Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 109

- frequency of inspection of metal (τ ins );
- requirements for the quality of metal: the permissible defect size
(permissible depth ( a i per ) and permissible length ( l i per ), permissible number
of defects ( k i rep );
- effectiveness of the means of inspection of metal characterised by
the dependence of the probability of detecting defects on the size of the
defects ( P ins ( a i ), P ins ( l i ));
- The duration of inspection of metal and subsequent repair (Δτ ins ).
In this case, adjustment of the size distribution and number of defects
in the metal structure due to metal inspection and subsequent repair is
different in the initial stage of operation (e.g. at the stage of preoperational
monitoring) and in subsequent stages of operation (e.g. during in-service
inspection). At the initial stage of operation during testing of metal defects
are detected and repaired in accordance with the effectiveness of inspection.
In this case, the missed defects remain in the metal of the structure. This
means that the following situation forms in analysis at the initial stage of
operation 57 :
- initial distributions of the depth and length of the calculated defect
are the distributions plotted on the basis of the defects identified in testing
of metal p o ( a i ), p o ( l i );
- projected distributions of the depth and length of the calculated defect
are determined on the basis of missed defects by means of probability of
detection, for example, in accordance with Ref. 57 the predicted depth
distribution of calculated defects was determined as follows:

i

paC ()

i i i

pa ( )=

o i

at aa < ;

d i per

pa ()

ins



i



pa () i i i i

pa ()=

o

− pa C a a () at ≥ ,

 

d o i per

i

pa ()

 

ins

￿ ￿ ￿ ￿ ￿

where

i i

a a

i i

per

pa ()

per

pa ()

∫

i

∫

i

C =

o

da +

o

da .

[4.40]

i i i i

pa () pa a ()p()

0 ins 0 ins o

The mathematical expectation of the number of defects in the i i-th element
of the structure in accordance with Ref. 57 is

v

i

( t ) = Cv ×t

i

( ),

[4.41]

d o i oo

i v t is the mathematical expectation of the number of projected
defects in the i i-th element after inspection of metal t the initial period of
operation of the facilities. The graphical layout of correction of the depth
distribution of defects in inspection of metal at the initial period of operation
of the facilities in shown in Fig. 4.3.

o ()

where