Assessing system reliability through binary decision diagrams using bayesian techniques.

Binary Decision Diagrams (BDDs) have been shown to be efficient for the numerical evaluation of the reliability of complex systems. They achieve exact results where Fault Tree Analysis could generally produce only bo unds. In this paper the approach to systems evaluation using a Bayesian method in co njunction with BDDs is explored. The advantages of the approach are discussed with r espect to both efficiency and the ability to deal with dependency within the system i n a natural manner. As an illustration a simple pump configuration is conside red which features a dependency. The results demonstrate both the flexibility of the approach and the ease of dealing with the additional complexity of dependency. Introduction The use of Binary Decision Diagrams (BDDs) have man y advantages for the analysis of complex reliability structures over Fault Tree A nalysis, see Andrews (2001) and Beeson and Andrews (2003). In section two there is a brief review of the major features of BDDs. A particular strength of using a BDD is the estimation of the failure probability of a system since BDDs provide exact calculation methods whereas in the past Fault Tree Analysis (FTA) has generally only allowed bounds. Another aspect of the BDD is its ability to explore depende ncy within the system such as that existing due to standby redundancy. This paper explores the use of the BDD model in a B ayesian evaluation of the system. Whilst there are many issues to address, the main a spect will be the approach to the analysis of a system’s reliability on the assumptio n hat there already exists data on the specific component’s failure times and elicited information on prior beliefs about these elements. The third section of the paper wil l explore the general concepts. These will include the use of BDDs to explore depen dency within the system, both at a component level but also through the data. To provide greater insight into the approach taken a simple example will be considered of a pump system with associated pressur relief valves. Obviously some will appreciate that the model chosen has resonance within safety critical systems. It will be assumed that information regarding the fail ure time distribution for the valves used is well established but that there is relative ly little known about the pumps involved. The specific system will be described al ong with the data available for analysis.