The paper presents a critical review of the state-of-the-art in probabilistic assessment of pressure vessel and piping reliability. First the differences in assessing the reliability directly from historical failure data and indirectly by a probabilistic analysis of the failure phenomenon are discussed and the advantages and disadvantages are pointed out. The rest of the paper deals with the latter approach of reliability assessment. Methods of probabilistic reliability assessment are described and major projects where these methods are applied for pressure vessel and piping problems are discussed. An extensive list of references is provided at the end of the paper.

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