Qualitative Analysis
Qualitative analysis identifies what combinations of events cause the top event to occur. It can be performed prior to the entry of failure or repair data in the properties for fault tree events. Based on gate logic, qualitative analysis determines the minimal cut sets for the top event. While a cut set is any set of events that cause the top event to occur, a minimal cut set is the smallest group of events, which, if they all occur, cause the top event to occur. Cut sets and minimal cut sets are used to quickly find the upper bounds on the probability of occurrence for the top event.
The events that belong to a minimal cut set provide information such as single point failures and the relative contribution of each minimal cut set. Generally, the minimal cut sets that have the highest probability of occurrence are the ones that have the fewest number of events. If reliability and maintainability information is entered in the properties for events, a quantitative analysis may also be performed to provide the numeric probability of occurrence of the top event and of each minimal cut set.
While it is possible to determine minimal cut sets visually for a small tree, doing so is virtually impossible for a large tree. Thus, computer algorithms have been developed to automate cut set generation. The following table describes the three most common cut set generation methods.
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Method
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Description
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MOCUS
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MOCUS stands for method of obtaining cut sets. Proposed by Fussell and Vesely in 1972, it uses a top-down approach based on the observations that OR gates increase the number of cut sets and AND gates enlarge the size of the cut sets. This method is used in the FTA module as well as in other fault tree tools. For more information, see MOCUS. |
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MICSUP
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MICSUP stands for minimal cut sets upward. While this method works in a manner similar to MOCUS, it uses a bottom-up approach, finding cut sets for gates at the lowest level of the tree. (These gates have only basic events as inputs). MICSUP then obtains minimal cut sets of the upper level gates by substituting minimal cut sets of lower level gates, using Boolean reduction rules when applicable.
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ZBDD
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ZBDD stands for zero-suppressed binary decision diagram. It is based on advanced data structures known as binary decision diagrams (BDDs).
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Qualitative analysis can also be used to find path sets, which are sets of events that, if they do not occur, guarantee the non-occurrence of the top event. Path sets are also sometimes called tie sets. Path sets are based on a second tree that is referred to as a dual fault tree or a success tree. This second tree is constructed to represent the non-occurrence of the top event. The non-occurrence of the events in a path set ensures successful system operation.
To build the second tree, the original tree is copied and all events are replaced with their complements. This means that all AND gates are changed to OR gates, and all OR gates are changed to AND gates. Any of the algorithms used to find cut sets can then be used to find path sets.