Asking questions about problem structure in VS .NET

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21.6.5.1 Asking questions about problem structure
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The most common way of decomposing an engineering problem is by building an event tree or a fault tree, which were the subjects of the previous chapter. An event tree starts with some initiating event and then considers all possible chains of events, which could lead
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CONDUCTING A PROCESS TO ELICIT QUANTIFIED JUDGMENT
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from that rst event to various performances by the system. Some of these chains of events lead to adverse outcomes or failures, some do not. For each event in the tree, a probability is assessed presuming the occurrence of all the events preceding it in the tree, that is, a conditional probability. The total probability for a particular chain of events or path through the tree is found by multiplying the sequences of conditional probabilities. Bury and Kreuzer (1986) describe how an event tree might be structured for a gravity dam. A fault tree decomposes the problem in the reverse direction. The fault tree starts with some failure condition and then considers all possible chains of faults that could lead to that failure. Conditional probabilities for each fault are assessed in the same way as with an event tree, but the total probability is calculated by starting at the failure and moving backwards, rather than starting from an initiating event and moving forward, as in an event tree. The advantage of the event tree is that it comprehensively uncovers combinations of events leading to failures; the disadvantage is that event trees can become bushy messes. The advantage of a fault tree is that it focuses only on chains of events leading to failures; the disadvantage is that it may fail to uncover important combinations of events. An event tree can be used to decompose a problem at different levels of detail. Usually, judgment is more easily applied to smaller components, and research suggests that more detailed decomposition, within reason, enhances the accuracy of calculated failure probabilities. One reason, presumably, is that the more detailed the event tree is, the less extreme the conditional probabilities which need to be estimated. Both event trees and fault trees require a strict structuring of a problem into sequences. This is what allows probabilities to be decomposed into manageable pieces and provides the accounting scheme by which those probabilities are put together. In the process of decomposing a problem, however, it is sometimes convenient to start not with highly structured event or fault trees, but with an in uence diagram. An in uence diagram is a graphical device for exploring the interrelationships of events, processes, and uncertainties. Once the in uence diagram has been constructed, it can be readily transformed into event or fault trees. Stedinger et al. (1996) show how in uence diagrams can be used in assessing hydrologic risks of dam projects.
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21.6.5.2 Finding an appropriate level of detail
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Decomposition of a probability estimation problem relies on disaggregating failure sequences into component parts. Usually, these are the smallest sized pieces that can be de ned realistically and analyzed using available models and procedures. Decomposition can be used for any failure mode that is reasonably well understood. Clearly, decomposition cannot be used for failure modes for which mechanistic understanding is lacking. Internal erosion leading to piping is arguably one such, poorly understood failure mode. In most cases, the extent of decomposition, that is the size of the individual events into which a failure sequence is divided, is a decision left to the panel of experts. Most real problems can be analyzed at different levels of disaggregation. Considerations in arriving at an appropriate level of disaggregation include the availability of data pertinent to the components, the availability of models or analytical techniques for the components, the extent of intuitive familiarity experts have for the components, and the magnitude of probabilities associated with the components. Typically, best practice dictates disaggregating a failure sequence to the greatest degree possible, subject to the constraint of being able to assign probabilities to the individual components. Usually, it is a good practice to
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