Probability values, fault tree analysis

For acute releases, the fault tree analysis is a convenient tool for organizing the quantitative data needed for model selection and implementation. The fault tree represents a heirarchy of events that precede the release of concern. This heirarchy grows like the branches of a tree as we track back through one cause built upon another (hence the name, "fault tree"). Each level of the tree identifies each antecedent event, and the branches are characterized by probabilities attached to each causal link in the sequence. The model appiications are needed to describe the environmental consequences of each type of impulsive release of pollutants. Thus, combining the probability of each event with its quantitative consequences supplied by the model, one is led to the expected value of ambient concentrations in the environment. This distribution, in turn, can be used to generate a profile of exposure and risk. 

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 ... 

It was noted in Chapter 15 that the second-order term for fault tree analysis is often not significant when probability values are low. With reliability work, where values typically are... 

Using fiizzy interval analysis, a possibility distribution for the top event probability (chance), 7r(q), is obtained by calculating lower and upper a-cut values of the top event probability (chance) using the corresponding lower and upper a-cut values for the basic event probabilities (chances). The reader is referred to Singer (1990) for further details on the fiizzy set approach to fault tree analysis. 

Chapter 11 of this text discusses the use of fault tree analysis in determining system reliability, failure potential, and even accident cause factors through examination of specific or general fault paths. Additional information on the application and use of probability values in fault tree analysis is also provided in Chapter 11. 

Figure 12.8 Probability values in fault tree analysis.

In this subsection it has been described characterization changes of resources from states defined in 0,1 to state defined in l,m. Probability to be at each state can be obtained from Fault-Tree for state value and m . The third step is to deduce function states from the resource analysis, with more than the two usual binary states. 

Frequency Phase 3 Use Branch Point Estimates to Develop a Ere-quency Estimate for the Accident Scenarios. The analysis team may choose to assign frequency values for initiating events and probability values for the branch points of the event trees without drawing fault tree models. These estimates are based on discussions with operating personnel, review of industrial equipment failure databases, and review of human reliability studies. This allows the team to provide initial estimates of scenario frequency and avoids the effort of the detailed analysis (Frequency Phase 4). In many cases, characterizing a few dominant accident scenarios in a layer of protection analysis will provide adequate frequency information. 

There are many different models that can be used to apply common causes, but the most common (and the one preferred by EC 61508) is the Beta factor (j8) model. This model applies a /J factor between 0 and 1 representing the fraction of the failure of all affected inputs resulting from the common cause. For instance, a fl value of 0.1 implies that 10% of failures where aU inputs fail were in fact the result of a common cause. There are some specialised resources for appropriate CCF values that can be apphed, but fundamentally a sensitivity analysis should be performed to determine how much an effect the CCF has on the top event probability. A large influence would indicate the need for further analysis [see NASA Fault Tree Handbook paragraph 7.2]. 

When the likelihood of an event is known and a probability value has been assigned, then analysis of these events on a fault tree will also yield quantitative results. As cutsets are identified, the probability of occurrence as a result of cutset interactions can be quantified and the associated risk can be more readily evaluated. 

The starting point for all quantitative reliability assessments lies with the determination of values allocated to the primary events. The probability of a certain event occurring is usually derived from either predictive analysis, or relevant experience-based data, combined with assessment techniques such as fault tree analyses. This is illustrated in Fig. 10.4. 

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