No, Impurities quantified are process related impurities. If your formulation is API then those need to check and if your dosage form is Solid Oral, Liquid or any other formulation then need not to check. Process related impurities never increase over the shelf-life period.
The quantification of API manufacturing process-related impurities should be compared to the API manufacturer's COA. Comparison with the manufacturer's COA suffices because the impurity and assay specifications in the manufacturer's COA would have referenced the BP, USP, Eur Ph, Japanese Ph, etc.
In the absence of the manufacturer's COA, comparing your results to any internationally accepted pharmaceutical compendia suffices.
Yes you could compare your assay and impurities quantification method with compendial method, but you should do the validation of your method and after that you can compare those 2