Modeling dynamic reliability using dynamic Bayesian networks

Abstract

This paper considers the problem of modeling and analyzing the reliability of a system or a component (system) where the state of the system and the state of process variables influences each other in addition to an exogenous perturbation influence: this is the dynamic reliability. We consider discrete time case, that is the state of the system as well as the state of process variables are observed or measured at discrete time instants. A mathematical tool that shows interesting properties for modeling and analyzing this problem is the so called Dynamic Bayesian Networks (DBN) that permit graphical representation of stochastic processes. Furthermore their learning and inference capabilities can be exploited to take into account experimental data or expert's knowledge. We will show that a complex interaction between system and process on one hand and between system, process and exogenous perturbation on the other hand can simply be represented graphically by a dynamic Bayesian network. With their extended tool, known as influence diagrams (ID) that integrate actions or decisions possibilities, one can analyze and optimize a maintenance policy and/or make reactive decision during an accident by simulating different scenarios of its evolution for instance.

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“…For absorbent Markov models, the transition matrix can be written as follows where I is an identity matrix ( k is the number of absorbing states. An absorbing state is a state that once entered cannot be left.…”

“…An absorbing state is a state that once entered cannot be left. ); hence, the fundamental matrix is defined as follows …”

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A Model to Support Risk Management Decision-Making

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