Environmental Engineering Reference
In-Depth Information
b
+
3
T
a
(
LT
+
)
a
q
= −
1
exp
−l
+
−
−
0
2
(
bbb T bbb
++ +
1)(
2)(
3)
(
++ +
1)(
2)(
3)
b
+
2
a
L
a
d
b
+
1
−
L
+
.
[2.21]
It is clear that the use of such cumbersome dependence makes the analysis
of initial data and calculations of PSA very difficult.
In some studies
42-44
the authors considered cases of expansion of the
linear model or the Weibull model to simulate the mixed flow competing
failures (risks concurrent model), i.e. random failures and failures caused
by ageing.
So, for the linear model NUREG 5052
43
suggests using the following
relationship:
(
bbb Tbb
++ +
1)(
2)(
3)
(
++
1)(
2)
Ld
+
λ (
t
) = λ
0
at 0 <
t
<
t
0
and
λ (
t
) = λ
0
[1 + β (
t
2
t
0
)] at
t
>
t
0
[2.22]
In this interpretation of the linear model λ
0
is the intensity of random
failures and is constant in time,
t
0
is the time at which the ageing process
begin to affect the reliability; b is a coefficient
By analogy with the linear model, the Weibull model can be represented
as follows:
λ (
t
) = λ
0
at 0 <
t
<
t
0
and
λ (
t
) = λ
0
(
t
/
t
0
)
β
at
t
>
t
0.
[2.23]
The unavailability values are calculated with the following assumptions:
• periodic testing does not affect the age of equipment ('bad as old');
• complete restoration after failure ('good as new');
• failure can be detected with probability
P
= 1 during periodic testing
and with probability
P
= 0 at any other time;
• the duration of testing and restoration is negligible compared with the
test interval
T
.
Unavailability of components is calculated at time
t
with
nT
<
t
<
(
n
+1)
T
,
n
= 0, 1,...,
N
,
t
/
T
<
N
.
[
]
q kT t
(
,
)
=− l−
1
exp
(
t nT
) ,
if
(
n k T t
− <
)
;
0
l
0
b
+
1
b
q kT t
(
,
)
= −
1
exp
−l t−
(
nT
)
−
(
t kT
−
)
−t
,
0
(
b
+t
1)
b
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