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Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)

Michael G. Stamatelatos
Michael G. Stamatelatos
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Harold S. Blackman
Harold S. Blackman
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ASME Press
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Monte Carlo simulation of an accident risk model of a complex safety critical operation provides valuable feedback to the decision makers that are responsible for the safety of such operation. By definition, such a Monte Carlo simulation model differs from reality at various points and levels. Hence, the feedback to the decision makers should include an assessment of the combined effect of these differences in terms of bias and uncertainty at the simulated risk level.

In literature the assessment of risk bias and uncertainty due to differences in parameter values has received most attention, e.g. Morgan and Henrion (1990) [1], Kumamoto and Henley (1996) [2]. Obviously, there are many other differences between model and reality than due to parameter value differences only.

The paper presents a structured approach for the assessment of bias and uncertainty in Monte Carlo simulation of accident risk due to differences in parameter values as well as differences that fall beyond the parameter level. For the assessment of differences in parameter values we follow the first-order differential analysis of bias and uncertainty in the accident risk under log-normal assumptions, e.g. [1], and combine bias and uncertainty estimates of parameter values with log-normal risk sensitivities for these parameter variations. Because the number of parameter values may be large, this assessment is performed in two phases. In the first phase an initial bias and uncertainty assessment of parameter values is performed largely using expert knowledge. The second phase focuses on the parameter values that have the largest effect on the risk level; for these, statistical data is collected and sensitivity analysis is performed by running dedicated Monte Carlo simulations.

For the assessment of bias due to other differences than parameter value differences, the paper combines the two structured approaches by Zio and Apostolakis (1996) [3]. One of their approaches assumes alternate hypotheses for the risk case considered, develops an alternate model for each alternate hypothesis, assesses the risk level for each alternate model, and elicits experts on the probability that each alternate model is correct. Their second approach uses an adjustment factor to compensate for differences between model and reality, and elicits experts for the estimation of this adjustment factor. The novelty in this paper is to combine, per non-parameter difference, one alternate hypothesis with one adjustment factor, and to evaluate the bias through the following two estimates for each non-parameter difference:

1. the probability that there is a difference, i.e. the alternate hypothesis is correct; and

2. the conditional risk bias given that the alternate hypothesis is correct, i.e. the conditional adjustment factor.

These estimates per non-parameter difference are evaluated by teams of safety experts and operational experts, and then combined into an overall bias estimate for all non-parameter differences. The estimation of these two factors by experts appears to work quite naturally, especially since the estimation of the conditional risk bias is supported by the risk sensitivity knowledge for each of the model parameters stemming from assessment of the parameter value differences. The novel structured bias and uncertainty assessment approach is illustrated for a Monte Carlo simulation based accident risk assessment for an air traffic operation example.

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