It is important to take the uncertainty of the inspection method into account when performing
the updating on the basis of the inspection finding. This is the equivalent to the likelihood
discussed previously.
The inspection uncertainty may appropriately be modelled in terms of the Probability of
Detection (POD) and the Probability of Sizing (POS). The probability of detection models the
event that the inspection method misses a defect of a given size, where as the POS models the
measurement uncertainty given a crack has been found. Here the POD is modelled by an
exponential distribution with parameters PODPOD 1 mm.
It is assumed that the steel bar is inspected at year 6 and that no crack is found. This gives
basis to update the probability of failure as:
(()0()
(()0() 0)
(() 0)crit
critPa an an POD
Pa an an POD
Pan POD0)
(12.24)
which may readily be evaluated by FORM/SORM analysis.
The updated probability of failure given a no-find result of the first inspection is calculated as
is seen in Figure 12.14. It is seen that the updated probability of failure will exceed the
acceptable level again after 11 years of service. The updating can then be repeated again
assuming a no-finding result at the performed inspection. This scheme is may be followed
until the end of the service life and is a simple way to establish an inspection plan which
satisfies a given requirement to the safety of the considered structure. Note that the inspection
events i.e. the POD’s at subsequent inspections shall be modelled by new independent random
variables. If at some time a crack is found the inspection plan is readily updated accordingly
by conditioning on the observed crack length, taking into account the sizing uncertainty.
Optimal planning of inspections can appropriately be performed within the framework of
decision analysis. Numerous publications are available on the subject see e.g. Madsen et al.
(1986), Goyet et al. (1994) and Faber (1995).