5th International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 2007 Uncertainty analysis in food engineering involving imprecision and randomness C´ edric Baudrit cbaudrit@grignon.inra.fr Arnaud H´ elias arnaud.helias@grignon.inra.fr UMR782 G´ enie et Microbiologie des Proc´ ed´ es Alimentaires INRA, AgroParisTech F-78850 Thiverval-Grignon, France Nathalie Perrot nathalie.perrot@grignon.inra.fr Abstract During the cheese ripening, airflow pattern and climatic conditions inside cheese-ripening rooms are determinant for cheese weight losses. Due to the variation of air ve- locity inside ripening chambers, homogeneity in the dis- tribution of climatic conditions is very hard to achieve at every single point of it. We are hence faced with impre- cise and incomplete knowledge. In practice, it is common that some model parameters may be represented by sin- gle probability distributions, justified by substantial data, while others are more faithfully represented by possibility distributions due to the partial nature of available knowl- edge. This paper applies recent methods, designed for the joint propagation of variability and imprecision, to a cheese ripening mass loss model. Joint propagation meth- ods provide lower & upper probability bounds of exceed- ing a certain value of cheese mass losses. Keywords. Imprecise probabilities, p-boxes, belief func- tions, possibility, food processing, cheese ripening. 1 Introduction In the food industry, end-products must achieve a compro- mise between several properties, including sensory, san- itary, technological properties. Among the latter, sensory and sanitary properties are essential because they influence consumer choice and preference. Nevertheless, managing these properties right from the fabrication stage with the aim of controlling them is no easy task ([23, 24]). One of the key reasons of this difficulty is the uncertainty that should be managed at different levels: • Uncertainty (more specifically imprecision) on the measurements, especially the measurements of the sensory properties [15]. It is obvious and accepted that there is a lack of efficient sensors, and that exist- ing sensors often provide incomplete information for taking action decisions on the process [17]. More- over, when adequate sensors exist, the configurations of industrial processes do not often allow an efficient placement. • Uncertainty on the phenomenon involved, even for control purposes. As a consequence the management of uncertainty on the parameters and also the struc- ture of the models built are crucial [16]. Few contributions about this topic are available. Among them Davidson et al. [5] used a fuzzy arithmetic that esti- mates peanut eating time and browning to control peanut roasting. Perrot et al. [24] developed a decision help system to control the cheese ripening process, integrating the uncertainty of human measurements. Petermeier et al. [25] used a hybrid approach to develop a model of the foul- ing behavior of an arbitrary heat treatment device for milk. This is developed by combining deterministic differential equations with cognitive elements for the unknown parts of the knowledge model. These authors emphasize the rel- evance of this open field of research in the context of food processes and the interest of fuzzy symbolic representation of expert reasoning. Nevertheless, they call into question the optimality of the approaches developed on the basis of imperfect and incomplete expert knowledge. The ripening process is one most important step for many cheese makers. Microbial activities, responsible for the organoleptic characteristics of cheeses, are influenced by climatic conditions (air temperature and relative hu- midity, gas concentration). So, controlling these climatic conditions inside cheese-ripening rooms is of paramount importance. Cheese mass loss dynamic is a key point in ripening process, with consequences on productivity and it introduces a risk that resulting product may be dropped in status (e.g., the Camembert-Normandie protected designation of origin requires a final weight of 0.25 kg). Ventilation is used to evacuate heat and humidity gener- ated by cheeses and the spatial distribution of climatic conditions inside cheese-ripening rooms is dependent on airflow (air velocity, air change rate). Nevertheless, only a few studies on interaction between climatic conditions and