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This Technical Report aims to close the gap between the state-of-the-art and the application of probabilistic calculations for the safety systems of the petroleum, petrochemical and natural gas industries. It provides guidelines for reliability and safety system analysts and the oil and gas industries to:• understand the correct meaning of the definitions used in the reliability field;• identify— the safety systems which may be concerned,— the difficulties encountered when dealing with reliability modelling and calculation of safety systems,— the relevant probabilistic parameters to be considered;• be informed of effective solutions overcoming the encountered difficulties and allowing to undertake the calculations of relevant probabilistic parameters;• obtain sufficient knowledge of the principles and framework (e.g. the modelling power and limitations) of the well-established approaches currently used in the reliability field:— analytical formulae;[1][2][13]— Boolean:• reliability block diagrams;[4]• fault trees;[5]— sequential: event trees,[8] cause consequence diagrams[10] and LOPA;[9]— Markovian;[6]— Petri nets;[7]• obtain sufficient knowledge of the principles of probabilistic evaluations:— analytical calculations (e.g. performed on Boolean or Markovian models);[1][2][3]— and Monte Carlo simulation (e.g. performed on Petri nets[7]);• select an approach suitable with the complexity of the related safety system and the reliability study which is undertaken;• handle safety and dependability (e.g. for production assurance purpose, see 3.1.1) within the same reliability framework.