Contribution to Temporal Fault Tree Analysis without Modularization and Transformation into the State Space

• Published in: arXiv.org
• Main Author: Schilling, Simon J
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.05.2015
• Subjects: Boolean algebra; Fault tree analysis; Modelling; Modularization; Operators (mathematics); Qualitative analysis; Reliability analysis; Sequences; State space models; Temporal logic; Transformations (mathematics)

Background: Fault tree analysis (FTA) is a well established method for qualitative as well as probabilistic reliability and safety analysis. As a Boolean model it does not support modelling of dynamic effects like sequence dependencies between fault events. This work describes a method that allows consideration of sequence dependencies without transformations into state-space. Concept: The new temporal fault tree analysis (TFTA) described in this work extends the Boolean FTA. The TFTA is based on a new temporal logic which adds a concept of time to the Boolean logic and algebra. This allows modelling of temporal relationships between events using two new temporal operators (PAND and SAND). With a set of temporal logic rules, a given temporal term may be simplified to its temporal disjunctive normal form (TDNF) which is similar to the Boolean DNF but includes event sequencies. In TDNF the top event's temporal system function may be reduced to a list of minimal cutset sequences (MCSS). These allow qualitative analyses similar to Boolean cutset analysis in normal FTA. Furthermore the TFTA may also be used for probabilistic analyses without using state-space models. Results: One significant aspect of the new TFTA described in this work is the possibility to take sequence dependencies into account for qualitative and probabilistic analyses without state-space transformations. Among others, this allows for modelling of event sequencies at all levels within a fault tree, a real qualitative analysis similar to the FTA's cutset analysis, and quantification of sequence dependencies within the same model.