Fault Tree Quantification

A very useful way of demonstrating how your safety system operates is through a success tree. The success tree will demonstrate the must succeed events. At times, this can be a very poignant method of demonstrating how difficult it will be to meet an exceedingly success-oriented project. 

The fault tree is drawn, and then the Boolean equations and minimal cut sets are derived for the top event. Probability estimates can be generated from hardware failure data, human error estimation, maintenance frequency, etc. Probability estimates are then assigned to the events. Be sure to take into consideration uncertainty limits to your failure data. Through the laws of probability, combine the 

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Appendix III of this report provides a detailed description of the reliability data used in event tree and fault tree quantification. Because of its extensive operating experience and the uniqueness of the BRP design, BRP plant-specific data was used whenever possible. Plant-specific data sources included plant maintenance orders, control room log books, surveillance tests, LERs, event reports, deviation reports, plant review committee meeting minutes, and USNRC correspondence. The plant-specific data used spanned the period from 1970 to 1979. Data before 1970 did not include maintenance orders or surveillance tests and therefore were excluded. The plant-specific data collected for BRP is presented in detail in Appendix XIII. Table III-4 summarizes 30 plant-specific component failure rates and Table 11-06 contains plant-specific maintenance unavailabilities for 20 components. These tables are a summary of the BRP component failure and maintenance outages. 

Results of fault tree quantification for top event GTOP. 

The results from the proposed system fault tree quantification analysis are shown in Table 3, where ( ds-sg denotes the unavailability of the system used for SBO mitigation, while Qads-rv denotes the unavailability of the system used for Large LOCA mitigation. 

A fault tree may either stand alone or be coupled to an event tree to quantif" bability. The top event in either case is the abjective of performing the analysis. If tht is the reliability of a system under specific conditions - then that is the top event. If it is to qua iify a node of an event tree the top event title is that of that particular node subject to the condi ons imposed by the preceding modes. 

VIEW is the quantification module. All minimal cutsets are stored in the speciiic libraries for the fault trees, supercomponents and sequences. VIEW recalculates the point estimates. It computes and displays the Fussel-Vesely importance, risk increase and risk reduction measures. 

The Systems Module constructs and displays fault trees using EASYFLOW which aic read automatically to generate minimal cutsets that can be transferred, for solution, to SETS. CAFT A. or IRRAS and then transferred to RISKMAN for point estimates and uncertainty analysi,s using Monte Carlo simulations or Latin hypercube. Uncertainty analysis is performed on the systems lev el using a probability quantification model and using Monte Carlo simulations from unavailability distributions. 

PSA Model Development Tools in the CAFTA Workstation include an event Wee developer, fault tree editor, quantification tools, cutset editor, and automated sequence eiiiio ... 

Potential accident scenarios and flood locations were identified from plant drawings and tlic RHR system fault tree that identifies the equipment and support needed for RHR system operation. The equipment location was correlated with flood areas with consideration for plant features which may impede or divert the flow. The flood scenarios identify the effect on systems required to prevent core damage. Quantification accounts for the rate of rise of the flood relative to the critical level in each specific plant area. The time available for any recovery action is calculated from tiic volume and the flow rate. 

If the results of the qualitative analysis are to be used as a starting-point for quantification, they need to be represented in an appropriate form. The form of representation can be a fault tree, as shown in Figure 5.2, or an event tree (see Bellamy et al., 1986). The event tree has traditionally been used to model simple tasks at the level of individual task steps, for example in the THERP (Technique for Human Error Rate Prediction) method for human reliability... 

INTEGRATION WITH HARDWARE ANALYSIS. The error probabilities obtained from the quantification procedure are incorporated in the overall system fault trees and event trees. 

The fault tree cited in literature for this process is shown in Fig. 26 (Battelle, 1985). Notice the similarity between Figs. 26 and 25, particularly in the structure of the two trees, and recognize that as a result of quantitative analysis. Fig. 26 has an and-gate as its top-level gate. More importantly, recognize that without complete quantification of the root causes, the fault tree given in Figure 26 may be incomplete. 

After the serious hazards have been identified with a HAZOP study or some other type of qualitative approach, a quantitative examination should be performed. Hazard quantification or hazard analysis (HAZAN) involves the estimation of the expected frequencies or probabilities of events with adverse or potentially adverse consequences. It logically ties together historical occurrences, experience, and imagination. To analyze the sequence of events that lead to an accident or failure, event and fault trees are used to represent the possible failure sequences. 

The construction of fault trees is by far not a trivial task, but requires a lot of expert knowledge and experience. The quantification of fault trees is for the time being extremely problematic, because the available databases for the determination of unreliability data of components and other probability data need significant further development. However, the existing databases and subjective estimated values may be used if two different plant designs are to be compared with each other, as the absolute values at the end of the calculation are not of interest but, instead, their relative comparison. 

Quantification of a fault tree itself is normally carried out through the use of cut sets so as to avoid redundant and repeat calculations. Each Cut Set is equivalent to an and Gate, and the cut sets combine with one another as if they are an or Gate. 

The quantification of block diagrams follows the same general principles as used for quantifying fault trees and event trees (see Chapter 15). To calculate the probability of success for each path in... 

Fault tree analysis (FTA) is a deductive method, which usually serves for quantification. Just like any method of systems analysis it requires in the first place a qualitative investigation of the system under analysis. After system failure or more generally the undesired or unwanted event (e.g. toxic release) has been defined, logic relationships with the so-called primary or basic events are identified and represented by a fault tree (vid. Fig. 9.8). The primary event may represent the failure of a technical component, an operator error or an impact from outside the plant like flooding or the spreading of a fire from neighbouring installations. 

The investigation has shown how the safety of the system can be improved. At the same time its availability is increased, although this was not the express objective of the analysis. Some of the results were already obtained in the qualitative part of the analysis. The quantification of the fault trees brought further insights and enabled one to identify areas of unbalanced safety measures. The latter are characterized by largely differing contributions of an individual initiating event to the expected frequency of an explosion (vid. Table 9.48). The proposals for... 

The quantification is done on the basis of a qualitative analysis, which is reflected by the fault tree of Fig. 11.3, and its evaluation in terms of probabilities. The fault tree of Fig. 11.3 has the following minimal cut sets... 

The fault tree for the system is shown in Fig. 11.4. Table 11.3 contains the data for its quantification. 

The NASA Fault Tree Handbook [paragraph 7.2] advises that Human Error quantification and Human Error reliability are different from Human Eactors analysis ... 

Detailed investigation of the most important scenarios identified in step 1 Creation of fault event trees Quantification of probabilities and consequences focus on safety-related measures and probability for loss of life Detailed investigation of the most important scenarios identified in step 1 Creation of fault event trees Quantification of probabilities and consequences, focus on economic indteators Economic loss given disruption, short and long term sur tvability of s)stem, which stakeholder is responsible for loss and which stallholder incurs loss for consequences... 

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. 

Fault trees, which are equivalent to reliabihty block diagrams, are common in industry. Moreover, they provide an efficient tool for SIL calculations, under some quantification warnings (Signoret, 2007). A fault tree based approach is therefore chosen in the present paper. 

When presenting an overall risk picture (step 4) the analyst s should present a nuanced and balanced risk picture to the decision-makers based on the cause analysis and consequence analysis. The analysis should establish a risk picture covering ah the dimensions (A, C, C, U, P, S, K). The probabhity quantification of for example a top event in a fault tree is presented along with uncertainty assessments, and a sensitiv-... 

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