On some aspects of the fault tree analysis methodology

Aim.  The paper aims to supplement certain aspects of the Fault Tree Analysis (FTA) methodology. Assuming that the input data, namely the failure rates of basic events, are random variables, an uncertainty analysis of the dependability indicator at the top event of the fault tree (FT) is usually performed. However, if the dependability indicator of the FT top event is random, then the decision on whether the requirements of the technical specifications (TS) are met should not be made by simply comparing the calculated indicator with the requirement. One of the goals in this situation is to construct decision-making criteria for the fulfillment of TS requirements using statistical hypothesis testing methods. If the uncertainty of the input data is modeled using a lognormal distribution, the choice of the error factor (EF) is often unjustified. The second objective of this paper is to provide a justification for the choice of EF. The ultimate goal is to introduce additional sensitivity measures in situations where the reliability indicators of interest for the FT top event are not the failure probability or unavailability, but the failure flow or mean time between failures.  Methods.  Classical methods of probability theory, mathematical statistics, and mathematical reliability theory are used.  Conclusions.  The paper shows that decision-making on the fulfillment (or nonfulfillment) of TS requirements, in cases where the input data (failure rates) have statistical uncertainty, should be based on statistical hypothesis testing methods, namely hypothesis testing using confidence intervals. Furthermore, in case of a lognormal distribution of failure rates, a justification for the choice of the error factor (EF) is provided. If the TS requirements concern the failure flow or the mean time between failures, and the sensitivity of the FT top event dependability indicator with respect to basic events is being investigated, then special sensitivity measures must be used.

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