Widely adopted for more than 20 years in industrial fields, business rules offer the opportunity to non-IT users to define decision-making policies in a simple and intuitive way. When used conjointly with probabilistic graphical models (PGM) their expressiveness increase by introducing the notion of probabilistic production rules (PPR). In this paper we will present a new model for PPR and suggest a way to handle the combinatorial explosion due to the number of parents of aggregators in PGM such as Bayesian networks and Probabilistic Relational Models in an industrial context where marginals should be computed rapidly.