Optimisation of non-destructive testing - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 241

 

Pk ()

D D > 1 − − yPk () t − yPk () ; t

[7.7]

  i 0 r r r i

t

 

r

t
−> t

dP
dk

y

i i

.

[7.8]

( D y + )

r 0 r

For class 2 equipment:

t
−= t

( +)
( +)

Dy

dP
dk

i 0i

[7.9]

D y

r 0 r

or if the inspection is combined with refuelling,

dP
dk

t y

− =

i

.
( +)

i

[7.10]

t D y

r 0 r

For class 3 equipment, the condition of disadvantageous inspection takes
the form:

dP
dk

t ( +) Dy

− <

i 0i

[7.11]

t ( +) D y

r 0 r

or if the inspection is combined with refuelling,

dP
dk

t y

− <

i i

.

[7.12]
The above equations include the probability of failure P . Since failure
may occur by different mechanisms (fatigue, stress corrosion cracking, etc.)
analysis using the formulae [7.6]-[7.12] should be performed for every
possible failure mechanism. In this case, the conditions for optimising
inspection on the basis of the the parameter of inspection frequency can
be rewritten as:

t ( D y + )

r 0 r

￿ ￿ ￿ ￿ ￿

dP >t D Y +

−

i

= t

i i 0 i i

,

[7.13]

dk < D Y +

i r i 0 r i

where the index i stands for a specific failure mechanism (damage).
Equations [7.3]-[7.6], [7.8]-[7.13] are the conditions of optimumity
of operational inspection with respect to the time interval between the
inspections (or inspection frequency). They combine together such features
of an integrated system of operational inspection as the quality of inspection
means and methods, the properties and state of the metal, the level of
reliability (strength) of equipment, the cost and time characteristics of
inspection and maintenance of equipment, and these equations make