Environmental Engineering Reference
In-Depth Information
5.2.1 Mathematical approximation of the detection of
discontinuities, depending on their size
V.N. Volchenko
75
derived the following equation for the curve of detection
of defects
W
= 1 - exp λ (
x
-
x
0
),
[5.3]
where
x
0
is the boundary smallest detectable defect size depending on the
sensitivity of the inspection method; λ is a constant.
A. Zimmer used the equation of the same type. However, he used it for
the probability of missing the defect
P
P
= ε + (1 - ε) exp (-γ
a
),
[5.4]
where ε and γ are constants.
Constant ε indicated that for any type of inspection there is
always a probability ε of missing the defect as a result of operator's
mistake. According to Ref. 86, the value ε = 0.005 was determined on the
basis of a survey of a large number of experts - NDT inspectors.
In Ref. 89, etc. the probability of defect detection was described using
the equation
W
= (1-ε) - (1-ε) exp [-α (
a
-
a
0
)], for
a
>
a
0
,
[5.5]
W
≡ 0, at
a
<
a
0
,
where ε is a constant characterising the fundamental limitations of this
inspection method; α is a constant characterising the detectability of defects
depending on their size;
a
0
is constant related to the sensitivity of the
inspection method.
Given the finite size of the vessel walls and pressure pipelines,
commensurate with the size of defects, the constant ε can be omitted, and
the influence of the human factor or of instrumentation and methodological
shortcomings will be taken into account by the coefficient α. In this case,
equation [5.5] transforms into equation [5.3].
The effect on detectability of two linear dimensions of the defect: the
depth in the direction of the surface
a
and length
c
, was described in Ref.
90 by the equation
W
= 1 - exp [-α(
a
-
a
0
) /
a
/c]. [5.6]
Equation [5.6] is valid in the region
a
≥
a
0
,
c
≥
a.
There are also other equations for describing the detection of defects
29
but the curves obtained for these dependences are close to the curves
obtained by the above-mentioned equations.
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