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Remarks on the statistical aspects of the safety analysis

We investigate the statistical methods applied throughout safety analysis of complex systems. The tolerance interval method implemented in the widely utilized 0.95|0.95 methodology is analyzed. We point out a remarkable weakness of the tolerance interval method concerning the principle of repeatability. It is proved that repeating twice the procedure, the probability that the second maximum will be larger/smaller than the first one is 50\%. This statement is not surprising, it holds for any random variable with continuous distribution function. In order to demonstrate the undesirable consequences of the tolerance interval method in the decision making, the results of the analysis of an elementary example are discussed. Instead of the tolerance interval method, we suggest another method based on the sign test which has more encouraging features, especially in the case of several output variables. The problematic aspects of the method are also discussed. Finally, we suggest a simple test case which is able to reveal if the tolerance interval method would not be capable of determining the risky states of the system, when there are only a few of them. If there are many, then the method may not explore each one in the analysis.