Page 293 - Pipelines and Risers
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266 Chapter I5
The following uncertainties are introduced (Bai and Song (1997)):
Model uncertainty, XM. Model uncertainty is introduced for the criteria to account for
modeling and methodology uncertainties. It reflects a general confidence in the design criteria
for a real life in-situ scenario. The model uncertainty is calibrated from the test results listed
below. A normal distribution is applied to fit this uncertainty.
Uncertainty for pressure, Xp. The characteristic value of the normalized pressure Xp is
obtained by substituting safety factors, characteristic values of the other parameters into the
design equation. In general, the annual maximum operating pressure is higher than the
nominal operating pressure. This is reflected by the mean bias in Xp. A Gumbel distribution is
used.
Uncertaintyforflow stress, Xf. The Xf mainly reflects the material property. Uncertainty of Xf
is largely dependent of the material grade. A log-normal distribution is assumed to fit the data
in the existing database.
Uncertainty for dent depth, XD. The uncertainty in the dent depth is associated with
inspection. A normal distribution is assumed for XD based on judgement.
Uncertainty for crack length, XL. It is similar to the discussion of XD. Normal distribution is
used for XL.
Uncertainty for geometry function, XY. Considering the uncertainties in geometry function
estimation, a log-normal distribution is applied for XY.
Uncertainty for pipe wall-thickness, Xt. The uncertainty in pipe wall-thickness is considered
by bias Xt following a normal distribution.
The statistical values for the above biases are given in Table 15.2 as below.
15.4.3 Reliability Analysis Methods
Generally, LSF is introduced and denoted by g(Z). Failure occurs when g(Z)SO. For a given
LSF g(Z), the probability of failure is defined as:
PF(t) = p[g(z) 01 (15.34)
The results can also be expressed in terms of a reliability index p, which is uniquely related to
the failure probability by:
P(t) = -W(PF(t)) = a-q- P F ( t)) (15.35)
where:
