Parallel decompositions have proved to be powerful tools for the analysis and interpretation of the physical information provided by Mueller matrices experimentally obtained. In this work, the procedure for the so-called arbitrary decomposition of Mueller matrices is validated through its application to a set of representative experimentally determined Mueller matrices. The covariance and passivity criteria required for the physical realizability of the Mueller matrices involved in the parallel decompositions are integrated in the procedure, which ensures the physical consistency of the results presented.