Dear Lucas,
I've encountered such situations rather often. The last case looked as follows. Customer asked for Cpk and Ppk values which were then used to calculate Process Yield (PY) and, correspondingly, 1-PY. We've analyzed process stability first, 'cause w/o it no metric is relevant. The process turned out to be stable. But its distribution function turned out to be non-normal. So there is no transition from capability indices values to PY. Of course, there is a possibility to calculate PY by direct calculation of the ratio of good items to all checked. However, this approach requires too big samples to control, and leads to cost increase. Finally we pusuarded customer to agree with the following procedure: we regurlarly demonstrate that our process is stable (Shewhart control chart) plus we regurlarly control a sample of reasonable (for us) size and we sum up all controlled samples in order to reach the required value in the future. But such an approach has an unspoken danger. Your customer must understand that the decision to stop the supply can be made only after the enough amount of items is checked. Hope this will help. Good Luck!