Overall Picture of Capability

Process capability indices are intended for single characteristics that are created by a unique “process”; hence the name process capability.
Product capability cannot be described by a single “variables” (continuous data) distribution as the totality of characteristics com from different processes and will have very different distributions. You can describe the total capability as a defect rate. You can combine the rates using the rules of probability. Some defects will be independent and the conditional proababilty formula will apply. Others are not independent and you will need to use the appropriate probability formula to do this. OR you can simply calculate the actual total defect rate over a substantial period of time and report that. This latter way is the most accurate, easiest and most believable as it comes from actual results and not statistical estimation which is subject to errors of assumptions of which models might apply.