Logic symbols

FTA is a deductive method that uses Boolean logic symbols (i.e., AND gates, OR gates) to break down the causes of the top event into basic equipment failures and human errors. The analysts begin with the top event and identify the causes and the logical relationships between the causes and the top event. Each of the causes, called intermediate events, is examined in the same manner until the basic causes for every intermediate event have been identified. 

Clean up any system logical/symbols/menu references. 

Figure 23.9. Common electronic logic symbols and truth tables. From S. P. Perone and D. O. Jones, Digital Computers in Scientific Instrumentation, New York McGraw-Hill, 1973, by permission of the publisher. Copyright 1973 by McGraw-Hill, Inc.

We can see the rose logic symbolism exquisitely carved in Michelangelo s Pieta, originally sculptured in 1499CE for St Peters Basilica in Rome. With breast exposed to suckle the newly bom infant, the Virgin Mary nurses the cmcified Jesus. She represents the Church at the precise moment of her transformation from the lover who has just presided over his death, to the tender mother present at his birth. 

One of the fundamental ideas of mathematics based on an extension of At is Group Theory. A group consists of variables x,X2... an identity constant / function symbols predicate symbol = punctuation (,) and logical symbols V, D. Three extra axioms are... 

Numerous symbols are used in the construction of a basic fault tree. These symbols, sometimes referred to as fundamental logic symbols, provide the analyst with a pictorial representation of the event and how it interacts with other events on the tree. Figure 12.2 shows the basic symbols used during the FTA process. Once the reader has a general understanding of these symbols and their use, as described below, fault tree construction will be greatly facilitated. 

Finally, the logical symbols V ( for alT) and 3 ( there exists ) are employed as abbreviations rather than as precise logical quantors. For truncated series expansions, we use the Landau notation 0(...) to denote the leading order in the expansion parameter of the truncated terms. 

FTA requires the use of logic symbols to trace the sequences of events that could result in an incident. The resulting diagram looks like a tree with many branches, with each branch listing sequential events or failures for different independent paths to the top event. Analysts then can better assign failure rate data to each event and calculate the probability of an undesired event occurrence. 

II-ll. A fault tree analyses a safety system from the perspective of the final outcome or failure, called the top event . Developing a fault tree is like analysing an event tree in reverse, in that the components of the safety system are assessed working backwards to find out what could have caused the top event. Fault trees also expressly include Boolean logic symbols, which can make their evaluation, especially numerical risk analysis, easier to carry out than for event trees. Another difference is that fault trees may be multinodal (i.e. one node or logic symbol may be connected to several preceding events), whereas event trees have only binary branches. 

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