Calculation and updating of Common Cause Failure unavailability by using alpha factor model

Abstract

The most lethal role of Common Cause Failures (CCFs), which motivate the experts to investigate it, is the dependent behavior therein contained, which leads to simultaneous failure of the systems. Highly redundant systems are more susceptible to be affected by CCFs and also CCFs have been recognized as the principal contributor in the terrestrial reactor accidents. In the past, plenty of work has been done regarding the calculation of unavailability of different types of systems due to CCFs by using different techniques such as fault tree analysis (FTA). But the qualitative aspects such as human errors, maintenance faults and poor components quality cannot be updated by using FTA as the changes occur. So in order to overcome this problem, multinomial distribution function and its conjugate Dirichlet distribution function has been used as likelihood and prior, respectively, in Bayes theorem to obtain an updated posterior function of the same form as Dirichlet distribution function thus improving the working and monitoring capability of Probabilistic Safety Assessment (PSA). Furthermore, the presented research highlights a mathematical model to estimate system unavailability due to CCF by using alpha factor model. By using this model, we can calculate failure probability (unavailability) of the systems quite accurately through the two parameters αk and Qt. The ease of using the proposed model can be assessed through the brief analysis of a case study of Auxiliary Feed Water System (AFWS). AFWS is used in all designs of Pressurized Water Reactor (PWR). It plays a vital role in maintaining a heat sink by providing feedwater to the steam generators.