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software, we should establish its reliability model according to characteristics of real-
time and multitask. By analyzing on characteristics of such kind of software, neural
network was used to model and research its reliability in module manner. The paper is
organized as follows. Section 2 gives evaluation model of real-time multitasking
system. Neural network models to evaluate reliability of general software and real-
time multitasking software are compared in section 3. Specific example is used to test
performance of proposed real-time multitasking software reliability model based on
neural network and section 5 concludes our work.
2 Real-Time Multitasking Evaluation Model
At any time
t
, actual running time
t
exe
of the task
A
i
is
t
,
t
≤
t
⎧
i
1
unit
⎪
⎨
t
=
t
+
t
=
t
,
t
<
t
≤
t
.
(1)
exe
i
1
i
2
i
unit
rel
⎪
⎩
t
+
p
(
t
−
t
),
t
>
t
i
i
rel
rel
We can see that actual running time
t
i
of
A
i
is used to estimate parameter
B
xi
and
b
i
.
At any time
t
(
t
>
t
rel
) after software was delivered, the task
A
i
may not run in time
interval [
t
i
,
t
rel
] and [(1-
P
i
)(
t
-
t
rel
),
t
], so the system will not fail, and then
t
can not be
used to estimate reliability of
A
i
directly. Based on the model, we can determine mean
of failure number
m
i
(
t
), failure intensity
Φ
i
(
t
) and running time ratio
P
i
. As to task set
S
={
A
1
,
A
2
,…,
A
n
} at
t
, there is
n
∑
=
m
(
t
)
=
m
i
t
(
)
(2)
i
1
and
n
∑
=
Φ
(
t
)
=
Φ
i
t
(
)
.
(3)
i
1
In some time interval [
t
s
,
t
]
, the Mean Time Before Failure (MTBF) is
(
t
≥
t
)
s
rel
t
−
t
s
MTBF
=
.
n
t
(4)
∫
∑
=
Φ
(
t
)
i
t
s
i
1
It we use
T
to represent the time from time 0 to software failure, the software reli-
ability
R
(
t
) is
n
t
t
∫
∑
∫
R
(
t
)
=
exp(
−
Φ
(
t
)
dt
)
=
exp(
−
Φ
(
t
)
dt
)
.
(5)
i
0
0
i
=
1
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