Probabilistic analysis of safety: Increasing the reliability and safety of nuclear power plant components - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 210

quality, reliability and product safety (curve 1 in Fig. 6.9). The regulatory
curve of the state of the product characterises the probability of the
existence of defects in the range from allowable manufacturing defects
[χ] man to critical size defects χ cr , including permissible defects in operation
[χ] ser .
The curve is based on the assumption that in the logarithmic scale of
the coordinates the relationship between the logarithm of probability and
the characteristic size of the defect is almost linear. This assumption is
confirmed by experiment 89 . The curve is plotted using the fixed points of
this curve: the points that characterise the probability of a defect of the
critical characteristic size and the point which characterises the probability
of occurrence of the defect of the characteristic size allowed in operation.
The product is inspected by any selected NDT method. The results of
inspection are used for repair (removal) of detected defects.
The inspection results are represented as a histogram in coordinates
N det - χ, where N det is the number of detected defects in inspection, χ is the
characteristic defect size (usually, χ is represented either by the linear size
of the defect or combination of the linear size of the defect, of the defect
area, or the defect volume).
The resultant histogram is approximate by the equation

{ }

( )

A −

n

 

( ) ( )

N c = c 1 − −η 1 exp −α c−c −η ,

  
where A, n , α, η are the constants determined from the condition of
maximum approximation of the equation N obn (χ) to the inspection results
presented in the form of a histogram; χ 0 is the minimum characteristic size
of the defect that can be detected.
The initial defectiveness N in = f (χ) is determined by the formula:

det 0

n
NA

−
= c

or N = A n exp( −c ).

in in

￿ ￿ ￿ ￿ ￿

The initial defectiveness is divided into reliable part χ ≤ χ d , and the
probabilistic part χ > χ d , where χ is the characteristic size of the defect, χ d
is the size of defects on the border between reliable and probabilistic parts.
The size of the defect χ d is determined from the equation

c max

( )

∫

f c c= d 1,

c

d

where χ max is the maximum possible size of the defects in the given product.
Th probabilistic part of the curve of the initial defect characterises the
probability of the existence of defects of a given size in the product.
The residual defectiveness N res = φ(χ) is defined as the difference
between the initial defectiveness N in and the number of defects detected in