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Dependability modeling and evaluation is aimed at investigating that a systemperforms its function correctly in time. A usual way to achieve a highreliability, is to design redundant systems that contain several replicas ofthe same subsystem or component. State space methods for dependability analysismay suffer of the state space explosion problem in such a kind of situation.Combinatorial models, on the other hand, require the simplified assumption ofstatistical independence; however, in case of redundant systems, this does notguarantee a reduced number of modeled elements. In order to provide a morecompact system representation, parametric system modeling has been investigatedin the literature, in such a way that a set of replicas of a given subsystem isparameterized 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 moredifficult to be defined and the standard approach is to 'unfold' the parametricmodel, in order to exploit standard analysis algorithms working at the unfolded'ground' level. Moreover, parameterized combinatorial methods still require thestatistical independence assumption. In the present paper we consider theformalism of Parametric Fault Tree (PFT) and we show how it can be related toProbabilistic Horn Abduction (PHA). Since PHA is a framework where bothmodeling and analysis can be performed in a restricted first-order language, weaim at showing that converting a PFT into a PHA knowledge base will allow anapproach to dependability analysis directly exploiting parametricrepresentation. We will show that classical qualitative and quantitativedependability measures can be characterized within PHA. Furthermore, additionalmodeling aspects (such as noisy gates and local dependencies) as well asadditional reliability measures (such as posterior probability analysis) can benaturally addressed by this conversion. A simple example of a multi-processorsystem with several replicated units is used to illustrate the approach.

Parametric Dependability Analysis through Probabilistic Horn Abduction