Tree Evaluation

Several procedures are available that evaluate the phylogenetic signal in the data and the robustness of trees (Swofford et al., 1996 Li, 1997). The most popular of the former class are tests of data signal versus randomized data (skewness and permutation tests). The latter class includes tests of tree support from resampling of observed data (nonparametric bootstrap). The likelihood ratio test provides a means of evaluating both the substitution model and the tree. 

Simulation studies indicate that the distribution of random MP tree lengths generated using random data sets will be symmetrical, whereas those using data sets with 

Bootstrapping is a resampling tree evaluation method that works with distance, parsimony, likelihood, and just about any other tree derivation method. It was invented in 1979 (Efron, 1979) and introduced as a tree evaluation method in phylogenetic analysis by Felsenstein (1985). The result of bootstrap analysis is typically a number associated with a particular branch in the phylogenetic tree that gives the proportion of bootstrap replicates that supports the monophyly of the clade. 

As the name implies, likelihood ratio tests are applicable to ML analyses. A subop-timal likelihood value is evaluated for significance against a normal distribution of the error in the optimal model. In ideal applications, the error curve is presumed to be a distribution. Thus, the test statistic is twice the difference between the optimal and test values, and the degrees of freedom is the number of parameter differences. 

Application of the test to alternative phylogenetic trees is problematic, especially because of the irregularity of [the] parameter space (Yang et al., 1995), but its use has been advocated for evaluating optimality of the substitution model when the number of parameters between models is known. 

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Erdmann, R. C., F. L. Leverenz, H. Kirch, WAMCUT, A Computer Code for Fault Tree Evaluation. EPRI-NP-803, June. 

Vesely, W.E. 1970. A Time Dependent methodology for Fault Tree Evaluation, Nuclear Engineering and Design, 13 337-360. 

In order to realize the requirements of hierarchical fault tree abstraction, different fault tree evaluation algorithms have been reviewed. The results of this survey and the requirements led to three major steps that can be used to abstract from a given failure realization. These three steps are merging internal failure modes, building a structure-independent form, and changing the information of internal events. 

Finally, the evaluation can be performed by rolling back the tree, starting at the leaves, and working backwards towards the trunk of the tree. 

Current research in LHASA is focused on developing new methods assisting users in choosing the most appropriate strategy for their target structures. Furthermore, the development of criteria for the evaluation of synthesis routes and/or algorithms for selecting optimal synthesis routes within the tree are discussed [34]. 

Process Hazards Analysis. Analysis of processes for unrecogni2ed or inadequately controUed ha2ards (see Hazard analysis and risk assessment) is required by OSHA (36). The principal methods of analysis, in an approximate ascending order of intensity, are what-if checklist failure modes and effects ha2ard and operabiHty (HAZOP) and fault-tree analysis. Other complementary methods include human error prediction and cost/benefit analysis. The HAZOP method is the most popular as of 1995 because it can be used to identify ha2ards, pinpoint their causes and consequences, and disclose the need for protective systems. Fault-tree analysis is the method to be used if a quantitative evaluation of operational safety is needed to justify the implementation of process improvements. 

A failure modes and effects analysis delineates components, their interaction.s ith each other, and the effects of their failures on their system. A key element of fault tree analysis is the identification of related fault events that can contribute to the top event. For a quantitative evaluation, the failure modes must be clearly defined and related to a numerical database. Component failure modes should be realistically and consistently postulated within the context of system operational requirements and environmental factors. 

A fault tree is a graphical form of a Boolean equation, but the probability of the top event (and lesser events) can be found by substituting failure rates and probabilities for these iwo-staie events. The graphical fault tree is prepared for computer or manual evaluation by pruning" it of less significant events to focus on more significant events. Even pruned, the tree may be so large that it IS intractable and needs division into subtrees for separate evaluations. If this is done, care must be taken to insure that no information is lost such as interconnections between subtrees. 

An early version of MET methodology was applied in the Interim Reliability Evaluation Program (IREP) that analyzed the ( ill vert Cliffs and Arkansas Nuclear lessons learned in IREP and other applications. Although MET is an extension of the fault tree analysis (Section 3.4,4), it warrants a. separate discussion (see NUREG/ CR 3268). Objectives of MET are ... 

FTAP - Give it a fault tree or equivalent as linked Boolean equations, and it will find the cutsets (Section 2.2), but it does not numerically evaluate the probabilities. 

The assembly process (Figure 10-1) brings together all of the assessment tasks to provide the risk, its significance, how it was found, its sensitivity to uncertainties, confidence limits, and how it may be reduced by system improvements. Not all PSAs use fault trees and event trees. This is especially true of chemical PSAs that may rely on HAZOP or FMEA/FMECAs. Nevertheless the objectives are the same accident identification, analysis and evaluation. Figure 10-1 assumes fault tree and event tree techniques which should be replaced by the equivalent methods that are used. 

The accident sequence frequencies are quantified by linking the system fault tree models together as indicated by the event trees for the accident sequence and quantified with plant-specific data to estimate initiator frequencies and component/human failure rates. The SETS code solves the fault trees for their minimal cutsets the TEMAC code quantitatively evaluates ihe cm sols and provides best estimates of component/event probabilities and frequencies. 

The second triad element was determined from international frequencies for the basic initiating events. One fault tree for sphere rupture was constructed and evaluated using the fault tree program FTW (1991). 

Fault tree or equivalent analysis is key to PSA. Small logical structures may be evaluated by hand using the iciples of Chapter 2 but at some point computer support eeded. Even for simple structures, uncertainty analysis VIonte Carlo methods requires a computer. However, t of the codes are proprietary or a fee is charged for their... 

Vesely, W. E. and R. E. Narum, 1970, PREP and KITT Computer codes for the Automatic Evaluation of a Fault Tree, INEL IN-1349. 

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