I have a problem. A dimension 39.5 -0/+0.5 is defined as a capability dimension. On completion of the study the cpk is 0.4289 with the mean 39.53 and an average range of 0.08. All readings are in tolerance with a minimum size of 39.5 and maximum 39.62. This cpk value was calculated using standard formula, is their an alternative formula to account for a one sided tolerance?

You supplied R-Bar but failed to supply subgroup size or an unbiased estimate of sigma. In order to calculate Cpk, I need one of these two variables.

For your reference: The capability number you are interested in is termed Cpk(upper), not Cpk, and is calculated:

Cpk(upper) = (USL - Xbar)/(3*sigma-hat)

We have the same type of tolerances - you must be a japan jv. We just set our nominal at {the nominal + 1/2 of the tolerance}

I think you calculated correctly. It is easy to see that your distribution is too close to the lower tolerance.

By my eyeball estimate, if you get the mean to 39.75, the middle of the tolerance band, and not change anything else, your Cpk should be around 3 - 3.5. So I would try to move the mean up if you need a better Cpk.