The idea of using Cpk is coming from management. Sample sizes and frequency haven't been established and are part of my initial question. There is only one cavity. Typically, a production run is about 300 pieces.

Only one cavity makes matters much simpler but "three critical features" leads to some interesting questions. Short run SPC methods are available for handling multiple product features but things get more complicated if they are correlated (multivariate normal). The bottom line is however that SPC techniques are available for multiple characteristics.

Cpk should not be recalculated for every sample, because this is as bad as allowing a control chart's control limits to adjust themselves when each subsequent sample goes into the process statistics. The idea is to fix the limits based on past experience, which includes an estimate of the process mean and variation which in turn give you Cpk and Ppk. (As this is apparently single-unit flow, Cpk and Ppk will HOPEFULLY be equal unless there are changes in process conditions during the run that cause the process mean to change.) 20 data (I am assuming one measurement per sample as it is a single-cavity mold) are not really adequate to estimate Cpk anyway. This could be an application of short-run SPC in which target means and standard deviations are assumed from past experience.

The only real reason to recalculate Cpk and Ppk is if a process improvement reduces the variation, in which case the control limits will need to be tightened to reflect this.