Probabilistic fault tree

From technical papers, there are several other types of FTA automation are also found. Probabilistic fault tree (PROFAT) is one approach where simulation algorithm ASH has been utilized. For the complex cases where there is unavailability of reliability data for the number of specific equipment, generic probabilistic data are used. Also, probabilistic data for human error are used. However, fuzzy approach in this regard is also found (especially for human error). Instead of specific values for human error hybrid approach with fuzzy logic is quite effective. In fuzzy logic, set failure rates are defined in linguistic way, which is more realistic. For human robot, offshore applications FTA with fuzzy approach produce better result in automating the process. 

The toolset takes as input a model written in the SLIM language, and a set of property patterns [17,20]. It generates several artifacts as output, among them traces resulting either from simulation of the SLIM specification or as counterexample for properties not satisfied by the specification (probabilistic) Fault Trees and FMEA tables diagnosability and performabihty measures. 

HAZAN, on the other hand, is a process to assess the probability of occurrence of such accidents and to evaluate quantitatively the consequences of such happenings, together with value judgments, in order to decide the level of acceptable risk. HAZAN is also sometimes referred to as Probabilistic Risk Assessment (PRA) and its study uses the well-established techniques of Fault Tree Analysis and/or Event Tree Analysis ... 

Safety. It is becoming increasingly common to conduct quantitative assessments of process risks by failure modes and effects, fault tree, or other analytical alternatives. Thus, the probability of an accident times the corresponding potential loss is a cost factor which, although probabilistic. 

The conceptual system selected in step 3 is designed. Reliability and maintainability of this design are assessed. Various methodologies, such as design review, failure mode and effect analysis, fault tree analysis, and probabilistic design approach, can be applied at this step. Reliability is a design parameter and must be incorporated in the system at the design step. 

Toward the end of the Second World War, systems techniques such as fault tree analysis were introduced in order to predict the reliability and performance of military airplanes and missiles. The use of such techniques led to the formalization of the concept of probabilistic risk assessment (PRA). The publication of the Reactor Safety Study (NRC, 1975)—often referred to as the Rasmussen Report after the name of principal author, or by its subtitle WASH 1400—demonstrated the use of such techniques in the fledgling nuclear power business. Although WASH 1400 has since been supplanted by more advanced analysis techniques, the report was groundbreaking in its approach to system safety. 

The standards allow any internationally accepted methodology for the purpose of performing the probabilistic calculations and the most common methods are described in this book -- simplified equation, fault trees and Markov models. 

The main tool of a probabilistic analysis is fault tree analysis. It is based on deriving deductively the failure of a system from the failure of its sub-systems and sub-sub-systems and so forth. The failure of the latter is in turn derived from the failure of its components. The result of this analysis is represented by the so-called fault tree, which shows the logical relationships between the failure of a system and that of its components. In general, only two states of the system and its components are admitted functioning and failure. These states occur with a certain probability. The probabUity of failure of the system then results from a... 

As already mentioned the fault tree represents the logical relations between the primary events (in what follows often denoted by component failures for the sake of simplicity) and the undesired (unwanted or top) event (in what follows often denoted by system failure for the sake of simplicity). The relations represented by the fault tree are deterministic. We arrive at probabilistic statements only if probabilities are assigned to the component failures. 

Chu TL, Apostolakis G (1980) Methods for probabilistic analysis of noncoherent fault trees. IEEE Trans Reliab R-29(5) 354-360... 

The probabilistic analysis of a plant is usually performed by the construction of event trees, for any single group of similar initiating events, and of fault trees, for any single system or component whose fault probability is important for the study of the various accident sequences. 

In order to calculate the fault probability of the component under study on the basis of its fault tree, it is possible to proceed directly combining the various probabilities of the events represented in the tree. This method, however, except for rather simple cases, can be rather tiresome and doesn t highlight the most important factors. The method more generally used, instead, is based on the use of Boolean algebra (the algebra of binary systems Is and Os) and on the fact that a correspondence exists between its results, when applied to a fault tree, and the results of a direct probabilistic analysis, mentioned above. 

It is necessary to add here that a remarkable freedom exists in the proportion in which event trees and fault trees can be used in a specific probabilistic analysis. Indeed, large event trees and small fault trees can be chosen (or vice versa) with all the intermediate grades. Here, reference has been made to the most common way, which uses event trees up to the primary safety systems, and fault trees for the determination of the failure probabilities of the primary systems, also on the basis of the failure probabilities of their support systems. 

The Fault tree analysis is the most known tool in the family of probabilistic analysis of safety. There are others probabilistic analysis, but the fault tree mechanic s is very simple and easy to use. 

Preliminarily a suitable risk analysis tool for explosives manufacturing would be any probabilistic method, like the fault tree, whereas with explosives no one want to deal with an unexpected explosion. So, it is always fair control the frequency of occurrence. 

Instrumentation and Control (I C) systems are very often subject of probabilistic examination either within separate structural reliability analysis or Probabilistic Safety Assessment of a whole technological complex (e.g. Nuclear Power Plant). Use of programmable components in the design of these systems represents a challenge and utilizes the methods, which have been developed for components with a different behaviour. The typical method used for above mentioned examination is Fault Tree Analysis (FTA) (Vesely et al., 1981). The way of software faults modelling within Fault Trees vary a lot between particular models and there is no generally accepted modelling technique. 

The experience is that for I C systems approval the probabilistic goals are set and needs to be fulfilled. Reasonable consideration of software reliabihty is desired. This could lead to sometimes senseless way of involvement of software faults into Fault Trees and their quantification. The sensitivity analysis of system tolerance to software faults and their common cause aspects is much more meaningful and could reveal the weak points of the I C design. Even if this analysis is mostly quahtative unless we have applicable methodology to estimate particular basic events prob-abftistic parameters, the Fault Tree Analysis Method represents a good base to demonstrate a sound fault tolerant design. 

The lack of data to support claims for failure rates is an issue which is widely investigated by data uncertainty analyses. For example, Hauptmanns, 2008 compares the use of reliability data stemming from different sources on probabilistic safety calculations, and tends to prove that results do not differ substantially. Wang, 2004 discusses and identifies the inputs that may lead to SIL estimation changes. Propagation of error, Monte Carlo, and Bayesian methods (Guerin, 2003) are quite common. Fuzzy set theory is also often used to handle data uncertainties, especially into fault tree analyses (Tanaka, 1983, Singer, 1990). Other approaches are based on evidence, possibihty, and interval analyses (Helton, 2004). 

Dutuit, Y, Innal, R, Rauzy, A. and Signoret, J.-P. 2008. Probabilistic assessments in relationship with safety integrity levels by using Fault Trees, Reliab. Eng. Syst. Safety vol. 93 Issue 12, Dec. 2008. 

Handling epistemic uncertainties in fault tree analysis by probabilistic and possibilistic approaches... 

In the context of interest here, namely that of fault tree analysis, Lindley Singpurwalla (1986) present a formal probabilistic (Bayesian) procedure for the use of expert opinions, assuming expert input in the form of mean and standard deviation of lognormally distributed failure rates. In Tanaka et al. (1983), Liang Wang (1991) and Huang et al. (2001), basic event probabilities (chances) are treated as trapezoidal fuzzy numbers and the extension principle is applied to compute the probability (chance) of occurrence of the top event. In order to deal with repeated basic events in fault tree analysis. Soman Misra (1993) provide a simple method for fuzzy fault tree analysis based on the a-cut method, also known as resolution identity. Another approach to fuzzy fault tree analysis based on the treatment of the system state as a fuzzy variable has been proposed by Huang et al. (2004). 

Human reliability models (HRA-trees) They depict the human actions considered in the event- and fault-trees and finally provide probabilistic assessments for the failure / success of the actions. 

Failures of human actions are embedded either as basic events in the fault-tree or as function events in the event-tree models of a PSA. Corresponding probabilistic assessments are obtained from the application of HRA (Human Reliability Analysis)-trees. 

But how to quantify the uncertainty on the concept of the fault-tree and event-tree models How realistic are the probabilistic assessments of the consequences of accident sequences which are derived from these static models Of course, the models may be appropriate, if details of the timing or of process conditions are not relevant. But, can this assumption be held for the complex dynamics of incident and accident scenarios ... 

To quantify this kind of uncertainty, a comparison of the results of the conventional fault-tree and event-tree analysis with the results of a probabilistic dynamics method might be useful. Probabilistic dynamics methods are able to cover the spectrum of event sequences which may evolve in the course of time and to achieve a more realistic probabilistic safety assessment. Moreover, the application of these methods generally reduces the analyst-to-analyst variability, because it requires less expert judgment. 

Usually the Probabilistic Safety Analysis is performed for a varying extent of initiating events (internal and external initiators). In order to assess for example the impact of external initiators (explosion e.g.), the frequency of occurrence has to be considered. Usually methods like Fault Tree Analysis (FTA), Event Tree Analysis (ETA) and Monte Carlo Simulation (MCS) are applied and combined forthe purpose of evaluating the frequency and probability of initiating events. 

Hazard Identification Earher discussion covered hazard identification and some methods for it. Hazard identification may include engineering failure assessment, which consists of evaluating the reliability of specific segments of a plant operation and determining probabilistic results. Fault-tree analysis (see Chapter 36) is a common form of engineering failure assessment. 

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