Physico–statistical approach: Procedures using the defect-free model of structural material - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 93

deviation s a ; υ sa - the coefficient of variation of stress amplitude.
Using arguments similar to the previous case leads to:

M 1 − n

u = = − ,

[3.17]

P

s

υ +υ

2

n

2

M

s s

2

− lg

=ss is the ratio of the average stress amplitude in the compo-
nent to the average value of the endurance limit,

n / where

a − lg

υ

is the coefficient of

s− lg

variation of the endurance limit.
Using the known quantile u p , the failure probability P is calculated from
normal distribution tables.
For other distribution laws failure probability can be determined from
the relation:

y

∞

( )

 ∫

∫

P P z y =  −<= 0  f y f z dzdy ( ) () ,

[3.18]



y

0 0

where y and z can be substituted by the variables from [3.17] for cyclic
loading.
In non-stationary random cyclic loading the problem is more complicated.
A solution to this problem based on the linear hypothesis of damage
cummulation is described in Ref. 55.
The task of taking fatigue damage into account is solved in the
framework of the Automated control system of residual life (SAKOR) 5 ,
installed at a number of nuclear power plants with VVER-1000 reactors.
The advantage of the above-described methods for determining the
relative probability of failure is their simplicity and clear physical meaning
of the models. Their drawback is that they neglect the real state of the
structure, particularly its defectiveness.

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