Page 249 - Pipelines and Risers

222 Chapter I3

where a(.) standard normal distribution function.
is
Two general approaches are available to solve Equation (13.2) namely analytical and
simulation methods respectively.

Analyticul Methods: Analytical methods consist of first- and second-order reliability methods
(FORM and SORM). The advantage of these methods is that they do usually not require
excessively large computing cost. The drawback is that they do not give exact results, but
only approximations that may not always be sufficiently accurate. Details of FORM and
SORM are available from standard textbooks, e.g. Thoft-Christensen and Baker (1982).

Simulation Methods: A Monte Carlo simulation technique is an alternative or complementary
tool for estimation of failure probability. The advantage of this technique is that the methods
are very simple and give solutions, which converge towards exact results when a sufficient
number of simulations are performed. The disadvantage of the simulation methods is that
their computing efficiency is low. Many refined simulation methods have been developed to
improve the efficiency of simulations.

13.3 Uncertainty Measures

13.3.1 General
Failure probability is evaluated based on uncertainties associated with the considered LSF,
which is composed of a set of basic random variables and analysis models. Uncertainty
measures are a critical and fundamental step in reliability analysis. The major steps involved
in the measurement of uncertainty include the following:

Classification of uncertainties,
Selection of distribution functions,
Determination of statistical values of those random variables in the LSF.

13.3.2 Classification of Uncertainties
Uncertainty of a random variable can be measured using a probability distribution function
and statistical values. The major uncertainties considered in this study include the following
(Thoft-Christensen and Baker (1982)):

Physical uncertainty: Caused by random nature of the actual variability of physical quantities,
such as pipe geometry (wall-thickness), etc.

Statistical uncertainty: This is uncertainty due to incomplete information of the variable. It is
a function of the type of distribution function fitted, type of estimation technique applied,
value of the distribution parameters and amount of underlying data. Statistical uncertainty
may further occur due to negligence of systematic variations of the observed variables. This