In December 2016, the Data on the Web Best Practices Working Group (Group Page, Group Charter) have published the Data Quality Vocabulary. This vocabulary is a meta-framework for frameworks that similar to one you need.
In the document, these points are relevant to your question:
- Feel free to create your own framework; moreover, you rather should create your own framework;
- W3C, as it seems, does not insist on 5-star data quality scheme;
- W3C even does not insist on ubiquitous RDF usage when publishing open data;
- However, W3C insists on RDF usage when measuring data quality
(by the very fact of publishing this document in a form of RDF vocabulary).
See also this answer for more details.
From a practical point of view, it is easier to measure quality of 5-star data, than of 3- or 4-star.
There are common requirements for Linked Open Data, whereas non-Linked Open Data quality depends on particular technical and non-technical requirements that should be fulfilled. These requirements may vary from format to format or from country to country.
For example, this is the rating page of random Russian federal body in special system that measures open data quality, this page also provides links to:
Finally, have a look at: