Hi Martin,
IPC-A-610 "Acceptability for Electronic Assemblies" is pretty much the industry standard. It is extremely detailed (372 pages) and covers the criteria for everything you can think of. There are also some other IPC standards that cover other aspects, such as PCBs, rework, etc., but if you're looking at 'screwing down som suppliers' then 610 would be the one to apply.
Hope that helps.