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In the case of suppliers, you are the interested party. The main question for suppliers is therefore how to meet your needs and wants?
Risk is that which might constrain the supplier from providing your needs and wants. What can go wrong? Again, it is based on your needs:
Processes are defined so people know what to do
Adequate and correct raw material
Control of processes
Inspection and test, including instruments
Suitable work environment to produce what you need, including cleanliness and sound infrastructure
Personnel readiness and training
I have clients who additionally consider business sustainability risks from environmental and/or safety concerns: specifically, in noting conditions that might result in crippling fines and/or shutdown by regulators.
Dos this help?