Cut set method

Fault Trees and Reliability Block Diagrams are both methods of showing probability combinations. There have been a number of solution techniques developed to solve probability combinations. These include Cut Sets, Tie sets. Event Space, Decomposition Method, Gate Solution Method, and many others. In this appendix three examples will be shown - the Event Space method and the Cut Set method, and the Gate Solution Method. Details and full development of the methods can be found in (Ref. 1) Chapter 5. 

The "Cut Set" method was named from the reliability block diagram. Notice in Figure C-3 that if one "cuts" across a set of blocks in parallel that the system fails. The reliability block diagram is draw in the "cut set" style to show those cut sets. 

Problem Using the cut set method, solve for probability of system failure for the 2oo3 power system using the failure probabilities from EXAMPLE C-1. 

The cut set method could also be used to solve the problem. One must be careful, however, to make sure that the unions are properly calculated. The cut set solution is given by ... 

When trees with repeated events are to be analysed, this method is not appropriate since intermediate gate events will no longer occur independently. If this method is used, it is entirely dependent upon the tree structure whether an overestimate or an underestimate of the top event probability is obtained. Hence, it is better to use the minimal cut-set method. 

Fault Tree Solution. Solving the fault tree means obtaining the minimal cut sets. The minimal cut sets are all the combinations of equipment failures that can result in the fault tree TOP event. Computer programs are requked to determine the minimal cut sets for large fault trees (72). The solution method has four steps ... 

A final remark should be made regarding the use of the minimal cut set approximation (rare event approximation) method in determining the top event probability (chance). Using this method, the obtained top event probabihty (chance) is an upper bound. The question then arises whether this approximation introduces an element of uncertainty that has a larger... 

ABSTRACT When a fire Probabilistic Risk Assessment (PRA) is modeled and quantified by using predeveloped internal PRA model, if components are damaged by a fire, the basic event values of the components became True or one (1), which removes the basic events related to the components from the minimal cut sets, and which makes it difficult to calculate accurate component importance measures. Thus, a new method to accurately calculate Fussell-Vesely importance measure in fire PRA is recently introduced. However, the new method has a drawback when the failure probability of the damaged component is small. Thus, another new method could be proposed. Two methods are compared, and the condition in which each method is accurately applicable is derived in this paper. 

ABSTRACT Nuclear power plant includes multiple components and systems, which are maintained in order to limit or prevent failures resulting from the ageing and deterioration. These components and systems are imavailable during the maintenance activities. The unavailability of the safety systems results in increased risk of the nuclear power plant. A method for optimization of the maintenance activities in the nuclear power plant applying heuristics algorithms is presented. The maintenance optimization is modelled as a combinatorial problem. The minimal cut sets identified in the prohahiUstic safety assessment are used for assessment of the risk in the optimization function. The periodically tested component model is apphed for the modelling of the components included in the maintenance. The developed method is apphed on test models and the obtained results are presented. Results show that optimization of maintenance decreases the risk and thus improves the plant safety. 

The main idea of the FTTD analysis is to find the minimal cut sets (MCSs), which can really lead to a hazard according to the time dependencies of their events and gates. In papers (Magott Skrobanek, 2002, Magott Skrobanek, 2000, Skrobanek, 2005) the method of FTTD analysis which is based on a system of inequalities and equalities has been given. 

Outline the general manual method for determining cut sets. 

In this example, given approach of a threatening storm, failure to depart is a credible threat and the failure of any sub-system in the B series could lead to a dangerous failure. Necessary risk reduction is provided by systems C with parallel logic of B2-C1, B3-C2 AND B4-C3. The method is useful for high level summary of analyses and the various cut sets leading to failure are identified at sub-system level as B1 OR(B2 AND Cl) OR(B3 AND C2) OR(B4 AND C3) OR B5. 

Cut set (Clause 3.1.3) method can P)e deployed to identify components which provides the highest probability contribution to the unwanted top event. 

Critical Properties From Equations of State. In industrial work calculating the critical locus of a mixture is frequently necessary. Because this is done at perhaps 0.05 mole fraction intervals for a binary system, the repetitive nature of the calculation demands as direct and clear cut a method of solution as possible. This precludes solving simultaneous equations, such as setting the second and third derivatives of the free energy with respect to composition equal to zero as indicated below ... 

For the large complex system, when calculating the minimal cut sets in FTA, the computation is very large, even results in the NP problem. Petri net is a special directed net, which contains the static performance as well as the dynamic performance. The petri net can describe the status changing and the events developing, so the petri net is considered as the reliability modeling method instead of the FTA. The static performance of the petri net... 

Minimal cut vectors There are a lot of methods in reliability analysis that use conception of Minimal Cut Sets (MCSs). For example, some of them are presented by Choi Cho (2007) and Yeh (2008). These methods have been proposed for BSS reliability analysis firstly (Shooman 1968, Rosenberg 1996). 

The simplified hybrid method is proposed for evaluation of the seismic safety of existing research reactor facilities or the seismic design review of new ones. This method is especially effective for research reactors, where the success path or the plant damage state cut set can be determined with less effort than for an NPP. 

Related Work. A wide range of FTA methods exists Classically, one obtains the minimal cut sets in the FT [5]. This enables to order components based on their structural importance. Further, with additional information one can compute the system reliability. A popular technique is to exploit Bayesian networks, which are useful both in discrete time [9] and in continuous time [8]. Our approach focuses on continuous timed systems, with currently no maintenance. Therefore, we will translate DFTs into continuous time Markov chains (CTMCs) and use state of the art techniques as described in [2,3]. This allows us to compute reliability measures by use of efficient techniques for transient analysis of CTMCs. 

Seismic Reliability Assessment, Alternative Methods for. Fig. 2 Reliability problems for the special case of only two uncertain parameters Xj and X2. cut-set system. The gray area represents the side of the failure domain... 

Open-pit zinc mining is not common, since most mines ate below the surface. The Kidd Creek Mine in Ontario, Canada, is a combination open-pit—underground mine. It is one of the richest deposits in the world with an estimated 62.5 x 10 t grading 7.08% zinc, 1.33% copper, and 151 g silver (14). Underground mining methods include room-and-pdlar, shrinkage, cut-and-fill, and square set. In the United States, ca 20 mines account for more than 98% of zinc production. 

Size selectivity is the most thorough method of expressing classifier performance under a given set of operating conditions. Cut size and sharpness can be calcinated from size-selectivity data. Size selectivity is defined by... 

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