Conjoining Fault Trees with Petri Nets to Model Repair Policies

Abstract

Right from the beginning, the fault tree language gained great acceptance in reliability modeling, because it bears a striking resemblance to the operators found in the classical logic. Therefore, only by using ‘AND’ as well as ‘OR’ gates a number of system failures can be expressed even by engineers not related to reliability analysis. Doubtless, intuition accompanying fault tree models is their greatest merit. Therefore each attempt to increase their expressive power by introducing a set of very specific model extensions strives to retain the intuitiveness. The most remarkable extensions are dynamic gates and repair boxes. However, these extensions are strictly limited to expressing time dependencies like a sequence of time consuming activities or time redundancy. From this viewpoint, fault trees and Petri nets complement one another. The latter offer huge modeling power comparative to Turing machines, but their models turned out to be obscure to engineers. Hence, this severe limitation hampers widespread popularity of Petri Nets. By analyzing the constraints of the two languages, we come up with a new modeling technique blending fault trees with Petri nets. We extend the expressive power of fault trees by adding Petri net immediate transitions. The obtained fault graphs with time dependencies are investigated by modeling several repair policies on some exemplary computer system. Availability calculations of the system are possible owing to a dedicated tool.