Minimal cutsets-based reduction approach for the use of binary decision diagrams on probabilistic safety assessment fault tree models

Abstract

Binary decision diagrams (BDDs) are a well-known alternative to the minimal cutsets (MCS) approach to assess Boolean reliability models. While the application of fault tree analysis can be considered to be consolidated, its application to the event trees involved in the probabilistic safety assessment (PSA) studies of the nuclear industry require extended efforts. For many real PSA models the full conversion procedure remains out of reach in terms of computational resources owing to their size, non-coherency, redundancy, and complexity. A potential solution to improve the quality of assessment methods is to design hybrid algorithms that combine the information derived from the calculation of MCS with the BDD methodology.As a first step to develop this new approach, this paper explores various procedures and strategies based on this principle. First, a method is presented to reduce the fault tree model by considering only the domain of the most relevant MCS of the system prior to the BDD conversion and the impact on the final probability of the model is analysed. Second, several ordering heuristics derived from the MCS and the structural information of the model are proposed and compared, both in terms of their general performance and their sensitivity to the initial rewriting of the model. This preliminary study is applied on a set of fault tree models belonging to a real PSA study. The results obtained lead to some promising conclusions: it is shown that the topological information proves to be essential for the ordering and conversion procedures; it is also revealed that the rewriting strategies should be considered when designing variable ordering methods; and, finally, it is demonstrated that the reduction procedure provides a faster computation process without affecting the final probability. The long-term objective, which has motivated this work, is to apply this reduction procedure to quantify sequences of linked fault trees, both static and dynamic, a task for which further work is required. Downloaded from Proc. IMechE Vol. 223 Part O: J. Risk and Reliability JRR259 JRR259 Proc. IMechE Vol. 223 Part O: J. Risk and Reliability MCS-based reduction approach for the use of BDDs *OM denotes BDD computation out of memory. JRR259 Proc. IMechE Vol. 223 Part O: J. Risk and Reliability MCS-based reduction approach for the use of BDDs

The extended living probabilistic safety assessment

“…Other algorithms differ mostly in how to handle the basic events within the qualitative evaluation of PSA, which is performed via Boolean algebra. 25 The difficulty is that the problems are too complex to be analytically solved, so the approximations are needed. The details are not repeated here because they are presented in the literature, 14,23 where the special importance needs to be placed on understanding what is neglected at approximations and what are the implications.…”

Combining different binary decision diagram techniques for solving models with multiple failure states

“…In order to reach this aim the technique of BDD [2,3], are used to control the combinatorial explosion. The widely known BDDs are often used in the domain of reliability analysis [4][5][6][7] to avoid the combinatorial explosion. Multiple variations of BDDs exist.…”

A reduction approach to improve the quantification of linked fault trees through binary decision diagrams

“…In particular, it can be applied to each fault tree model appearing in the heading of the event tree sequences, and thus it can be integrated in the incremental approach. Additionally, the topological information available, essential for an efficient BDD conversion [27], can be kept.…”