By Philippe Weber, Christophe Simon
The software of Bayesian Networks (BN) or Dynamic Bayesian Networks (DBN) in dependability and chance research is a contemporary improvement. lots of clinical guides exhibit the curiosity within the functions of BN during this field.
Unfortunately, this modeling formalism isn't absolutely approved within the undefined. The questions dealing with cutting-edge engineers are serious about the validity of BN versions and the ensuing estimates. certainly, a BN version isn't really in response to a particular semantic in dependability yet deals a common formalism for modeling difficulties lower than uncertainty.
This booklet explains the foundations of data structuration to make sure a legitimate BN and DBN version and illustrate the flexibleness and potency of those representations in dependability, probability research and keep watch over of multi-state structures and dynamic systems.
Across 5 chapters, the authors current numerous modeling equipment and commercial functions are referenced for representation in actual commercial contexts.
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This ebook is the results of lectures which I gave dur ing the educational 12 months 1972-73 to third-year scholars a~ Aarhus collage in Denmark. the aim of the booklet, as of the lectures, is to survey the various major subject matters within the smooth conception of stochastic strategies. In my prior publication likelihood: !
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An illustration of these speciﬁc structures can be found in telecommunication systems with n relay stations that can be modeled as a linear consecutive-koon:G system if the signal transmitted from each station is strong enough to reach the next k stations. An oil pipeline system for transporting oil from point to point with n spaced pump stations is another example of a linearconsecutive-koon system. A closed recurring water supply system with n water pumps in a thermo-electric plant is a good example of a circular system.
To solve this problem, the FT modeling is based on a descending approach. Starting from a top event that characterizes the undesired event, the analysis goes down the tree by the deﬁnition of intermediate events identiﬁed as direct causes of upper events, until elementary events are obtained. 5 shows the FT of the ﬂow distribution system, which is obviously quite simple. 5. FT of the ﬂow distribution system If a FT is available, it is very simple to translate it into a BN by simple mapping. As shown earlier for tie-sets and cut-sets, deterministic CPT can map Boolean relations between variables with logical operators: AND and OR.
It is, therefore, necessary to take into account uncertainties relating to the link probabilities, the leak probability and the state of parent variables xi . Scientiﬁc contributions already exist in relation to the problem of uncertainty in logical structures such as N-OR or LN-OR. Srinivas [SRI 93] and Diez [DIE 93] proposed an extension of the N-OR structure for non-Boolean variables. Antonucci [ANT 11] developed an imprecise LN-OR structure with uncertainty on the link probabilities that can be extended to uncertainty on the leak probability with Diez’s parameterization.