yes, sorry about turning a and b around, these A, B, and party of the third part, always get me confused! Just stop thinking about one of them owning the other. One is a consumer of the product of the other, and since both of them hold their ISO certifications separately you can think in terms of independent companies. Of course, in your assessment and approval of suppliers, you might have some special requirements. In my company, it was "buy everything you can from our sister division, but if they cannot get it to you, you can buy from someone else". Some of it was product not produced by sister division, sometimes it was delivery requirements, and sometimes if the quality dropped we'd buy from their competitor to help force the issue that we meant business and would not accept substandard product.