L-moments and Bayesian inference for probabilistic risk assessment with scarce samples that include extremes

In structural applications, uncertainties are unavoidable and play a significant role in risk assessment. Probabilistic risk assessment (PRA) is used to determine the level of risk associated with complex systems such as nuclear power plants, space missions, earthquakes, tornado and floods. The Bayesian inference is often regarded as an effective framework for analysing probabilistic risk and the prior probability and likelihood function are inferred from available data. The traditional approaches usually approximate likelihood functions using conventional moments (C-moments). If data are insufficient, approximations are inadequate, leading to inaccurate conclusions. Therefore in order to determine the amount of risk, it is desirable to develop a PRA framework that is distribution independent and less sensitive or insensitive to extremes in the scarce data. In this paper, L-moments are proposed to characterise or approximate likelihood functions in the Bayesian inference. L-moment ratio diagram is employed to select the appropriate distribution of conditional probabilities. The Bayesian approach is paired with L-moment approach to perform PRA and uncertainty quantification. The efficacy of the proposed approach is demonstrated on three engineering examples. In assessing risk from few samples in the presence of extremes, L-moments based Bayesian inference for PRA framework significantly outperformed its C-moment counterpart.