<rant on>

This is my professional opinion and personal advice.
First let me disclose that I am viscerally opposed to capability indexes. I feel that to describe variation in terms of a single number is not only an oxymoron but a non-value-add requirement. Why on earth would I want to essentially throw away all of that data to concentrate only on the final resulting index?
We want to understand our process capability for two reasons: to predict yields (& field failure rates) and to understand the variation in the case of stackup tolerances and wear failure modes (especially when tolerances cannot be precisely engineered).
Industry
desires to use these numbers to know if we can reduce inspection from 100%, understand potential impacts to delivery and availability, cost ramifications of rework or safety stock, protential escape to teh customer's line and or the end user, effect on reliability,etc.
The common indices are based on an assumption of Normality. The Normal distribtuion near and beyond
+3 sigma is very susceptable to large inaccuracies even when the distribution is symmetrically bell shaped. Thsi results in very misleadign information for both reasons for a process capability study.
Additionally, many of features, dimensions and functions are not clear cut double sided tolerances. This results in our doing 'extra' math work to come up with that single number...and GD&T makes this even more complex.
So is this work non-value-add? unfortunately, too often our Customers are inundated wiht indices and to save tiem they only check to see if the number is greater than the required level. they check the box...after all this work is done ask yourself: what have I learned? what has my Customer learned? How will my products be made better by this analysis? Is there a better analysis that woudl be even more effective? Do I have time to do that after calculating a bunch of Cpk values?
These issues are even more destructive when it comes to 'bonus' tolerances. Remember that bonuses tolerances are benefit of a lack of variation reduction of the feature or dimension to the target specifications. You get to 'take advantage' of this extra variation.
In reality if we are concerned about REDUCING PROCESS VARIATION, the index should be calculated based only on the native variation to the specified tolerance without any bonus. If we are only interested the YIELD, then a simple defect rate using the bonus tolerance (back calculated to a Cpk if you must) should be sufficient. If I were pushed to submit a single number in yoru case I would choose this latter option. It's quick and easy. Then you might have some time to work on really understanding your process capability.
The only thing 'wrong' with plotting our data in time sequence against the specification limits so we can see all of the components of variation (within piece, piece to piece, lot to lot, raw material lot to lot, time to time, etc.) is that we must engage our brains and THINK about our data collection strategy and then think about the resulting plot. So to avoid this we spend our time on figuring out how to check the box...
But I readily admit that my position on this is a bit like emptying chamber pots into the incoming tide. Society - and industry is just a microcosm of society - is just too enamored of the quick fix, simple explanation, great sounding sound bite...
<rant off>