Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
6,
No.
4,
August
2016,
pp.
1929
–
1938
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i4.9991
1929
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Softwar
e
Reliability
Pr
ediction
using
Fuzzy
Min-Max
Algorithm
and
Recurr
ent
Neural
Netw
ork
A
ppr
oach
Manmath
K
umar
Bhuyan
*
,
Dur
ga
Prasad
Mohapatra
**
,
and
Srini
v
as
Sethi
***
*
Computer
Science
Engineering
and
Application,
Sarang,
Utkal
Uni
v
ersity
,
V
ani
vihar
,
India
**
Computer
Science
Engineering,
National
Institute
of
T
echnology
,
Rork
ela,
India
***
Computer
Science
Engineering
and
Application,
IGIT
,
Sarang,
India
Article
Inf
o
Article
history:
Recei
v
ed
Dec
23,
2015
Re
vised
May
23,
2016
Accepted
Jun
8,
2016
K
eyw
ord:
Fuzzy
Min-Max
K-Means
Softw
are
Reliability
Prediction
Recurrent
Neural
Netw
ork
Back-propag
ation
ABSTRA
CT
Fuzzy
Lo
gic
(FL)
together
with
Recurr
ent
Neur
al
Network
(RNN)
is
used
to
predict
the
softw
are
reliability
.
Fuzzy
Min-Max
algorithm
is
used
to
optimize
the
number
of
the
k-
g
aussian
nodes
in
the
hidden
layer
and
delayed
input
neurons.
The
optimized
recurrent
neural
netw
ork
is
used
to
dynamically
reconfigure
in
real-time
as
actual
softw
are
f
ailure.
In
this
w
ork,
an
enhanced
fuzzy
min-max
algorithm
together
with
recurrent
neural
netw
ork
based
machine
learning
technique
is
e
xplored
and
a
comparati
v
e
analysis
is
performed
for
the
modeling
of
reliability
prediction
in
softw
are
systems.
The
model
has
been
applied
on
data
sets
collected
across
se
v
eral
standard
softw
are
projects
during
system
testing
phase
with
f
ault
remo
v
al.
The
performance
of
our
proposed
approach
has
been
tested
using
distrib
uted
system
application
f
ailure
data
set.
Copyright
c
2016
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Manmath
K
umar
Bhuyan
Utkal
Uni
v
ersity
V
ani
vihar
,
Bhubanesw
ar
Phone:
09437931445
Email:
manmathr@gmail.com
1.
INTR
ODUCTION
Softw
are
reliability
prediction
in
softw
are
systems
plays
a
k
e
y
part
for
an
y
softw
are
or
g
anization
to
produce
quality
and
reliable
softw
are.
The
k
e
y
part
of
softw
are
quality
is
it’
s
reliability
.
So
predicting
softw
are
reliability
plays
a
k
e
y
part
for
producing
good
quality
softw
are.
As
per
IEEE
Standard
Glossary
of
Softw
are
Engineering,
a
definition
of
softw
are
reliability
is
the
probability
of
the
f
ailure
free
operation
of
a
computer
program
for
a
specified
period
of
time
in
a
specified
en
vironment
[1,
2,
3,
4].
Computational
Intellig
ence
(CI)
can
of
fer
promising
approaches
to
softw
are
reliability
prediction
and
modeling,
because
the
y
require
only
f
ailure
hi
story
as
input
without
an
y
assumption
[5].
As
per
IEEE
Standard
Glossary
of
Softw
are
Engineering,
a
definition
of
softw
are
reliability
is
the
probability
of
the
f
ailure
free
operation
of
a
computer
program
for
a
specified
period
of
time
in
a
specified
en
vironment
[1,
2,
3,
4].
The
time
duration
between
successi
v
e
f
ailures
or
the
cumulati
v
e
f
ailure
time
is
a
vital
f
actor
of
softw
are
reliability
[6,
7].
CI
can
of
fer
promising
approaches
to
softw
are
reliability
prediction
and
modeling,
because
the
y
require
only
f
ailure
history
as
input
without
an
y
assumption.
In
reply
to
this,
neuro-fuzzy
approach
has
been
applied
to
softw
are
reliability
assessment.
Fuzzy
Mi
n-Max
algorithm
is
used
to
optimize
the
neural
netw
ork
architecture
after
e
v
ery
occurrence
of
softw
are
f
ailure
time
data.
The
main
contrib
ution
of
this
paper
is
to
propose
h
ybrid
model
of
fuzzy
logic
and
neural
netw
ork
to
handle
dynamic
data
set
of
softw
are
reliability
between
number
of
observ
ed
f
ailure
along
with
successi
v
e
softw
are
f
ailures.
W
e
propose
an
adapti
v
e
softw
are
reliability
prediction
model
fuzzy
min-max
with
r
ecurr
ent
neur
al
network
(FMM-
RNN)
approach
based
on
multiple-delayed-input
single-output
architecture.
W
e
structured
the
data
set
relationship
between
f
ailure
sequence
number
and
f
ailure
time
data.
Optimization
technique
is
used
to
model
the
inter
-relationship
among
softw
are
f
ailure
time
data.
In
addition,
we
made
a
comparati
v
e
study
about
the
performance
of
some
well-
kno
wn
e
xisting
softw
are
reliability
prediction
models
ag
ainst
our
approach
model.
Neuro-Fuzzy
system
is
used
in
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.
1930
ISSN:
2088-8708
predicting
the
softw
are
reliability
from
the
aspects
of
prediction
ability
for
short-term
prediction.
The
paper
is
or
g
anized
as
follo
ws:
Section
2.
describes
the
related
w
ork
proposed
so
f
ar
in
reliability
predic-
tion.
Section
3.1.
presents
our
proposed
model
fuzzy
min-max
with
r
ecurr
ent
neur
al
network
(FMMRNN)
architecture.
The
basic
terminologies,
application,
architecture
de
v
elopment
is
discussed
i
n
Section
3..
Section
4.
focus
on
compu-
tation
of
measure
criterion
of
the
propose
model
and
observ
ations
are
presented.
In
Section
5.,
the
concluding
remarks
and
future
w
ork
are
included.
2.
B
A
CKGR
OUND
OF
RELA
TED
W
ORK
Karunanithi
et
al.
[8]
first
propose
a
neural
netw
ork
for
softw
are
reliability
prediction.
The
authors
[9,
10,
11,
12]
de
v
eloped
a
connectionist
model
for
reliability
prediction.
Raj
Kiran
et
al.
[13,
14]
implemented
the
use
of
wavelet
neur
al
networks
(WNN)
and
emplo
yed
w
a
v
elets
as
transfer
function
to
predict
softw
are
reliability
.
P
ai
et
al.
[15]
used
support
v
ector
machines
and
simulated
annealing
algorithms
for
reliability
forecasting.
The
y
used
lagged
data
in
their
analysis
by
di
viding
the
101
observ
ations
such
as:
33
observ
ations
for
training,
8
observ
ations
for
v
alidation,
60
observ
ations
for
test.
Since
it
is
not
a
standard
method
of
splitting
the
data
set
for
e
xperimentation.
[16]
used
neural
netw
ork
approach
for
softw
are
defect
prediction
and
pointed
out
that
the
approach
is
poor
at
at
predicting
number
of
softw
are
defects,
b
ut
qualitati
v
ely
good
at
classifying
program
modules.
Sitte
[17],
analyzed
tw
o
methods
(i.e.
Neur
al
Networks
(NN)
and
2)
parametric
recalibration
models)
for
reliability
prediction.
An
early
reliability
prediction
approach
at
design
phase
is
proposed
by
Mohanta
et
al.
[18].
The
f
ault
is
estimated
using
product
metrics
collected
during
design
phase
of
the
components.
Then
these
product
metrics
are
used
for
reliability
prediction.
Adnan
et
al.
[19]
and
Cai
et
al.[20]
determined
the
number
of
input
neurons
and
the
number
of
neurons
in
hidden
layers
were
determined
using
a
pre-specified
ra
n
ge
of
v
alues
(i.e.
20,
30,
40,
and
50
input
neurons
selected
in
Cai
et
al.
[20],
while
1,
2,
3,
and
4
input
neurons
were
selected
in
Adnan
et
al.
[19]
and
Cai
et
al.[20]
used
genetic
algorithm
as
an
optimiza
tion
search
scheme
to
determine
the
optimal
or
near
optimal
netw
ork
architecture.
T
ian
and
Noor
[6]
predicted
softw
are
reliability
using
RNN.
Su
et
al.
[21]
b
uild
a
dynamic
weighted
combinational
model
using
NN.
Lo
[22]
designed
a
model
e
xamines
s
e
v
er
al
con
v
entional
softw
are
reliability
gro
wth
models.
3.
PR
OPOSED
MODEL
FMMRNN
RELIABILITY
PREDICTION
In
this
section,
we
discuss
about
our
proposed
model
FMMRNN
architecture
and
its
applicability
in
softw
are
reliability
prediction.
Fuzzy
Min-Max
is
a
specific
type
of
neuro-fuzzy
that
has
high
ef
ficienc
y
rather
than
other
com-
putational
methods
[23].
The
FMMRNN
architecture
comprises
of
tw
o
steps
1)
Netw
ork
optimization,
2)
Reliability
prediction.
The
complete
architecture
frame
w
ork
of
our
propose
model
is
sho
wn
in
Fig.
1.
The
model
recei
v
e
the
f
ailure
data
as
input
then
Fuzzy
Min-Max
algori
thm
is
use
to
optimizing
the
neural
netw
ork
architecture.
The
Fuzzy
Min-Max
algorithm
optimization
process
determines
the
optimal
or
near
-optimal
numbers
of
‘k’
hidden
neurons
and
initializes
the
k-centers.
On
the
basis
of
numbers
of
neurons
in
the
hidden
layer
,
the
netw
ork
is
framed.
The
cumula-
ti
v
e
e
x
ecution
time
is
tak
en
as
input
and
the
number
of
cumulati
v
e
f
ailures
is
tak
en
as
output
to
the
netw
orks.
As
this
is
a
supervised
learning,
so
the
netw
ork
is
trained
with
input
and
output
data
pro
v
ed
to
the
model.
This
information
is
then
used
to
dynamically
reconfigure
the
neural
netw
ork
architecture
for
predicting
the
ne
xt-step
f
ailure
^
d
i
+1
.
Optimization Using
Fuzzy
Min
-Max
Algorithm
No of Hidden
Neurons
Output Data
Error Deviation Between
Actual and Predicted Output
Input Data
Failure Data Set
K
-Means
Algorithm
Find numbers of the
k
-center
Compute the Various
Measurement Criterion
(
AE
,
RMSE
,
NRMSE
,
MAE)
Initialization of
K
-Means
Algorithm
Recurrent Neural Network
Training
Figure
1.
A
simple
architecture
of
FMMRNN
model
IJECE
V
ol.
6,
No.
4,
August
2016:
1929
–
1938
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1931
3.1.
Recurr
ent
Neural
Netw
ork
The
RNN
is
based
on
standard
feed-forw
ard
neural
netw
orks.
RNN
is
a
dynamic
netw
ork
as
it
is
a
netw
ork
with
output
feedback
[24].
OUT
PUT
STATE/
HIDDEN
STATE/
HIDDEN
(
t
-1)
STATE/
HIDDEN
(
t
-2)
INPUT
(
t
-1)
STATE/
HIDDEN
(
t
-3)
INPUT
(
t
-2)
Weights
W
Weights V
Weights U
Weights U
Weights U
Weights V
Weights V
INPUT
Copy (delayed to
previous state)
Copy (delayed to
previous state)
Copy (delayed to
previous state)
Figure
2.
An
graphical
presentation
of
unfolding
netw
ork
associated
with
recurrent
back-propag
ation
through
time
learning.
Fig.
2
sho
ws
the
RNN
with
back-propag
ation
through
time
learning
that
consists
of
c
ycles
with
its
states.
In
FMMRNN
model,
the
hidden
layers
are
recursi
v
e
relationship
in
nature.
In
recurrent
netw
ork
an
e
xtra
layer
of
neurons
which
cop
y
the
current
acti
v
ations
in
memory
(i.e.
in
the
hidden
layer
neurons)and
mo
v
e
forw
ard.
Later
on,
it
delays
these
v
alues
for
one
time
instant
[25],
feed
them
back
as
additional
inputs
into
the
hidden
layer
neurons
as
sho
wn
in
Fig.
2.
As
a
result
of
this,
each
node
1
sends
acti
v
ation
along
a
recurrent
connection,
has
at
lea
st
number(s)
of
copies.
In
the
supervised
learning,
an
error
de
viation
is
the
Euclidean
distance
between
the
predicted
output
of
the
netw
ork
and
actual
output.
That
error
de
viation
is
propag
ated
through
time
[26].
Each
time
the
error
is
calculated
and
the
weights
are
folded
back
and
added
with
error
to
compute
the
ne
w
updated
weights
using
netw
ork
training
method.
y
k
(
t
)
=
f
2
(
net
k
(
t
))
;
(1)
w
her
e;
net
k
(
t
)
=
m
X
j
y
j
(
t
)
w
k
j
+
k
Here,
f
2
is
an
acti
v
ation
function
between
the
hidden
and
output
nodes.
In
this
paper
,
we
consider
y
i
as
the
output
(predicted
f
ailure)
with
acti
v
ation
function
f(.)
and
w
ij
as
the
weight
from
node
j
to
node
i
associated
with
this
link.
Here
the
input
nodes
x
i
recei
v
e
e
xternal
inputs
(i.e.
the
f
ailure
number).
The
desired
state
of
unit
i
denoted
as
d
i
corresponding
to
x
i
.
The
accumulated
cost
function
(i.e.
the
Summed
Squar
e
Err
or
(SSE))
‘L
’
in
Equation
2
measures
t
he
de
viation
(i.e.
dif
ference
between
the
actual
and
desired
v
alues)
of
the
netw
ork
outputs
y
i
(
t
)
from
the
desired
functions
d
i
(
t
)
from
t
=
t
0
to
t
=
t
1
for
all
copies
of
the
output
nodes.
L
=
1
2
n
X
k
=1
(
d
k
(
t
)
y
k
(
t
))
2
=
1
2
n
X
k
=1
L
2
k
(2)
Where
L
k
=
(
d
k
y
k
;
k
th
output
node
0
;
other
w
ise
Here,
n
is
the
total
no
of
output
nodes
and
is
an
inde
x
o
v
er
the
training
sequence
d
k
(
t
)
;
y
k
(
t
)
(
these
are
the
desired
and
predicted
output
functions
of
time
respecti
v
ely).
The
change
in
weights
W
and
V
are
calculated
as
W
(
h
)
=
m
W
(
h
1)
+
g
L
k
f
0
(
h
)
y
k
(3)
V
(
h
)
=
m
V
(
h
1)
+
g
L
k
g
0
(
h
)
x
k
(4)
where
m
;
g
[0,1]
are
the
constant
parameters.
The
last
step
in
the
training
process
is
the
updation
of
net
weights
using
Equations
3
&
4,
which
is
gi
v
en
belo
w:
The
training
process
aim
is
to
update
the
net
weights
using
Equati
on
s
5
and
6.
W
(
ne
w
)
=
W
(
old
)
+
W
(5)
V
(
ne
w
)
=
V
(
old
)
+
V
(6)
The
aim
of
this
weight
updation
is
to
minimize
the
error
de
viation
between
the
desired
output
and
actual
output.
1
In
this
paper
the
term
unit,
node
and
neuron
are
used
interchangeably
.
Softwar
e
Reliability
Pr
ediction
using
Fuzzy
Min-Max
Algorithm
...
(Manmath
K
umar
Bhuyan)
Evaluation Warning : The document was created with Spire.PDF for Python.
1932
ISSN:
2088-8708
3.2.
FMMRNN
T
raining
This
section
gi
v
es
a
brief
discussion
about
RNN
training
using
back-propag
ation
learning
rule.
W
e
can
interpret
number
of
f
ailures
as
a
function
of
cumulati
v
e
e
x
ecution
time
x
i
.
Both
cumulati
v
e
e
x
ecution
time
and
number
of
f
ailures
are
normalize
in
the
range
0
to
1.
Suppose
f
is
the
function
of
x
i
,
it
can
be
written
as
f
(
x
i
)
=
d
i
.
The
normalized
v
alues
of
the
input
to
the
netw
ork
such
as
f
(
x
1
)
;
f
(
x
2
)
:::f
(
x
i
)
are
used
to
predict
the
^
d
i
+1
.
In
other
w
ay
,
we
can
forecast
^
d
i
+1
by
using
f
x
1
;
d
1
g
;
f
x
2
;
d
2
g
;
:::
f
x
i
;
d
i
g
,
where
d
i
+1
is
tar
get
v
alue
is
kno
wn
as
short
term
pr
ediction
or
1-step
ahead
pr
ediction
or
ne
xt-step
pr
ediction
.
In
this
study
,
we
assume
that
the
logistic
function
binary
sigmoidal
F
(
x
)
=
1
=
(1
+
e
x
)
is
used
for
each
neuron,
where
is
the
steepness
parameter
.
The
range
of
this
transfer
function
v
aries
from
0.0
to
1.0.
The
logistic
transfer
function
is
used
to
reduce
the
computational
b
urden
during
training.
The
cross-v
alidation
process
splits
the
entire
representati
v
e
data
set
into
tw
o
sets:
a)
a
training
data
set,
used
to
train
the
netw
ork,
b)
a
test
data
set
used
to
v
alidate
the
output
of
the
model.
W
e
split
the
data
set
as
follo
ws:
80
%
for
training
and
20
%
for
testing.
The
training
process
is
continued
and
the
weights
are
updated
until
the
last
hidden
layer
state
is
reached.
In
the
first
epoch,
the
weights
are
typically
initialized
to
a
small
random
v
alue.
On
ne
xt
onw
ards
a
set
of
weights
are
chosen
at
random
and
the
weights
are
adjusted
in
proportion
to
their
contrib
ution
to
error
[27].
W
e
emplo
yed
MA
TLAB
V
ersion
7.10.0
en
vironment
for
prediction
pu
r
po
s
e.
The
weights
are
initialized
with
small
random
v
alue
before
first
epoch
starts.
After
then,
the
weights
are
adjusted
randomly
.
The
error
tolerance
for
back-propag
ation
algorithm
is
E
min
=0.005.
The
netw
ork
model
FMMRNN
is
trained
with
init
ial
weights
and
continues
until
the
stopping
criteria
gets
satisfied
and
the
best
weights
are
recorded
for
ne
xt-step-prediction
of
the
reliability
.
4.
EXPERIMENT
AL
RESUL
TS
AND
OBSER
V
A
TIONS
In
our
reliability
prediction
e
xperiment,
we
considered
the
f
ailure
data
during
system
testing
phase
of
dis-
trib
uted
system
application
ha
ving
defect
se
v
erities
2
and
3
[28]
as
pro
vided
in
T
able
1.
As
per
our
e
xperimental
T
able
1.
Defect
se
v
erities
le
v
el
Sl.
no.
Se
v
erities
le
v
el
T
ype
Description
Need
of
solution
1
0
No
impact
Can
tolerate
No
need
2
1
Minor
Can
tolerate
Solution
e
v
entually
3
2
Major
Can
tolerate
Solution
needed
4
3
Critical
Intolerable
Solution
ur
gently
needed
requirements,
we
ha
v
e
tak
en
a)
F
ailure
Number
,
b)
T
ime
Between
F
ailures
(TBF)
for
our
analysis.
Belo
w
,
we
present,
the
list
of
some
prediction
parameters
used
in
our
approach.
The
A
v
erage
Err
or
(
AE
)
,
ho
w
adequately
a
model
determines
all
o
v
er
the
system
testing
phase
[29].
AE,
mea-
sures
ho
w
well
a
model
predicts
throughout
the
testing
phase
[30].
A
v
erage
Error(%):
AE
i
=
(
j
(
F
i
D
i
)
=D
i
j
)
100
The
Root
Mean
Squar
e
Err
or
(
RMSE
)
,
is
used
to
determine
ho
w
f
ar
on
a
v
erage
the
error
(i.e.
between
actual
and
tar
get
v
alue)
is
fr
om
0.
The
lo
wer
is
RMSE,
the
higher
is
prediction
accurac
y
.
Mathematically
,
R
M
S
E
=
h
p
P
n
1
(
F
i
D
i
)
2
i
=n
Normalized
Mean
Square
Error
(NRMSE)=
h
p
P
n
1
(
F
i
D
i
)
2
i
=
P
n
1
F
i
2
Mean
Absolute
Err
or
(
MAE
)
is
an
a
v
erage
of
an
absolute
error
that
computes
ho
w
close
predictions
are
to
the
final
result.
The
MAE
and
RMSE
are
used
together
to
analyze
the
v
ariation
in
the
errors
on
data
set.
M
AE
=
[
P
n
1
j
(
F
i
D
i
)
j
]
=n
Here,
F
i
denotes
the
predicted
output
and
D
i
denotes
the
desire
output
of
i
th
node.
In
our
e
xperiment,
we
consider
data
set
(DS)
[31]
for
prediction
and
analysis
purpose.
The
number
of
hidden
layers
is
one
and
the
numbers
of
neurons
present
in
the
hidden
layer
calculated
by
optimization
process
are
recorded
from
10
to
50.
T
able
5
represent
the
result
of
the
model
during
v
alidation.
After
the
proposed
netw
ork
model
is
succes
sfully
trained
with
80%
data,
then
the
netw
ork
under
goes
for
ne
xt-step
predictions
IJECE
V
ol.
6,
No.
4,
August
2016:
1929
–
1938
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1933
T
able
2.
Some
Data
Sets
Used
F
or
Reliability
Prediction
[28]
&
[31]
Pr
oject
Code
Pr
oject
Name
Number
of
F
ailur
es
De
v
elopment
Phases
DS1
Real
T
ime
Command
&
Control
System
136
System
T
est
Operations
DS2
Military
101
System
T
est
DS3
Commercial
System
73
Subsystem
T
est
DS4
Real
T
ime
Command
&
Control
System
54
System
T
est
Operations
DS5
Real
T
ime
Command
&
Control
System
53
System
T
est
Operations
DS6
Military
41
System
T
est
DS7
Real
T
ime
Command
&
Control
System
38
System
T
est
Operations
DS8
Military
38
System
T
est
DS9
Real
T
ime
36
System
T
est
DS10
Distrib
uted
System
[31]
191
System
T
est
and
v
alidation
using
rest
20%
test
data.
The
MAE
and
RMSE
are
used
together
to
analyze
the
v
ariation
in
the
errors
on
data
set.
The
v
alues
of
v
arious
parameters
such
as
AE,
RMSE,
and
NRMSE
of
our
e
xperiment
are
listed
in
T
able
5.
W
e
obse
rv
ed
that
the
netw
ork
model
produce
best
result
at
45
numbers
of
neurons
in
the
hidden
layer
.
Fig.
3
and
4
summarize
in
terms
of
AE
and
6
in
terms
of
RMSE.
Figure
3.
Ne
xt-step
prediction
on
training
data.
Figure
4.
Ne
xt-step
prediction
on
test
data.
The
best
results
found
for
data
set
for
short-term
pr
ediction
(STP)
are
as
follo
ws:
the
v
alues
of
AE,
RMSE,
NRMSE,
and
MAE
are
3.0019,
0.00438,
0.0261,
and
0.0331
respecti
v
ely
.
The
STP
for
measurement
unit
AE
on
training
is
sho
wn
in
Fig.
3
(i.e.
the
desired
output
and
predicted
output)
and
de
viation
between
actual
and
forecasted
v
alue.
Figure
4
sho
w
the
prediction
graph
of
actual
data
and
predicted
result
for
data
set
DS10.
The
corresponding
de
viation
between
the
actual
and
computed
output
is
sho
wn
i
n
Figure
5.
The
figure
sho
ws
ho
w
close
predictions
are
to
the
predicted
results.
The
accurac
y
of
AE,
we
found
in
this
e
xperiment
has
been
greatly
impro
v
ed
and
is
consistent
than
some
well-kno
wn
methods
that
are
arri
v
ed
at
T
able
6.
The
performance
of
the
netw
ork
during
training
i
s
presented
in
Fig
6
in
terms
of
RMSE
during
training.
It
is
dra
wn
in
the
form
of
number
of
epochs
vs
error
rate
in
terms
of
RMSE
during
training.
It
sho
ws
ho
w
the
error
rate
decreases
with
number
epochs
during
training
the
netw
ork.
Softwar
e
Reliability
Pr
ediction
using
Fuzzy
Min-Max
Algorithm
...
(Manmath
K
umar
Bhuyan)
Evaluation Warning : The document was created with Spire.PDF for Python.
1934
ISSN:
2088-8708
T
able
3.
Data
set
by
Iyer
and
Lee
[31]
for
DBS10
F
ailur
e
No
C
E
T
ime
F
ailur
e
No
C
E
T
ime
F
ailur
e
No
C
E
T
ime
F
ai
lur
e
No
C
E
T
ime
1
9.9898
49
472.18
97
1048.3
145
1661.8
2
18.747
50
483.2
98
1062
146
1669.4
3
28.962
51
494.25
99
1075.8
147
1677.5
4
40.719
52
505.39
100
1089.6
148
1686.3
5
52.872
53
516.55
101
1103.3
149
1695.5
6
61.037
54
527.7
102
1117.1
150
1705.1
7
70.447
55
539.81
103
1130.9
151
1715
8
80.03
56
551.94
104
1145.4
152
1727.8
9
88.819
57
563.97
105
1159.9
153
1740.6
10
100.3
58
576.01
106
1174.5
154
1753.5
11
110.31
59
588.08
107
1189
155
1766.3
12
117.3
60
600.39
108
1203.5
156
1779.1
13
124.36
61
612.71
109
1218.3
157
1792.4
14
130.85
62
625.03
110
1233.3
158
1806.6
15
137.48
63
637.37
111
1248.2
159
1820.8
16
143.67
64
650.49
112
1263.1
160
1835.1
17
149.64
65
664.14
113
1278
161
1847.8
18
154.47
66
677.97
114
1284.3
162
1861.5
19
164.37
67
691.79
115
1296.5
163
1875.7
20
177.25
68
705.63
116
1309.4
164
1890.3
21
183.9
69
719.47
117
1322.4
165
1904.9
22
191.83
70
733.31
118
1336.2
166
1916.9
23
200.02
71
747.19
119
1349.9
167
1930.2
24
208.79
72
761.09
120
1363.9
168
1943.5
25
218.06
73
775
121
1377.8
169
1957.9
26
227.6
74
788.92
122
1383
170
1972.3
27
237.5
75
802.83
123
1388.2
171
1986.7
28
247.47
76
816.77
124
1396.9
172
2001.3
29
257.56
77
830.72
125
1409.4
173
2015.8
30
267.7
78
844.69
126
1422.5
174
2025.7
31
280.18
79
858.68
127
1436.2
175
2038.1
32
292.96
80
872.67
128
1449.8
176
2050.9
33
305.79
81
879.07
129
1463.7
177
2062.3
34
319.6
82
885.46
130
1478.2
178
2075.6
35
328.15
83
889.07
131
1485.7
179
2088.9
36
336.82
84
902.73
132
1496.8
180
2102.8
37
345.49
85
916.75
133
1509.7
181
2113.5
38
354.17
86
930.94
134
1522.8
182
2124.3
39
362.81
87
945.24
135
1536.9
183
2135.6
40
369.61
88
959.53
136
1551.3
184
2147.4
41
379.51
89
973.83
137
1565.9
185
2160.1
42
391.11
90
988.13
138
1580.5
186
2172.8
43
403.37
91
993.81
139
1595.2
187
2186
44
417.38
92
1001.5
140
1609.8
188
2199.1
45
431.38
93
1009.5
141
1620.8
189
2212.3
46
445.39
94
1017.5
142
1628.6
190
2225.5
47
453.99
95
1025.9
143
1639.5
191
2238.7
48
462.8
96
1034.6
144
1650.7
T
able
4.
T
raining
Result
of
Data
Set
DS10
Neur
ons
in
each
lay
er
AE
RMSE
NRMSE
MAE
1,8,1
4.6714
0.02321
0.0544
0.0423
1,23,1
4.4113
0.0178
0.0432
0.0328
1,30,1
3.6215
0.0021
0.0159
0.0331
1,38,1
3.7614
0.0113
0.017
0.0333
1,40,1
3.4311
0.0093
0.01501
0.0351
1,46,1
4.6715
0.00572
0.0261
0.0331
1,47,1
3.0017
0.00433
0.0262
0.0489
1,49,1
3.9912
0.01989
0.0493
0.0416
IJECE
V
ol.
6,
No.
4,
August
2016:
1929
–
1938
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
1935
T
able
5.
Selection
for
number
of
neurons
in
hidden.
Neur
ons
in
each
lay
er
AE
RMSE
NRMSE
MAE
1,8,1
4.6714
0.02321
0.0544
0.0423
1,10,1
4.8714
0.00798
0.0534
0.0423
1,23,1
4.4113
0.0178
0.0432
0.0328
1,25,1
4.5113
0.00547
0.0441
0.0328
1,38,1
3.7614
0.0113
0.0317
0.0333
1,45,1
3.0019
0.00438
0.0261
0.0331
1,49,1
3.9912
0.01989
0.0493
0.0416
1,50,1
5.6312
0.00993
0.0493
0.0446
Figure
5.
Eror
De
viation
of
Ne
xt-step
prediction
on
test
data.
4.1.
Obser
v
ations
The
comparati
v
e
data
are
sho
wn
in
T
able
6
for
the
gi
v
en
data
set
with
v
arious
models.
It
is
also
observ
ed
that
the
training
results
sho
ws
better
accurac
y
than
the
prediction
result.
The
ne
xt-step
prediction
in
T
able
6
sho
ws
that
our
proposed
model
has
less
NRMSE
v
alue
i.e
0.0261
and
AE
is
3.0019.
Beside,
the
measurement
criteria
NRMSE
is
also
found
minimum
than
the
v
arious
reliability
prediction
models
[13,
14,
32]
and
RMSE
v
alue
with
[10,
33,
34].
Model
quality
is
observ
ed
if
its
predictions
are
close
to
the
ideal
line
passing
through
the
zero
error
[8].
Fig.
3,
4
ans
5
sho
w
the
prediction
closeness
between
the
actual
v
alue
and
prediction
v
alue.
Some
observ
ations
on
softw
are
reliability
prediction
using
our
proposed
feed
forw
ard
neural
netw
ork
model
are
listed
belo
w:
The
training
results
of
the
proposed
model
are
better
than
the
prediction
result
of
the
corresponding
trained
neural
netw
ork.
It
means
that
producing
good
result
at
approximating
does
not
certainly
good
at
forecasting.
Unlik
e
statistical
techniques,
no
unrealistic
assumption
is
made
in
recurrent
neural
netw
ork
approach.
As
we
in
the
cate
gory
of
black-box
model
approach,
so
some
useful
information
is
ignored.
T
able
6.
A
comparison
with
dif
ferent
model
A
ppr
oach
Model
Measur
e
P
arame-
ter
V
alue
Mohanty
et
al.
[32]
NRMSE
0.07292
FMMRNN(Proposed)
NRMSE
0.0261
Su
et
al.
[21]
AE
3.24
FMMRNN(Proposed)
AE
3.0019
Softwar
e
Reliability
Pr
ediction
using
Fuzzy
Min-Max
Algorithm
...
(Manmath
K
umar
Bhuyan)
Evaluation Warning : The document was created with Spire.PDF for Python.
1936
ISSN:
2088-8708
Figure
6.
Performance
result
during
training.
Our
model
is
a
generic
model
that
can
w
ork
in
an
y
stabilize
smooth
trend
data
set
and
in
an
y
en
vironment.
.
4.2.
Thr
eats
to
V
alidity
Belo
w
we
discuss
the
possible
threats
to
the
v
alidity
of
our
w
ork.
Arbitrary
data
set
partitioning
for
training
and
testing
the
netw
ork
can
be
a
limiting
f
actor
.
As
our
e
xperiment
uses
MA
TLAB
for
computation,
so
it
suf
fers
the
same
threats
to
v
alidity
as
MA
TLAB
does.
As
we
discussed
in
Section
4.,
The
weights
of
the
neural
netw
ork
are
chosen
as
random
v
ariables
with
specified
distrib
utions.
So
computed
v
alue
may
not
produce
the
same
result
for
e
v
ery
run.
That
is,
e
v
en
if
for
same
input
dataset
and
the
same
learning
scheme
are
emplo
yed,
e
xpecting
the
same
output
is
dif
ficult.
So
f
ar
there
is
no
such
criteria
on
range
for
training
and
testing
partitioning
with
respect
to
the
performance
v
alidation.
The
FMMRNN
model
sho
ws
that
it
yields
a
lo
wer
a
v
erage
relati
v
e
prediction
error
and
Normalized
Mean
Square
Error
compared
to
other
model
[13,
14,
32]
approaches.
5.
CONCLUSION
In
this
approach,
we
presented
a
no
v
el
technique
for
softw
are
reliability
prediction
using
fuzzy
min-max
algorithm
together
with
recurrent
neural
netw
ork
technique.
W
e
presented
e
xperimental
e
vidence
sho
wing
that
fuzzy
max-min
algorithm
with
recurrent
netw
ork
(using
back
propag
ation
learning)
is
gi
ving
the
accurate
result
comparable
to
other
methods.
Softw
are
reliability
prediction
is
used
to
impro
v
e
softw
are
process
control
and
achie
v
e
high
softw
are
reliability
.
This
finding
gi
v
es
a
good
sign
of
prediction
capabilities
of
the
de
v
eloped
fuzzy-neural
netw
orks
model
for
estimating
the
soft
w
are
reliability
.
More
datasets
and
other
types
of
computational
intelligence
and
simulat
ion
tools
need
to
use
for
further
justify
our
findings.
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BIOGRAPHIES
OF
A
UTHORS
Manmath
K
umar
Bhuyan
is
currently
a
Ph.D.
candidate
in
the
Department
of
Computer
Science
and
Engineering
at
Utkal
Uni
v
ersity
,
V
ani
V
ihar
,
INDIA.
M
T
ech
in
Computer
Science
and
Engineering
from
NITTR,
K
olkata.
He
w
ork
ed
with
v
arious
MNC
compan
y
as
mem
ber
in
R&D
group.
He
w
ork
ed
as
an
Asst
prof
in
Computer
science
&
engineering
department
for
more
than
10yrs.
Dur
g
a
Prasad
Mohapatra
recei
v
ed
the
M
E
de
gree
in
computer
science
engineering
in
2000
from
REC
and
the
Ph
D
de
gree
in
Computer
Science
Engineering
in
2005
from
Indian
Institute
of
T
ech-
nology
,
INDIA
.
He
is
an
Associate
Professor
in
the
Department
of
Computer
Science
Engineering
at
National
Insti
tute
of
T
echnology
.
He
has
published
more
than
70
papers
in
the
areas
of
softw
are
engineering,
neural
netw
orks
and
genetic
algorithms.
He
serv
e
a
members
of
T
echnical
Societies
IEEE,
Institution
of
Engineers
(I),
CSI
Srini
v
as
Sethi
is
an
Associate
Professor
in
the
Department
of
Computer
Science
Engineering
in
Indira
Gandhi
Institute
of
engineering
and
T
echnology
.
He
recei
v
ed
the
master
de
gree
in
computer
application
(MCA)
in
1995
from
Berhampur
Uni
v
ersity
,
INDIA,
and
the
Ph
D
de
gree
in
Computer
Science
in
2011
from
Berhampur
Uni
v
ersity
,
INDIA,
He
is
an
Assistant
Professor
in
the
Department
of
Computer
Science
Engineering
&
Application
at
IGIT
Sarang.
He
has
published
mor
e
than
30
papers
in
the
areas
of
softw
are
engineering,
netw
orking,
cloud
computing,
etc.
IJECE
V
ol.
6,
No.
4,
August
2016:
1929
–
1938
Evaluation Warning : The document was created with Spire.PDF for Python.