In the course of preparing a revision to Chapter (111) of the U.S. Pharmacopeia, the revision committee came to a unanimous agreement that the method for assessing parallelism that is currently presented in (111) and in the European Pharmacopeia's Chapter 5.3 is flawed and should be replaced. The symptoms are that perfectly acceptable assay results may fail due to good precision and that obviously faulty assay results may pass due to poor precision. The flaw is that the wrong statistical technique has been used. We propose an alternative approach based on the equivalence testing paradigm that does not have these shortcomings. Equivalence testing requires the establishment of equivalence limits. Specific approaches for establishing equivalence limits are discussed.