Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 99

by the formula:

i i i ni −

[4.18]
where P ( t ) is the probability of failure of one of heat exchanger pipes over
time interval t , assumed to be the same for a group of heat exchanger pipes
and defined by [4.18], and C n i is binomial coefficient defined as
!

P t C Pt ( ) = [ ( )] [1 − Pt ( )] ,

n n

n

C

i
n

= . [4.19]

ini !( − )!

In this case, the total likelihood of leaks or large-scale destruction in n
heat exchanger pipes is

n

= ∑

i

P P . [4.20]

n n

i =1

Reliability indices of pipes are determined on the basis on the failure
rate and transition to the limiting state. The probability and rate of large-
scale destruction (limiting state) and of formation of leaks (failure) are
related as follows:

dP t dt ( )/

l ( )= t .

[4.21]

1 − Pt ()

The calculations were carried out to estimate the probability of formation
of continuous cracks and, consequently, the occurrence of leaks, as well as
the probability of large-scale destruction for different variants of setting
the probability of detecting defects and the accuracy of their size. The
permissibility of the investigated variants is assessed by the reliability
criterion.

4.2.2 Development of methodology based on MAVR-1.1
program

￿ ￿ ￿ ￿ ￿

The development of a probabilistic methodology described in section 4.2.1
led to a more sophisticated and efficient method for analysis of the reliability
of equipment and pipelines of the reactor installation 56,58-60 .
Key provisions of this technology are as follows:
- the rate of of failures and limiting states associated with the
propagation of defects in metal components and piping under pressure in
the primary and secondary circuits are determined using the probabilistic
methods of fracture mechanics;
- reliability (reliability, durability, availability coefficient) of equipment
and pipelines under pressure of the primary and secondary circuits, defined
by failure rate and limiting state, including the failure rates obtained on the
basis of propagation of defects in the metal of elements;