Civil Engineering Reference
In-Depth Information
Table 15.1
RV model parameters
RV 1
RV 2
RV 3
Parameters
COV
TF
=
0.3
COV
TF
=
0.6
COV
TF
=
0.9
Shape (
η
)
13.1111
4.7778
3.2346
Scale (
δ
)
0.1651
0.5294
0.8950
Table 15.2
Results for the combined damage: shocks
+
progressive
deterioration
Case
Model
μ
TF
(years)
σ
TF
(years)
COV
TF
1
Shocks only
106.0
36.0
0.34
2
g
p
1
,
g
p
2
,
g
p
3
(*)
50.0
3
Shocks
+
g
p
3
42.1
4.2
0.1
4
Shocks
+
g
p
2
38.2
12.1
0.32
5
Shocks
+
g
p
1
33.9
6.7
0.20
6
RV 1
+
Shocks
32.4
7.6
0.24
7
RV 2
+
Shocks
29.9
9.6
0.30
8
RV 3
+
Shocks
27.9
9.6
0.34
* Deterministic cases.
The combined effect of shocks and the various graceful deterioration
models was compared by evaluating the mean, standard deviation and COV
of
the time to failure
; the results are summarized in Table 15.2. It can be fi rst
observed in Table 15.2 that the results of the models are organized accord-
ing to the MTTF. The fi rst two rows show the basic cases; i.e., shocks only
and deterministic degradation only. Note also that the combined effect of
shocks and the deterministic graceful deterioration models (cases 3-5)
leads to larger mean time to failure than the case of shocks and RV progres-
sive deterioration (cases 6-8). When comparing cases 3-5 it is interesting
to observe that the mean time to failure exhibits the following behavior:
MTTF
5
MTTF
3
. The main reason for this is that the deteriora-
tion rate in, for instance,
g
p
3
(case 3) is rather small at the beginning of the
process compared with the rate of the rate of
g
p
1
(case 5). By the time it
starts growing faster, the system is already close to failure. This situation
may change as the size of shocks become smaller; in this case the progres-
sive deteriorating function will dominate the process.
In cases 6-8, it is noticed that the MTTF increases as the COV of the
time to failure of the progressive deterioration model (Table 15.1) decreases.
This means that larger variability produces smaller MTTF; this is, the failure
<
MTTF
4
<
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