How to argue Cpm over Cpk

Hello all, I have a question:

I have a process that has a USL of 10 and a LSL of 1 with an OPT of 2. We monitor Cp and Cpk right now. My Cp is running around 3.00 but my Cpk is running <1.00. My mean is 2.162 with a sigma of 0.4796 (n=30)

I'm fairly new to process capability indices and ran across Cpm when I was investigating why my Cpk was so low. I think I have determined that Cpm would be applicable in this situation because it takes into account the variance of the mean from the target, not the middle of the spec band like Cpk does.

I've been trying to win over my boss so we can change all of our process to Cpm that have an OPT that is not the middle of the spec band, but have had no success. He is concerned that Cpm will not warn us if the process will begin to go outside of tolerances.

What I have tried:

-show data tables comparing Cpm to Cpk with different samples means, sigmas, and targets showing how each changes as the data is accumulated

-rearranged the Cpm equation to:

Cpm = (USL - LSL) / 6*sqrt[sigma^2+(mean-OPT)^2].

This showed that Cpm takes into account 6(sigma+variance from mean) not just sigma like Cp. I just can't figure out how to show Cpm will warn us when we start "getting close" to a spec.

Anyone know a good arguement for Cpm over Cpk?