Reliability and Diagnostic of Modular Boolean Systems

Model-based reasoning about a system requires an explicit representation of the system’s components and their connections. Diagnosing such a system consists of locating those components whose abnormal behavior accounts for the faulty system behavior. The system in this paper is represented by Boolean functions and the variables represent the components. For each component a probability is given expressing the reliability of the component. The modular Boolean functions define a tree, such that each subtree is representing a subsystem of the whole system. The reliability calculus explained in the first part, computes the reliability for each subsystem and for the whole system. In the second part, the diagnosis of a system in this representation is defined. For the diagnosis the conditional probabilities of each component given the observation on the system is computed. Then each component can be diagnosed based on the computed probability. A little example is closing the section. In the third part these computations are compared to a Bayesian network.