A Comparison of Different Monte Carlo Approaches to RAMS Analysis (PSAM-0355)


Monte Carlo simulation for reliability and risk analyses of complex systems, such as nuclear power plants, is a recognized powerful approach. In spite of the considerable computer power available at present, the study of high reliable systems often requires the use of variance reduction techniques, as far as the crude Monte Carlo turns out to be inefficient. Different approaches to Monte Carlo simulation, which are equivalent in the crude Monte Carlo, yield different results when reduction techniques are applied. These differences are highlighted analytically and numerically in the paper.

The approaches considered are:

• the direct approach;

• the indirect approach;

• the new direct approach;

• the system failure function approach.

The last two approaches have been developed by the authors and are briefly resumed in the paper.

A simple 4-components system is considered, for the sake of comparison, and the investigation is limited to the case of exponential biasing and exponential distributions.

It is worth to notice that the unreliability estimate and the variance estimate have to be studied as functions of the biasing parameter, in order to understand the role that the biasing plays.

The results of the Monte Carlo runs are presented in the following modes:

• the unreliability estimates and the variance estimates of all four approaches;

• the direct approach versus the new direct approach;

• the indirect approach versus the system failure function approach.

Firstly, the results indicate that the system failure function approach allows to achieve impressive performances, since its variance is considerably smaller than the variances associated with the other three approaches considered in the comparison.

Furthermore, we point out that the variance of the new direct approach and the variance of the indirect approach are almost identical (overlapped, if plotted). As a matter of fact, also the weight spectra of these two approaches are practically the same. In other words, the new direct approach is statistically equivalent to the indirect one, while the standard direct approach seems to be slightly different.

  • Summary/Abstract
  • Nomenclature and Acronyms
  • Case Study
  • The Traditional Approaches
  • The System Failure Function Approach
  • Numerical Results and Comparisons
  • Conclusions
  • Acknowledgments
  • References

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