Event tree analysis dependence

Chapter 12 discusses the distribution software BETA for preparing event tree analysis from a work processor table. BETA allows the use of binary conditionals so the nodal probabilities in a vertical line are not necessarily equal but depend on preceding events. 

Sequences 6 and D correspond to hazard event RS-1 of the hazard analysis from Appendix 3C. The assessed event frequency per year for hazard event RS-1 was frequency bin III. This agrees well with the Sequence B frequency bin of III in the event tree analysis but not with the Sequence D frequency bin of IV. Sequence D was not considered typical of the overall operation of a radioactive material storage area. The failure to detect an electrical short or overheat and remove power in Sequence D depended on an operator being present Since operators are only present in a radiological material storage area approximately 5% of the time, this operating condition was not assessed as typical. Thus, the event tree analysis confirms the frequency assessment of the hazard analysis. 

There exist different methods like Fault Tree Analysis (FTA), Event Tree Analysis (ETA) and Monte Carlo Simulation (MCS) that can be applied and combined for the purpose of evaluating the frequency and probability of initiating events. However, the MCS can be handled much easier in order to accoimt for bormdary conditions like stochastic dependence, time dependence and physical impact (Hauschild Meyna 2007). The MCS has been apphed successfully for PSA in order to assess the safety of nuclear power plants (Devooght Smidts 1996, Woltereck2001) and especially for taking into account uncertain input data (BfS 2005). 

Dynamic event tree analysis method is a quantifiable risk analysis approach that treats time-dependent evolution of plant hardware states, process variable values, and... 

The initiators are separated into two classes those for which the event iree/fauJt tree analysis is appropriate and those for which it is not. The former are called internal initiators and the latter, external initiators (externalities). If dependencies are accounted for by modifying the branching probabilities of the event tree, both internal and external initiators can be accounted for in the same event tree. 

A dependency analysis determines which systems depend on other systems. This may require iterating the event tree construction to put a support system before the systems affected. 

Identification and quantitative estimation of common-cause failures are general problems in fault tree analysis. Boolean approaches are generally better suited to mathematically handle common-cause failures. The basic assumption is that failures are completely independent events, but in reality dependencies will exist and these are categorized as common cause failures (CCFs). Both qualitative and quantitative techniques can be applied to identify and assess CCFs. An excellent overview of CCF is available (AIChE-CCPS, 2000). 

The growth of a defect into what becomes a fault or a faulty component really depends on many factors, which is predominantly the type of corrosion that is progressing. In the fault-tree analysis context, the fault event of a component is defined as a state transition from the normal state to a faulty state of that component. These state transitions are irreversible, which means that a faulty state does not return to the intended state even if the influences that caused the fault event in the first place disappear. 

Step la This CMA process is performed to verify that AND events (e.g. in the Fault Tree Analysis (FTA) or Dependence Diagrams (DD), or any quahtative probabihty declaration) are truly independent. 

The modelling of the system unavailability is based on the results of the fault tree analysis and the identified minimal cut sets. The simplified equation for the time-dependent system unavailability, for mutually independent basic events, is ... 

In most current PSAs, the analysis of the event sequence is carried out by a combination of event tree and fault tree analysis since this has been empirically found to be the most efficient way of handling the large logical models that are necessary for a nuclear power plant. However, it is possible to carry out the analysis using fault trees or event trees alone, and, for specific event analysis, dynamic time dependent analysis techniqnes can be used. 

The stochastic analysis framework, that has shown its value in financial mathematics (e.g. Glasserman, 2004), is exploited by the TOPAZ methodology to develop Monte Carlo simulation models and appropriate speed-up factors by risk decomposition. The power of these stochastic analysis tools lies in their capability to model and analyse in a proper way the arbitrary stochastic event sequences (including dependent events) and the conditional probabilities of such event sequences in stochastic dynamic processes (Blom et al., 2(X)3c Krystul Blom, 2004). By using these tools from stochastic analysis, a Monte Carlo simulation based risk assessment can mathematically be decomposed into a well-defined sequence of conditional Monte Carlo simulations together with a subsequent composition of the total risk out of these conditional simulation results. The latter composition typically consists of a tree with conditional probabilities to be assessed at the leaves, and nodes which either add or multiply the probabilities coming from the subbranches of that node. Within TOPAZ such a tree is referred to as a collision risk tree (Blom et al., 2001, 2003). 

The event may develop and escalate to a number of different eventual outcomes with a range of consequence severity, depending on a number of intermediate events. Analysis of the likelihood of each outcome is a specialist task, often based on event trees (Figure 5). 

Black Event or factor Not Applicable. Depending upon the nature of the top event, there may be some areas of the comprehensive MORT event tree that simply do not apply to the particular investigation. In this case, the event and/or an entire event block is colored black or simply crossed-out. Although it may be obvious in many instances when a set of events is not applicable, the analyst must truly verify (not assume) that specific events are not contributory to the investigation. Inadvertent elimination of a possible contributing factor could jeopardize the overall analysis process. 

An important concept of fault tree analysis is that all the events and subevents are independent of each other. So for example in the CIRIA 152 fault tree the cause of ventilation cannot be dependent on a factor that also causes ignition (i.e. entry into the cupboard). 

Yuge, T, Ozeki, S., Yanagi, S. 2013. Fault tree analysis considering sequence dependence and repairable input events. Journal of quality in Maintenance Engineering 19(2) 199-214. 

Mahboob Straub (2011). This may be a serious limitation for civil engineering applications. In principle event trees can deal with such dependencies however this requires great care during an analysis as observed by Faber Stewart (2003). Moreover both methods suffer from the difficulty in updating based on new information. Petri Nets provide a powerful platform, but the evaluation often takes basis in Monte Carlo simulations requiring considerable computational demands, Nishijima et al. (2009). These drawbacks can be overcome by the use of Bayesian probabilistic networks with discrete nodes supplemented by decision and utility nodes, Nielsen Jensen (2007). 

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