Negating a Generalized Cut Sequence: Bridging the Gap Between Dynamic Fault Trees Quantification and Sum of Disjoint Products Methods

Abstract

Dynamic fault trees (DFTs) are powerful tools to model industrial systems having dynamic failure mechanisms, such as sequence‐ and function‐dependent failure behaviors. Yet for large and complex DFTs, their quantitative analyses are still of great challenges. Up to now, many researchers have presented several approaches to deal with this problem, and among which, the sum of disjoint products (SDP) methods, such as dynamic binary decision tree, sequential binary decision diagram (SBDD), and improved SBDD, have proven to be an efficient way. In SDP methods, negating a generalized cut sequence is an unavoidable task. Yet, for a complex cut sequence expression where normal, cold and warm spares basic events coexist, its negating operation is still difficult and needs to be further studied. In this paper, based on De Morgan theorem, improved explicit formulas for negating a generalized cut sequences are presented. The new concept of universal set of basic event and its operating rules are proposed to deduce the simplified expressions of general enforcing occurring cut sequences and warm spares occurring cut sequences. To validate the presented approaches, a typical system DFT is analyzed. The results indicate the reasonability and effectiveness of the improved negating formulas. Copyright © 2016 John Wiley & Sons, Ltd.

An adapted component-connection method for building SBDD encoding a dynamic fault tree

“…Coarse formulas for negating general SEs were first proposed. 43 When basic events in SEs are all normal, that is, the system does not contain any spare components (i.e. cold and warm spares), the coarse formulas are correct and can be easily implemented.…”

“…Analyzing methods for a DFT. 43 (: e 2 ) + (: e 3 ) + e 1 !e 3 !e 2 + e 2 !e 3 !e 1 + e 2 !e 1 !e 3 + e 3 !e 2 !e 1 + e 3 !e 1 !e 2 , where '':'' is a negation operator. If an SE is placed at a higher level of SBDD, it means that more chances of SE should be involved in operation with other SEs.…”

A Hierarchical Approach for Dynamic Fault Trees Solution Through Semi-Markov Process

“…The method was appropriate for both reparable and nonreparable systems. In 2017 the research work of [50] has been extended and published in [57]. The research has covered spare and sequence gates through De Morgan theorem, and for negating a generalized cut sequences, they have improved explicit formula.…”