Nowadays technical system’s safety is a significant issue due to widespread usage of technological processes in modern society, increasing consequences of facilities' failures and their increased importance. Over the last thirty years the probabilistic safety analyses have been increasingly applied in technical engineering practice. Various failure modes of system of concern are mathematically and explicitly modelled by means of fault tree structure. Statistical independence of basic events, from which the fault tree is built, is not acceptable for an event category referred to as common cause failures. These are the failures which simultaneously affect two or more redundant components of the same type, and have the same underlying root cause. These are the causes that represent the residual, sometimes difficult to catch, dependence among the components, whose mechanisms are not explicitly built into the facilities' logical models. The doctoral thesis deals with dependent failures and their mechanisms, displays common cause failure phenomenology and presents their mathematical models. Furthermore, the thesis describes operational history of common cause failures and the strategies for implementation of periodical testing for standby components. The concept of so called event impact vector was introduced and the procedure for their development, based on operating experience from the source system, was defined. Per that procedure, each source impact vector is specialised, modified to reflect the likelihood of occurrence of the event in the plant of interest. The doctoral thesis proposes and elaborates a method for common cause failure model parameters estimation, for two in practice most often used mathematical models, multiple Greek letter model and alpha-factor model, in the form of both point estimates and probability distributions, for staggered and non-staggered testing scheme. Uncertainty distributions are estimated by Bayesian approach based on operating history. The method has been applied in demonstration example, on selected piece of standby equipment in nuclear power plant for a specific failure mode. In addition, the method has been implemented on the level of whole nuclear power plant PSA model and selected results were presented. In principle, analytical approach proposed in this thesis is applicable to any technical system. The doctoral thesis ends up with the most important observations and considerations as an outcome of the research, method development, and its implementation in concrete PSA model, and points to some areas in which the further research activities can be focused.