Environmental Engineering Reference
In-Depth Information
5.2.2 Quantitative assessment of residual defectiveness
If the function of initial defectiveness
N
in
(
a
, c) is known, and the
distribution function of the defects detected in inspection is
N
det
(
a
, c), the
residual defectiveness
N
res
can be defined as
N
res
(
a
, c) =
N
in
(
a
, c) -
N
det
(
a
, c).
[5.7]
The number of detected defects depends on the initial defectiveness
N
in
(
a
,c) and on the reliability of inspection that can be characterised by the
probability of detection of defects
W
(
a
, c).
N
det
(
a
, c) =
N
in
(
a
, c)
W
(
a
, c).
[5.8]
Substituting the last expression in equation [5.8] leads to
N
res
(
a
, c) =
N
in
(
a
, c)-
N
in
(
a
, c)
W
(
a
, c)
[5.9]
or
N
res
(
a
, c) =
N
in
(
a
, c) [1-
W
(
a
, c)].
[5.10]
Equation [5.10] is valid for the region where
W
> 0. This region is
determined by the minimum values of discontinuities
a
0
,
c
0
, which can be
detected by this inspection method. In the region (
a, c
) < (
a
0
,
c
0
)
W
≡ 0,
N
res
≡
N
in
.
[5.11]
In a particular case it can be assumed that
N
in
=
A
/
a
n
, and the expression
for
W
is [5.3], then
A
[
]
N a
( )
=
exp
(
aa
−α −
) .
[5.12]
res
0
n
a
In repeated inspection by the same method, the number of detected
defects is equal to
II
I
NaNaWa
()
=
() ()
[5.13]
det
det
or
A
(
)
[
[
]
]
N a
II
det
( )
=
exp 1
(
aa
−α−
)
exp
(
aa
−α−
[5.14]
) ;
0
0
a
n
I
I
II
NaNaNa
()
=
()
();
[5.15]
res
res
det
[
]
N a N
I
(
)
=
I
(1
exp 1
−
(
aa
−α −
[5.16]
) .
ost
ost
0
Converting formula [5.16] for the
k
-th ispection gives
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