For risk analyses, it is frequently necessary to evaluate the consequences of low-probability, high-consequence failures (i.e., failures that occur with a very low frequency, but have a significant impact on the system). Because the models for such systems are often complex (and hence need significant computer time to simulate), it can be difficult to use the conventional Monte Carlo approach to evaluate these low-probability, high-consequence failures, as this may require excessive numbers of realizations.
To facilitate these type of analyses, GoldSim allows you to utilize an importance sampling algorithm to modify the conventional Monte Carlo approach so that high-consequence, low-probability failures are sampled with an enhanced frequency. That is, importance sampling serves to increase the rate of occurrence of the failure. During the analysis of the results that are generated, the biasing effects of the importance sampling are reversed. The result is high-resolution development of the high-consequence, low-probability "tails" of the consequences (resulting from low-probability failures), without paying a high computational price.
Importance sampling for Reliability elements is specified by selecting the checkbox for Use Importance Sampling for this element. The algorithm that is used is discussed in detail in Appendix B of the GoldSim User’s Guide.
Four points regarding importance sampling of failures for Reliability elements should be noted:
•Importance sampling is only applied to the first occurrence of the failure. The increased sampling frequency is not applied to subsequent occurrences within the same realization.
•Importance sampling of Reliability elements should only be used to represent failures that are rare. As used here, “rare” indicates a failure that would not be represented adequately without enhanced sampling. As a general rule of thumb, a failure event will be adequately sampled if the product of the number of realizations and the expected number of failures over the course of a single realization is at least 10 (this would indicate that the failure would occur on average at least 10 times if that many realizations were executed). For example, if the rate of failure was once every thousand years, and the simulation was run for 10 years, one could expect 0.01 failures per realization. If 100 realizations were run, the total expected number of failures (over all realizations) would therefore be 1. This is a rare failure and importance sampling should be applied (or more realizations should be run).
•There is a limit to the effectiveness of importance sampling for extremely rare failures, such that in some cases, it may become necessary to increase the number of realizations in order to effectively represent the failure. In particular, the degree of biasing for low probability failures that GoldSim can provide is (at most) equal to the number of realizations. For example, if the failure rate was once every 100,000 hours, and the simulation was run for 10 hours, one could expect 1e-4 failures per realization. If 100 realizations were run, the total expected number of failures (over all realizations) would therefore be 0.01. This is a rare failure and importance sampling should be applied. However, importance sampling could only increase the total number of failures (over all realizations) by a factor of 100 (the number of realizations) to 1 (which would still provide inadequate representation). If 1000 realizations were run, the total expected number of failures (over all realizations) without importance sampling would be 0.1, but importance sampling would improve it by a factor of 1000.
•You should use importance sampling sparingly (i.e., only for those elements that really need it). This is because, as stated above, the degree of biasing for low probability failures that GoldSim can provide is at most equal to the number of realizations, and the actual biasing provided decreases with the number of elements for which importance sampling is applied.