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116 Reliability and Maintainability of In-Service Pipelines

variance reduction techniques (e.g., importance sampling, Latin hypercube, and
directional simulation) can be employed. However, in cases that the main empha-
sis is on serviceability failure, which can be estimated by a crude Monte Carlo
simulation with very good accuracy within a relatively short computation time,
such techniques are not necessary to be used (Val and Chernin, 2009).
Importance sampling is a variance reduction technique that can be used in the
Monte Carlo method (Melchers, 1999). The idea behind importance sampling is
that certain values of the input random variables in a simulation have more
impact on the parameter being estimated than others. If these “important” values
are emphasized by sampling more frequently, then the estimator variance can be
reduced. Hence, the basic methodology in importance sampling is to choose a dis-
tribution which “encourages” the important values. The use of “biased” distribu-
tions will result in a biased estimator if it is applied directly in the simulation.
However, the simulation outputs are weighted to correct use of the biased distri-
bution, and this ensures that the new importance sampling estimator is unbiased.
The fundamental issue in implementing importance sampling simulation is the
choice of the biased distribution which encourages the important regions of the
input variables. Choosing or designing a good biased distribution is the “art” of
importance sampling. The rewards for a good distribution can be significant run-
time savings; the penalty for a bad distribution can be longer run times than for a
general Monte Carlo simulation without importance sampling.
The details of the Monte Carlo method including sampling techniques can be
found in Ditlevsen and Madesn (1996), Melchers (1999), and Rubinstein and
Kroese (2008).

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