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A Bayesian network is applied in this contribution in order to assess the risks of a selected production unit in a fossil power station. A general framework for the risk assessment of production units of a power station is presented first by implementing statistical methods and Bayesian networks. Special emphasis is given to the input data consisting of failure rates which are obtained on the basis of recorded data and expert judgements. The consequences of failure are divided into economical and human (societal): economic consequences include outages of key technological devices, societal consequences cover potential injuries and fatalities. Probabilistic risk assessment methods are applied to the selected production unit of a power station. The influence of the uncertainties in the considered technical parameters on the availability of the unit is assessed and the acceptance of the calculated availability represented through the mean value and the standard deviation is discussed. Societal risks given in terms of weighted injuries and fatalities are obtained and respective risk acceptance criteria are presented. Uncertainties affecting the risks are discussed. It appears that the proposed framework provides a valuable assessment of the influence individual devices and their components on availability and societal risk. For that purpose the used methodology, intentionally simplified for operational applications, includes important factors affecting risks of production units. It is concluded that Bayesian networks are a transparent method for the probabilistic risk assessment of complex technological systems. The results of the performed analyses can be easily updated when additional information becomes available as illustrated in characteristic examples.