  We analyze safety problems of complex systems using the methods of
mathematical statistics for testing the output variables of a code simulating
the operation of the system under consideration when the input variables are
uncertain. We have defined a black box model of the code and derived formulas
to calculate the number of runs needed for a given confidence level to achieve
a preassigned measure of safety. In order to show the capabilities of different
statistical methods, firstly we have investigated one output variable with
unknown and known distribution functions. The general conclusion has been that
the different methods do not bring about large differences in the number of
runs needed to ensure a given level of safety. Analyzing the case of several
statistically dependent output variables we have arrived at the conclusion that
the testing of the variables separately may lead to false, safety related
decisions with unforseen consequences. We have advised two methods: the sign
test and the tolerance interval methods for testing more than one mutually
dependent output variables.
