This abstract presents a method for computing Probabillity of Failure (PoF) namely the method integrating the so-called "Bayesian approach". PoF along with the assessment of the consequences of failure are required when it comes to assessing "risks". More and more frequently, in modern industries, the trend is to rely on the use of risk-based approaches for the scheduling of the inspection of static pressure vessels. Equipment PoF is the main driver for scheduling periodical inspections. Within the Bayesian approach, it is expected that the performance of inspection, provided effective techniques are used, increases the knowledge we have on the equipment condition and help us gain confidence in the planning of future inspections. The paper thus describes the theoretical principles yielding to the calculation of the PoF prior to conduct an inspection and after its performance. PoF calculation within a Risk-Based Inspection (RBI) planning is one of the aspects covered by the EU project called "RIMAP" (Risk-Based Inspection and Maintenance Procedure). PoF calculation using Bayes theorem is the cornerstone of the RBI methodology described in American Petroleum Institute reference "API 581". (C) 2004 Elsevier Ltd. All rights reserved.