Let's play a game. You want to begin quarterly quality reviews with your top choice suppliers. Perhaps it's integrated into a quarterly business review meeting. Anyway, as the supplier quality engineer, compile a hit list of quality related topics you want your suppliers to report on as they pertain to your supplied material at their facility. The customer audience is you, functional and management reps from operations, engineering, quality, purchasing, and program management.
Here's a couple to start:
Continual improvemtent activities
Return material status
Let it fly and appreciate your inputs.