Environmental Engineering Reference
In-Depth Information
Reliability is determined as a function of the probability of detecting
defects
P
dd
(χ) for each of the characteristic defect size
P
dd
(χ) =
N
det.ts
(χ) /
N
emb.ts
(χ),
where
N
det.ts
is the number of defects found in inspection of the test sample;
N
emb.ts
is the number of defects embedded in preparation of the sample.
The inspection results are used to plot the curves of probability of
detection of defects for the given product by the given NDT method,
depending on the characteristic size of defects. The curve of the probability
of detecting defects on the size of defects
a
and
c
(any defect in the material
can be conservatively described by an ellipse with semiaxes
a
and
c
) can
be approximated by the equation which describes most most accurately the
experimental results, for example
[
]
P
= − −η
1
(1
) exp
−α
(
aacc
a
−
)(
−
)
−η
;
dd
NDT
0
0
P
= − −η
1
(1
) exp
−α
(
aa
c
−
)
−η
;
dd
NDT
0
[
]
P
= − −η
1
(1
) exp
−α
(
c−c −η
)
,
dd
NDT
0
where α
NDT
is the NDT reliability coefficient which characterises the
increase in the detectability of defects, depending on its size; η is a constant
characterising the detection limit of inspection by this method for an
arbitrary large size of the defect; if the product is small, then this value
can be ignored by adjusting the value α
NDT
; χ is the characteristic size of
the defect, for example, its area; χ
0
is the minimum characteristic size of
the defect;
a
0
,
c
0
are the minimum sizes of defects available for detection
by NDT.
This is followed by inspection of the product, and the test results are
presented in the form of a histogram in the 'characteristic size of the defect
χ - the number of identified defects of the given size
N
det.prod.
' coordinates.
Initial defectiveness
N
in
is defined as the ratio
N
det.prod
/
P
dd
(χ); the
resulting histograms are approximated by the equation of the type
N
in
=
A
χ
exp (-
n
χ
χ) or
N
in
=
A
χ
χ
-
n
χ
or
N
in
=
A
a
χ
-
n
a
, or
N
in
=
A
a,c
(
a
2
,c
)
-
n
a,c
or
N
in
=
A
F
F
-n
F
or
N
in
=
A
-
n
a
ρ(
c
)
or
1
−
n
2
2
N Aa
=
exp (
cc Dc
−
)
/ 2
( ) ,
in
ac
,
2
π
D
where
a, c
are the linear dimensions of the defect, ρ
c
is the distribution
function of
c
, for example, a normal distribution,
F
is the area of the defect,
n, A, D
,
c
¯ are the coefficients, chosen from the condition of maximal
pproximation of the analytical curve to the experimental data, in this case
c
¯
is the average value of
c
and
D
is dispersion.
Search WWH ::
Custom Search