Reasoning modelling and efficient numerical computation seem a priori incompatible: on one hand, Expert Systems are usually designed in order to deal with symbolic data. They are able to solve problems in domains where computers failed before, but they are not able to perform efficiently sophisticated computation or complex numerical data analysis. On the other hand, many disciplines regularly face the need to analyse large volumes of numerical data, and many efficient algorithms have been set up in the past. Nevertheless, use of experience and specialized knowledge are required in numerical processing, either to understand output or to adjust input parameters. Our aim is that Expert Systems may be used in order to achieve these tasks, i.e. both to interpret symbolic features extracted from numerical data by classical techniques and to adjust input parameters according to automatic expert diagnosis. Therefore, Expert Systems may be used not only in dealing only with symbolic data, but also in merging symbolic data with numerical data. We present in this article the overall LITHO project which is a numerical processing including an Expert System, describing the Expert System itself and the whole chain surrounding it. Moreover, we show that even though their success and their ability to be included in numerical data process, diagnostic systems need to be completed by a diagnostic system environment containing tools both for interpreting results and for preventing contradictions--in Knowledge Base and in Fact Base.