In this paper we present a methodology for the solution of binary systems that allows the simultaneous use of all the available information. We give a statistical criterion to judge about the quality of the results. This methodology, based mainly on the Wilson-Price procedure devised by our group for the solution of binary systems (by Barone et al., in 1988 and 1990 and Milano et al. in 1989), has here been applied to the analysis of four W UMa binaries for which the existing solutions were, for different reasons, unsatisfactory. We show the cases for which more observational data are necessary or those for which a better analysis would be sufficient to give final answers. The new solutions found for the four systems fit well the data, overcome the discrepancies among results and observations found by previous investigators, and confirm that these systems belong to the W-type category. Finally, a working hypothesis on a possible new correlation that might link DT, q and the filling factor F of W UMa systems is shown, extending that suggested by Sarna & Fedorova in 1988.
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