Abstract: State of the art was the European patent application EP 99105884.3 (see application data sheet). This patent application used already non-linear systems of equations and conditional probabilities with one single item in the condition. It was necessary, however, to perfect these theoretical methods and make them practicable. Many improvements and innovative modifications were needed. The following list identifies the innovations that had to be provided: The accurate indication of all systems of equations concerning 2, 3 and 4 hypotheses. Those equations can be entered in exactly the presented form into the calculation program. The introduction of coefficients aik and bik that can be applied without changes for any areas of use. The delivery of a scheme that enables the mechanized production of the aik and bik. Introducing schematic tables with identical follow events in one row (e.g. Table 3). Using appreciation factors AF(i) if the hypotheses Ki? have the same a-priori probability.