Contribution toTemporal Fault Tree Analysiswithout Modularization and Transformation into the State SpaceOriginal german title:Beitrag zur dynamischen Fehlerbaumanalyse ohne Modulbildungund zustandsbasierte Erweiterungen

Background Fault tree analysis (FTA) is a well established method for qualitative as well as probabilistic reliability and safety analysis. Fault trees are Boolean models and thus do not support modelling of dynamic effects like sequence dependencies between fault events. In order to overcome this limitations, dynamic fault tree methods were defined previously. Most of these are based on complete or partial transformation of the fault tree model into state-space-models like Markov chains or Petri nets. These state-space-models generally suffer from exponential state explosion which imposes the necessity to define small “dynamic” modules which need to be independet from the rest of the model. Moreover, these state-space-models lack some of the FTA’s benefits like logical simplification of complex system functions or a real cutset analysis. Because of these deficiencies, a method is needed that allows consideration of sequence dependencies without transformations into state-space. This work describes such a new approach. Concept The new temporal fault tree analysis (TFTA) described in this work extends the Boolean FTA in order to take sequence dependencies into account. 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 Boolean operators (AND “∧”, OR “∨”, NOT “¬”) and 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. Probabilities and rates of MCSS may be calculated without using state-space models. Again the procedure is similar to the normal FTA: top event failure probabilities and rates are derived from the failure probabilities and rates of the basic events including sequence dependencies. Realisation Starting with the Boolean FTA this work describes a new notation and new rules for a temporal logic. This temporal logic aims at transforming temporal terms into a TDNF, which then may be transformed further into a form where all terms are mutually exclusive. This form is well suited for quantification, too. Several examples are provided which explain each step in detail. Furthermore, there are two probabilistic approximation methods described, which allow a significant reduction of the calculatory effort. 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.