Using Bayesian Networks in reliability evaluation for an (r, s)-out-of-(m, n):F distributed communication system

A Bayesian Network is a probability-based approach to infer or make decision in systems with stochastic parameters. It is used to model and predict the behaviour of a particular system. This prediction is based on the observed stochastic phenomena of the system. The main purpose of building a Bayesian Network is to estimate the certainty of unobservable (or costly observable) events called hypothesis variables. Bayesian Networks allow us to use the causal relationships and can then easily handle and predict a critical situation in distributed systems. The causal relationships are expressed as a joint conditional probability distribution to relate the different possible states of variables. We also say a situation is critical when, in spite of the failure of some components the system is still working but the next failure will cause a system failure. Most of the other models cannot give us an accurate prediction for such a critical situation, because they cannot recognize the correlations and relations between the events in the system. Bayesian Networks, however, can encode such dependencies. Furthermore, the table of conditional probabilities, which is the quantitative part of Bayesian Networks developed for reliability analysis, not only includes many straightforward probability functions, but also includes many 0s and 1s as the working or survival conditional probabilities. This can help us to simulate the model much faster in reliability studies. This paper shows how one may use Bayesian Networks as a statistical technique to develop a new approach to evaluate the reliability of an (r, s)-out-of-(m, n): F system. An (r, s)-out-of-(m, n): F system is a system that fails when at least an r × s matrix of its components fail.