Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 113

condition of calculated events CE k ;
- the probability of formation of through-wall defects and large-scale
destruction of an element, taking into account the probability of occurrence
of calculated events;
- complete probability of formation of through-wall defects and large-
scale of destruction of the structure.
When analyzing the formation of through-wall defects, three reasons for
their occurrence are considered:
- corrosion-mechanical nucleation of new defects;
- corrosion fatigue growth of surface and subsurface defects;
- critical growth of surface and subsurface defects. In this case, the
conditional probability of the formation of through-wall defects in the
i i-th element at time τ, when the calculated event CE k takes place due to
corrosion-mechanical nucleation and corrosion-fatigue defect growth, is:

∞

i

∫

i i

[4.52]

p ( )= t p a t [ ( )] , da

1/ cy CE 1 d 1

k

s

and that of critical growth of the defect is

s

∫

P

i

( )= t p a

i

t [ ( )] F a 

i

t  ( ) da

i

,

[4.53]

 

1 ck CE / 1 a 1 cr 1

k

0

i
Fa t is the distribution of critical defects for the i i-th element of
the structure at the time τ l , defined for each area of failure on the basis of
the relevant critical characteristics for the formation of through-wall defects.
The conditional probability of formation of a through-wall which takes
into account three reasons for its formation is:

where [ ( )]

cr 1

t t t−   [4.54]
The through-wall defect formed can be either stable or unstable, i.e. it
can continue to grow and lead to large-scale destruction. The conditional
probability of the resulting defect being unstable and can lead to large-
scale destruction is

p

i

()= p

i

()+ p

i

()1  p

i

(), 

1cont / CE l 1/ CE l 1cy/ CE l 1cont/CE l

2 k k k

￿ ￿ ￿ ￿ ￿

2 π R

i

∫

 

i i



i

p () t= p l () F l t () dl , t

[4.55]

  

1unst/ CE 1 d 1 cr 1

k

0

where

  is the distribution function of the critical defect length
for the i i-th element of the structure at the time τ l , defined for each area
of destruction on the basis of the relevant critical features for large-scale
destruction.
If the probability of formation of a through-wall defect and the
probability of its propagation to large-scale failure are known, then the
conditional probability of large-scale destruction in the presence of a single
defect in the i i-th element at time τ l , when a calculated event CE k took place,
is determined as follows



i



Fl

cr ()

l