Page 94 - Reliability and Maintainability of In service Pipelines

Methods for Structural Reliability Analysis 83

The uncertainty modeled by stochastic variables can be divided into the fol-
lowing groups:
Physical uncertainty: (or inherent uncertainty) Is related to the natural ran-
domness of a quantity, for example, the uncertainty in the yield stress due to
production variability.
Measurement uncertainty: Is the uncertainty caused by imperfect measure-
ments of, for example, a geometrical quantity.
Statistical uncertainty: Is due to limited sample sizes of observed quantities.
Model uncertainty: Is the uncertainty related to imperfect knowledge or ideali-
zations of the mathematical models used or uncertainty related to the choice
of probability distribution types for the stochastic variables.

All the above types of uncertainty can usually be treated by the reliability
methods. Another type of uncertainty which is not covered by these methods is
gross errors or human errors. These types of errors can be defined as deviation of
an event or process from acceptable engineering practice.
Generally, methods to measure the reliability of a pipeline can be divided in
four groups, see Madsen et al. (1986):
Level I methods: The uncertain parameters are modeled by one characteristic
value, as, for example, in codes of practice based on the partial safety factor
concept.
Level II methods: The uncertain parameters are modeled by the mean values and
the standard deviations, and by the correlation coefficients between the stochastic
variables. The stochastic variables are implicitly assumed to be normally distrib-
uted. The reliability index method is an example of a level II method.
Level III methods: The uncertain quantities are modeled by their joint distribution
functions. The probability of failure is estimated as a measure of the reliability.
Level IV methods: In these methods the consequences (cost) of failure are
also taken into account and the risk (consequence multiplied by the probability
of failure) is used as a measure of the reliability. In this way different designs
can be compared on an economic basis taking into account uncertainty, costs,
and benefits.
Level I methods can, e.g., be calibrated using level II methods, level II meth-
ods can be calibrated using level III methods, etc.
Several techniques can be used to estimate the reliability for levels II and III
methods, including the following methods:

Simulation techniques: Samples of the stochastic variables are generated and
the relative number of samples corresponding to failure is used to estimate the
probability of failure. The simulation techniques are different in the way the