
n
t of other g
r
o
w
th model
s.
Jein
ski-M
o
ra
nda
(J-M
) m
o
del [15]
is on
e of th
e e
a
rli
e
st failu
re
int
e
rval time
mo
del. Th
e
s
o
ftware failure
rate func
tion is
)]
1
i
(
N
[
)
Z(t
i
, where
N represent
s
initial num
ber of
defective
s,
Ф
rep
r
e
s
e
n
ts
ratio con
s
tant. The
presu
p
p
o
siti
on
of this model
is 1) the p
o
ssibility
of
each fault
det
ected
du
ring
the te
st pe
riod
influen
ce
the
failure
a
r
e th
e same. 2
)
ti
me for re
pai
ri
ng
the faults
can
be ign
o
re
d.3
)
all faults
ca
n be r
epai
re
d
perfe
ctly. Thus e
a
ch re
pa
irmen
of faults
cou
n
ts eq
uall
y
to improve the software’
s failure rate.
Littlewoo
d m
odel [16] a
n
d
G-O mod
e
l ar
e
expo
nential mo
d
e
ls.Littlewood
model
sup
p
o
s
e
s
tha
t
different fa
ul
ts influe
nt fail
ure
differe
ntly and
h
uge
fail
ure
s
are
avoi
ded i
n
the
e
a
rly
pha
se
s,
the
a
v
erage erro
r scale will
be smalle
r
a
nd
smaller. Little
w
oo
d propo
sed the Little
w
ood
nonh
omog
en
eou
s Poi
s
son
pro
e
ss m
o
d
e
l(L
NHPP
)
[1
7] later o
n
. G
oel an
d O
k
u
m
oto propo
sed a
failure
amo
u
n
t mod
e
l in
the te
st p
e
riod
(G-Om
odel).
They
su
ppo
se
d t
he a
c
cumul
a
ted
faultnumbe
r wa
s
)
N(t
i
in time
i
t
whi
c
h is a n
o
nhomo
gen
eo
us Poisso
n proce
s
s model
[18].
2.3.
Exponen
t
ial Distribu
ted
Model
Yamada [1
9] and oth
e
r
p
eople
pro
p
o
s
ed a te
st pe
ri
od not o
n
ly inclu
d
e
s
dete
c
ting the
faults but al
so inclu
d
e
s
isolating faults.
When
th
ere
come
s a fault
,
we nee
d to find the rea
s
on
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3634 – 36
41
3636
why fault
s
a
r
e di
sable
d
. T
herefo
r
e, th
ere exist
s
a
tim
e
del
ay for fi
nding
a fault
until we repo
rt it.
The
accum
u
l
a
ted time
del
ayed fault
s
a
c
cord
with
S
curve
di
strib
u
t
ion an
d thi
s
i
s
calle
d
dela
y
ed
S model wh
ich is al
so a reliabl
e incre
m
ent mo
del. S model meets the
requireme
nt of
nonh
omog
en
eou
s Poisso
n pro
c
e
s
s. Its CDF is
)
e
)
t
1
(
1
(
K
F(t)
t
, where t
rep
r
e
s
ent
s time; k repres
ents total faul
tnumbe
r;
λ
represent
s the
possibility of
detecting a faultt.
The PDF i
s
t
t
e
K
f(t)
2
.
In 1984, Og
h
ba [20] pro
p
o
s
ed a
nothe
r
S dist
ribute
d
model called transfo
rme
d
S
model.
This m
odel
consi
ders the
detecte
d fault
s
a
r
e in
te
rde
pend
ent an
d
the more faul
ts are dete
c
t
e
d
the more faults will be
detecte
d later. The accumulated faul
t
d
istributed function (CDF) is
)
e
1
/(
)
e
1
(
K
F(t)
t
t
, where t represe
n
ts time; k
re
pre
s
e
n
ts total fault num
ber;
λ
represents the possi
bilit
y of detecting a defect. Its PDF i
s
2
)
1
/(
)
1
(
K
e
K
f(t)
t
t
e
[21].
3.
The Fault Pr
ediction Mo
del for We
b application
s
during the
te
st period
Each te
chni
c
to predi
ct soft
ware faults a
r
e not inde
pe
ndent. Thi
s
p
aper
will com
b
ine G-
O model [15]
and Rayleigh
model to dev
elop a faul
t predictio
n mod
e
l for We
b application
s
[22].
Fault an
alysi
s
can
be
u
s
e
d
to u
nde
rsta
nd the
tren
d
of develo
p
me
nt quality a
n
d faults
analysi
s
provides two imp
o
rtant pa
ram
e
ters. On
e
is the trend of detecte
d faults, the other i
s
a
trend of
cum
u
lative faults.
Generally, detected faul
t curve will
be on
the
ri
se in the
ear
ly
stages
of the proje
c
t, and to the
middle
and
later p
e
rio
d
s of the p
r
oje
c
t, the curve
sho
u
ld
de
cline
overall. Finall
y
, it tends to zero. We m
a
y ens
u
r
e th
e develop
me
nt of the proj
ect thro
ugh t
h
e
contin
ually obse
r
vation of
these curve
s
. Also,
throu
gh analy
z
ing
and predi
ctin
g the time when
the found fa
u
l
t tends to
ze
ro, we can
set up the
a
cceptan
ce
crite
r
ion a
nd
rele
ase tim
e
. Fa
ult
predi
ction m
o
del mainly represent
s
the faults still in the software.
To devel
op t
he fault p
r
ed
iction m
odel
of We
b a
p
p
lication
s
, we
analyzed a
l
o
t We
b
appli
c
ation’
s
test data. By
studyin
g on
the fault d
a
ta, we
found
the fault d
a
ta
duri
ng th
e t
e
st
perio
d prese
n
ted a
s
exp
onential m
o
d
e
l simila
r to
G-O m
odel
and
Rayleigh
model. So
we
simulate
d the
s
e fa
ult data
based o
n
G
-
O mod
e
l a
n
d
Rayleig
h
mo
del. Thi
s
p
a
p
e
r utili
zed
G-O
nonh
omog
en
eou
s Poisso
n
model a
nd
Rayleig
h
mo
del, sh
owe
d
a fault pre
d
iction model
d
u
ring
the test perio
d of the proje
c
t [23, [25].
G-O mo
del suppo
se
d that:
1)
Found fault n
u
mbe
r
com
p
l
y
with Poisso
n distrib
u
tion;
2)
Found fault n
u
mbe
r
at each unit interva
l
is dire
ct pro
portion to the
remaini
ng fa
ult
numbe
rs in the software;
3)
All faults are i
ndep
ende
nt a
nd all
sh
are e
qual po
ssibility being dete
c
ted;
4)
All detected faults
will be
eliminated i
m
mediately and no new
error
will be i
n
volved
durin
g the eli
m
inating pe
ri
od.
Thus,
the
accumul
a
ted
fa
ult fun
c
tion
B(t)
is end by time t. If
“a”
repres
ent
s
the
detecte
d fault numbe
r at the end, we
ca
n con
c
lu
de th
at:
0
)
0
(
B
(1)
a
B(t)
Lim
t
(2)
Therefore, th
e num
be
r of f
aults i
n
( t, t +
∆
t
) i
s
in
di
rect p
r
op
ortio
n
to remai
n
in
g fault at
time t, the ration co
nsta
nt is rep
r
e
s
e
n
ted
by ”
m”, so the relation
shi
p
is as Equatio
n (3).
(3)
Suppo
se
0
t
，
then
B(t))
-
(a
m
(t)
B
'
, by
usin
g the boun
dary
con
d
ition
s
we
can obtai
n a model me
an
value functio
n
as in (4).
t
)
B(t)
a
(
m
B(t)
)
t
t
(
B
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Software F
a
u
l
t Distributio
n for We
b Appli
c
ation (Wa
n
ji
ang Han)
3637
)
e
1
(
a
B(t)
mt
(4)
This
model
is just li
ke th
e
expone
ntial d
i
stribute
d
mo
del
)
e
1
(
K
F(t)
t
duri
n
g
the test pe
ri
od, wh
ere t
rep
r
e
s
ent
s ti
me; k represents total fa
ult numbe
r,
λ
re
presents fault
detecte
d po
ssibility [26]. T
hus, we need
to determi
ne
the param
eter “a
” and
“m
” in (4). After the
para
m
eters a
r
e co
nfirme
d, we can get th
e f
ault predi
ction model fo
r Web ap
plications.
3.1.
Determinatio
n of the To
ta
l Number of
Faults
To estimate
the total nu
mber of fault
s
in the mod
e
l
，
we can
refer to the
Rayleig
h
model
，
F
ault
distributio
n den
sity function of the Rayleigh mod
e
l
2
)
/
(
2
e
)
t/c
(
a
2
f(t)
c
t
，
Cumul
a
tive distributio
n function of faults
)
e
1
(
a
B(t)
2
)
/
(
c
t
, where ”a” is
the total
faults
，
t s
t
ands
for time
，，
c is a
consta
nt
and
m
t
2
c
,
m
t
is the
time wh
en B
(t) rea
c
he
s th
e
maximum. T
h
is
model assumption i
s
：
Wh
en
the
r
e
are
39.3
5
%
faults
，
f(t)
re
ach
e
s the
maximum. Therefore
，
thro
ugh the
cu
rve
of faults havi
ng bee
n
foun
d, we can d
e
termin
e the time
m
t
, then determ
i
ne the accu
mulation fault
numbe
r “b”
of
m
t
moment, Eventually
determi
n
e
the total number of faults i
s
%
35
.
39
/
b
a
.
3.2.
Determination of the Probabilit
y
of Finding a Faul
t
The proba
bility of
finding
a fault is the
faults pe
r thousa
nd li
nes of code
numbe
r
(faults/KLO
C), can b
e
rep
r
e
s
ente
d
as
m
，
is the test
particl
e
size
,
)
N
/
N
(
1000
c
k
，
w
h
er
e
c
N
is ef
fective software
line
s
of code
and
k
N
is
th
e
nu
mb
er
of
t
e
st
ca
se.
is ca
se i
n
t
e
nsit
y
,
k
d
N
/
N
，
whe
r
e
d
N
is the n
u
m
ber
of soft
ware faults
found in the testing p
r
o
c
e
s
s. The pro
b
a
b
ility of
finding a fault describ
es the ab
ility of softwa
r
e
testing
ade
q
uacy. T
here
are two m
e
thod
s to
de
termine
this
para
m
eter,
o
ne i
s
u
s
in
g
the
nonlin
ear re
gre
ssi
on software, acco
rd
ing to
)
e
1
(
a
B(t)
mt
model ,matching
the
related m
odel
param
eters “m”, the othe
r is co
unting th
e test pa
rticle
size
α
of
simi
lar proje
c
t an
d
，
ca
se int
e
n
s
it
y
β
Finally cal
c
ulatin
g the d
e
tected
rate “m”.
3.3.
The Fault Pr
ediction Mo
del for Web
Application
T
his
se
ction
confirms
p
a
ram
e
ters of
the
model
according t
o
fault data
of Web
appli
c
ation p
r
oject [27]. Ta
ble 1 tells th
e
statistical
da
ta of found fault of a Web Appli
c
ati
on
proje
c
t. Usin
g
these d
a
ta d
r
aws the
foun
d faults curv
e
,
as
sh
own in
Figu
re
1. Fig
u
re
2 d
e
scrib
es
cumul
a
tive faults. Whe
n
Ti
me tends to i
n
finity, fault n
u
mbe
r
ca
n tend to 0.
Figure 1. Detected F
ault Distributio
n
Fi
gure 2. Cu
mulative Faul
t Distributio
n
0
5
10
15
20
25
30
35
1
3
5
7
9
11
13
15
17
19
21
23
Bu
gs
Bu
gs
0
50
100
150
200
250
300
350
1
3
5
7
9
1
11
3
1
51
7
1
92
12
3
Total
Bu
gs
Total
Bu
gs
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3634 – 36
41
3638
Table 1. Proj
ect’s F
ault Da
ta
Date
interval
Found faults
Number of
faults
2013.6.1
1
6
6
2013.6.2
2
8
14
2013.6.3
3
10
24
2013.6.4
4
12
36
2013.6.5
5
16
52
2013.6.6
6
21
73
2013.6.7
7
26
99
2013.6.8
8
29
128
2013.6.9
9
28
156
2013.6.10
10
27
183
2013.6.11
11
20
203
2013.6.12
12
19
222
2013.6.13
13
18
240
2013.6.14
14
16
256
2013.6.15
15
13
269
2013.6.16
16
10
279
2013.6.17
17
8
287
2013.6.18
18
6
293
2013.6.19
19
5
298
2013.6.20
20
4
302
2013.6.21
21
3
305
2013.6.22
22
3
308
2013.6.23
23
1
309
2013.6.24
24
1
310
For th
e p
a
ra
meter
of “m
”,
we
ca
n u
s
e t
w
o m
e
thod
s t
o
dete
r
min
e
, then
avera
ge i
t. One i
s
us
ing MATLA
B
to fit
)
1
(
320
B(t)
mt
e
curv
e (Seein
g
Fig
u
re 2
)
by the
data in Ta
bl
e 1 ,
then calculating pa
ramete
r m=0.03
26.
Anot
her m
e
th
od is to u
s
e t
he Equatio
n
of
m
to calculate the avera
ge value. Table 2
is the
statist
i
cal data of
7 proje
c
ts
which rep
r
e
s
e
n
ts
particl
e si
ze a
nd inten
s
ity of test case
s. So we ca
n ge
t the value o
f
“m “ usin
g (5).
)
(
7
1
m
i
i
(5)
In (5)
i
= Nu
mbers of test case/
N
um
b
e
rs
of cod
e
line
，
i
= Num
bers of foun
d
defect/
Numb
ers of te
st ca
se. Th
ro
ugh t
he data
in
T
a
ble 2, m i
s
a
pproxim
ately 0.0324. Fi
nall
y
get the mean
m=0.03
25.
Table 2.
Stati
s
tics Data of
Web Appli
c
ati
on
Project
Code line
Test case
Found faults
1 4125
132
110
2 4428
155
129
3 4724
165
151
4 10381
335
321
5 9982
298
291
6 2115
55
82
7 2392
67
96
So the fault predi
ction mo
d
e
l for Web a
pplicat
ion ca
n be app
roxi
mately represented as in
(6). B(t):
)
1
(
a
B(t)
0325
.
0
t
e
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Software F
a
u
l
t Distributio
n for We
b Appli
c
ation (Wa
n
ji
ang Han)
3639
Whe
r
e “a” is
the total number of faults i
n
t
he proje
c
t, which is different to the
different
proje
c
t. We d
e
fine Quality index “q
” as
t
e
0325
.
0
. The small
e
r
Quality inde
x is, the better the
product quality is. Moreov
er, we can estimate how long the sy
stem
test will last, as in (7):
0.0325
lnq
T
(7)
The total nu
mber of faults ca
n be esti
mated by th
e peak valu
e
of found faults. For
Figure. 1, pe
ak p
o
int of t
he curve i
s
2
9
whil
e “t”
e
qual
s to 8. T
herefo
r
e
，
the a
c
c
u
mu
la
tion
o
f
found faults i
s
128
wh
en “t
” equal
s to 8
，
then we
ca
n estimate th
at the total nu
mber of fault
s
is
128/0.4
320. So, for this project , the fau
l
t predictio
n
m
odel du
rin
g
system test
pha
se is a
s
in
(8).
)
1
(
320
B(t)
0325
.
0
t
e
(8)
In fact, fault a
nalysi
s
cha
r
t
can
tell u
s
a
l
o
t
of valuabl
e
inform
ation.
Such
as whet
her th
e
ratio of
hum
an resou
r
ces on
develop
ment an
d te
st is a
pprop
ria
t
e, and
so
o
n
. For ab
normal
fluctuation
s
,
W
e
sho
u
ld p
a
y more
attention to
them
and
see
what ha
s ha
pp
ened. T
hese
fault
analysi
s
can
help us to improve the d
e
velopme
n
t work.
4.
In the Ca
se
of the
Applic
ation
This sectio
n
will verify th
e
model,
u
s
ing
)
e
1
(
a
B(t)
0325
.
0
t
to p
r
edi
ct th
e p
r
oje
c
t
faults d
u
rin
g
the te
st p
hase. Figu
re
3
sho
w
s
th
e test
data
of first ten
d
a
ys of
a p
r
o
j
ect.
Acco
rdi
ng to
the fault cu
rve we
can
obt
ain the pe
ak
point of the curve is
13 wh
ile “t” eq
ual
s to
8. Then the a
c
cumulatio
n
of found faults is 63
whe
n
“t” equal
s to 8. So we can estimate t
he
total numbe
r of faults is 63/0.4
1
58. The
r
efo
r
e, fault m
odel of thi
s
proje
c
t is
)
e
1
(
158
B(t)
0325
.
0
t
. Figure
4
sh
ows the
actu
al data
of
faul
t distrib
u
tion.
Figure 5
sh
o
w
s
the differen
c
e
betwee
n
e
s
timated data
a
nd actu
al
dat
a. Obviou
sly, the two curv
es a
r
e ba
si
ca
lly
identical.
Figure 3. Data of the First Ten Day
s
du
ring
Test Peri
od
Figure 4. Actual Fault Dat
a
after Testin
g
If the quality index is 0.0
0
23, the test p
e
ri
od i
s
a
pproximately 20-day. And the actu
al
test perio
d is
19-d
a
y.
0
2
4
6
8
10
12
14
123
456789
1
0
Bu
g
Bu
g
0
2
4
6
8
10
12
14
1
3
5
7
9
1
11
3
1
51
7
1
9
Bu
g
Bu
g
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3634 – 36
41
3640
We
can eval
uate the accuracy of e
s
timati
on by M
R
E (Ma
gnitu
de of Rel
a
tive Erro
r).
Namely, MRE=|Actual
-Predicte
d
|/Actu
al. The MMRE
(Mean of t
he Mag
n
itude
of Relative Erro
r)
is also a useful evaluation
tool, Its Equation is a
s
in (9
).
n
i
i
MRE
n
MMRE
1
1
(9)
For Figu
re 5
,
the MMRE is 9.1%. The cal
c
ulate
d
MMRE of similar proj
ect
s
is
clo
s
e to
9.9%.
Figure 5. The compa
r
i
s
o
n
betwe
en the Predi
cted a
nd Actual Data
5. Conclu
sion
The
re
sea
r
ch
of fault m
o
d
e
l could
be
a
way to
evalu
a
te the
pro
d
u
c
t pe
rforman
c
e. Al
so,
it could be u
s
ed a
s
a ba
sis to prod
uct.
It is meaningful to set up rese
arch an
d prod
uct mo
del.
This p
ape
r, throu
gh the
G-O n
o
n
-
ho
mogen
eou
s
Poisson p
r
o
c
ess mod
e
l a
nd the Rayleigh
model,
pre
s
e
n
ts the
step
s of fault
pre
d
i
c
tion
mod
e
l f
o
r
We
b a
ppli
c
ation
softwa
r
e. Th
ro
ugh
this
model, we
can reali
z
e t
he qua
ntitative manage
m
ent of the testing pr
o
c
e
ss, predi
ct test
efficien
cy, and predi
ct the pote
n
tial numbe
r of
faults. With
the develop
ment of soft
ware
engin
eeri
ng t
e
ch
nolo
g
y, the fault p
r
e
d
i
ction te
ch
nol
ogy is
also f
a
cin
g
ne
w
challen
ges an
d it
requi
re
s con
s
tant innovatio
n to adapt to cha
ngin
g
nee
ds.
For future wo
rk, furthe
r inv
e
stigatio
n ca
n be studi
ed
on the slo
pe
of the model, and the
influen
ce on t
he pre
d
ictio
n
results.
Ackn
o
w
l
e
dg
ements
This work wa
s su
ppo
rted i
n
part by the National Natural Scie
nce Found
ation o
f
China
(Grant No. 61
1702
73).
Referen
ces
[1] Akiy
ama
F.
An example of so
ftware system
debugging
. In:
Proc. Of the Int’l F
ederatio
n o
f
Information
Proc. Societies
Congr
ess. Ne
w
York: Spri
ng
Scienc
e an
d Busin
e
ss Medi
a. 1971: 3
53-3
5
9
.
[2]
Halstead MH. Elements
of Soft
w
a
re Sci
enc
e
.
New
York: El
sevier. North-
H
o
lla
nd
. 1
977.
[3]
Lip
o
w
M. N
u
m
ber of fa
ults p
e
r li
ne
of cod
e
.
IEEE Trans. On Softw
are Engi
neer
in
g
.198
2; 8(4): 4
37-
439.
[4]
T
a
kahashi
M, Kama
yac
h
i Y.
An
em
piric
a
l
stud
y
of a
mo
del
for pr
ogr
am er
ror pr
edicti
on.
I
EEEE Trans
.
On Softw
are Engi
neer
in
g
. 19
89; 15(1): 8
2
-8
6.
[5]
Mala
yi
a Y, De
nton J.
Modu
le
si
z
e
distrib
u
tio
n
and
defect d
ensity
. In: Proc. Of
the 11th Int’d Sy
mp on
Soft
w
a
re Re
lia
bilit
y
En
gin
eeri
ng. Ne
w
York:
IEEE Compute
r
Societ
y
Pr
ess
.
2000: 62-
71.
[6]
Chul
an
i S. Ba
yesia
n
an
al
ysis
soft
w
a
r
e
cost a
nd q
ual
it
y
mo
d
e
ls. Ph.D. T
hesis. Los Ang
e
l
e
s:
Univcrsity
of Souther
n Ca
liforni
a
. 199
9.
0
20
40
60
80
100
120
140
160
180
200
12345
6789
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
pr
edi
c
ted
Ac
tu
al
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Software F
a
u
l
t Distributio
n for We
b Appli
c
ation (Wa
n
ji
ang Han)
3641
[7] Chul
an
i
S.
Re
sults of Del
phi
for the defect
introducti
on
mo
de
l, sub-
mo
del of
the c
o
st/qual
ity mo
de
l
extensi
on to C
O
COMO II.
T
e
chnic
a
l Re
port, USC-CSE-9
7
-504. 19
97.
[8]
Chulani S, Boehm B.
Modeli
n
g softw
are defect introducti
o
n
and re
moval:
COQUALMO
(COnstructive
QUALity MOde
l).
T
e
chnica
l R
eport. USC-CS
E-99-5
10. 19
9
9
.
[9]
Chil
lar
ege
R, Bhan
dari I, Ja
rik K, Micha
e
l
J,
Dian
e
S, B
onn
ie K, Ma
n-
Yuen W
.
Orthogo
nal
defec
t
classificati
on-
a
concept for in
-process me
as
ureme
n
ts.
IEEE T
r
ans. on Softw
are Engin
e
e
rin
g
.
199
2;
18(1
1
): 943-
95
6.
[10]
Mills H. On th
e statistical
v
a
lidati
on
of co
mputer pr
ogr
a
m
s.
T
e
chnica
l
Rep
o
rt, FSC-72-6
015, IBM
F
edera
l
S
y
ste
m
s Divisio
n. 19
72.
[11]
L
y
u M. Hand
bo
ok of Soft
w
a
r
e
Reli
ab
ilit
y Eng
i
neer
ing. Si
nga
pore: McGra
w
-
Hill. 19
96.
[12]
T
r
achtenberg
M. Discovcring
ho
w
to ens
ure
soft
w
a
r
e
reli
ab
ilit
y
.
R
C
A Eng
i
neer
. 19
82; 27(
1): 53-57.
[13]
Jr Gaffney
JE.
On predicting software relat
ed pe
rforance of
large-scale system
s
. Proc.
of the Int'
l
Conf. of the Co
mputerr Meas
u
r
ement
Group,
CMG XV. San
F
r
ancisco. 19
8
4
.
[14]
Putnarn L
H
, Myers W
.
F
a
mili
ar
metric mana
geme
n
t-reli
abi
li
t
y
.19
95.
[15]
Jelinsk
i Z, Moran
da P. S
o
ft
w
a
r
e
re
lia
bi
li
y
res
earch.
F
r
eiber
ger W
,
ed. Statistic
a
l C
o
mput
e
r
Performanc
e Evalu
a
tion. N
e
w
York: Academi
c
Press. 1972: 465-
484.
[16]
Littl
w
o
od B.
S
t
ochastic
r
e
li
a
b
ilit
y gro
w
t
h
: A
mo
d
e
l
for f
ault r
e
mova
l
i
n
com
puter
pr
ograms
an
d
hard
w
a
r
e d
e
si
gns.
IEEE Trans. On Reliab
ilit
y
. 198I; R-30:3
13-3
20.
[17]
[Abdel-Gh
a
l
y
AA, Cha
n
PY,
Little
w
o
o
d
B.
Eval
uatio
n
of comp
eting
so
ft
w
a
re
rcIia
b
il
ity
pre
d
ictio
n
s
.
IEEE Trans. on Softw
are. Engineer
ing.
1
986;
12(9): 95
0-9
6
7
.
[18]
Goel A
L
, Oku
m
oto K. A tim
e
-de
pen
de
nt e
rror-det
ecti
on r
a
te mo
del
for
soft
w
a
r
e
re
li
ab
ilit
y a
nd
other
performa
nce m
easur
es.
IEEE
Trans. on Rel
i
a
b
ility
. 19
79; R-
28(3): 20
6-2
1
1
.
[19]
J Yamad
a
S, Ohba M, Osak
i S.
S-Shap
ed
relia
bil
i
t
y
gro
w
t
h
m
o
d
e
li
ng f
o
r soft
w
a
re
err
o
r detecti
on.
IEEE Trans. on Reliability
. 198
3; R-32(5): 47
5
-
478.
[20]
Ohba M. Soft
w
a
re rel
i
a
b
il
it
y
a
nal
ysis m
o
d
e
ls
.
IBM Journal
o
f
Researc
h
an
d
Devel
o
p
m
ent
. 198
4; 28(
4):
428-
443.
[21]
Liu
HW
, Yan
g
XZ
, Qu
F
,
Z
hao J
H
. Soft
w
a
re rel
i
a
b
il
it
y gr
o
w
t
h
m
ode
ls
o
f
non
hom
oge
n
ous P
o
isso
n
process.
Jour
n
a
l of T
ong
ji U
n
iversity (N
atu
r
al Scie
nce)
. 200
4; 32(8): 1
071-
107
4 (in
Chincs
e
w
i
t
h
Engl
ish abstra
c
t).
[22]
Mend
es N, Mosle
y
N, Cou
n
se
ll S.
Early W
eb si
z
e
me
asur
es
and effort pred
iction for W
eb
costimatio
n
.
Proc. Of
the 9th Int’l Soft
w
a
re
Metrics S
y
mp.
(MET
R
ICS 2003). 200
3; 18-2
9
.
[23]
Che
n
HW
, W
ang J, Do
ng W
.
High c
onfi
den
ce soft
w
a
re
en
gin
eeri
ng tec
h
nol
ogi
es.
Acta Electronic
a
Sinic
a
.
200
3; 31(12A): 19
33-
1
938 (i
n Chi
nes
e
w
i
t
h
Eng
lish
abstract).
[24]
GUO SH, Lan
YG, Jin MZ
. Some iss
ues
abo
ut trusted
compo
nents r
e
search.
C
o
mp
uter Scie
nc
e
.
200
7; 34(5): 24
3-24
6 (in Ch
in
ese
w
i
th En
glis
h abstract).
[25]
Boehm
B. Val
ue-Bas
ed S
o
ftw
a
r
e
en
gin
eer
i
ng-
ov
ervie
w
a
nd
age
nd
a. T
e
chn
i
cal
Re
po
rt, USC-CS
E
200
5-50
4. 200
5.
[26]
Xi
n
Xi
a, Shu-
xin Z
hu.
A S
u
r
v
e
y
on W
e
ig
hted N
e
t
w
ork M
easur
ement
a
nd Mo
del
in
g.
TELKOMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(1): 1
81-1
86.
[27]
Jaralik
ar SM, Aruna M. Case stud
y
of a h
y
bri
d
(
w
i
n
d and so
lar)
po
w
e
r pla
n
t.
TELKOMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2011; 9(1): 1
9
-
26.
Evaluation Warning : The document was created with Spire.PDF for Python.