Parametric Dependability Analysis through Probabilistic Horn Abduction
  Dependability modeling and evaluation is aimed at investigating that a system
performs its function correctly in time. A usual way to achieve a high
reliability, is to design redundant systems that contain several replicas of
the same subsystem or component. State space methods for dependability analysis
may suffer of the state space explosion problem in such a kind of situation.
Combinatorial models, on the other hand, require the simplified assumption of
statistical independence; however, in case of redundant systems, this does not
guarantee a reduced number of modeled elements. In order to provide a more
compact system representation, parametric system modeling has been investigated
in the literature, in such a way that a set of replicas of a given subsystem is
parameterized so that only one representative instance is explicitly included.
While modeling aspects can be suitably addressed by these approaches,
analytical tools working on parametric characterizations are often more
difficult to be defined and the standard approach is to 'unfold' the parametric
model, in order to exploit standard analysis algorithms working at the unfolded
'ground' level. Moreover, parameterized combinatorial methods still require the
statistical independence assumption. In the present paper we consider the
formalism of Parametric Fault Tree (PFT) and we show how it can be related to
Probabilistic Horn Abduction (PHA). Since PHA is a framework where both
modeling and analysis can be performed in a restricted first-order language, we
aim at showing that converting a PFT into a PHA knowledge base will allow an
approach to dependability analysis directly exploiting parametric
representation. We will show that classical qualitative and quantitative
dependability measures can be characterized within PHA. Furthermore, additional
modeling aspects (such as noisy gates and local dependencies) as well as
additional reliability measures (such as posterior probability analysis) can be
naturally addressed by this conversion. A simple example of a multi-processor
system with several replicated units is used to illustrate the approach.
