Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 114

i i i

P ()= t P () t P ( . t [4.56]

1cr/ CE l 1cont/ CE l 1unst/ CE l

k k k

The conditional probability of a leak through a through-wall defect in the
i i-th element at time τ when when a calculated event CE k took place is

i i



i



P ()= t P ()1- t P (). t

[4.57]
The conditional probability of a leak through a through-wall defect
with the length in the range

 

1leak/ CE l 1cont/ CE l 1unst/CE l

k k k

i i i

l l ≤ t≤ is determined on the basis of () l ,

j l 1 +1

equtions [4.55] and [4.53]

l

j + 1

] }

{

i



i i i



i

∫



i

 

i i

P l l ≤ t≤ () l = P () p l t () 1 t − F l () dl t .

    

1leak/ CE j l j +1 1cont/ CE l d l cr l

k k

i
j

l

[4.58]

The volume of metal of the composite unit is divided into Q reference
volumes. In the presence of n defects in the reference volume the conditional
probability of formation of through-wall defects or large-scale destruction
of the i i-th element at time τ l , when a calculated event CE k took place 57,61 :

n Q

i



i



P ()=1- t lP − () t , [4.59]

 

n CE / l l/ CE l

k k

where

P t is the conditional probability of the formation of through-
walldefects or large-scale destruction in the presence of a defect in the i -th
element at time τ l when a calculated event CE k takes place.
The conditional probability of failure (formation of through-wall defects
or large-scale destruction) of i i-th element of the structure when a calculated
event CE k takes place for calculated defects is defined as follows:

i

()

1/ CE l

k

∑

i i i

P ()= t P () ( , t P t [4.60]

￿ ￿ ￿ ￿ ￿

CE l n CE / l n l

k k

n

where

P t is the conditional probability of formation of a through-
wall defect or large-scale destruction in the i i-th element at time τ l when a
calculated event CE k takes place;

i
n CE

()

/ l

k

P t is the probability of presence in the
reference volume of the i i-th element of n defects defined by, for example,
the Poisson law.
Determination of the total probability of failure (formation of through-
wall defects or large-scale destruction) of an element of the composite
unit is reduced to the summation of products of conditional probability of
failure by the probability of occurrence of the appropriate calculated events:

i
nl

()

N

PC

∑

i i

P () t= P () P , t

(4.61)

l n CE / l CE

k k

k = 1

where N CE is the number of calculated events CD k .