Explaining Cp and Cpk

When we speak about the capability of processes we often refer to a couple indices called Cp and Cpk. These two indices, used together, can tell us how capable our process is and whether or not we have a centering issue.  For the math geeks out there here are the formulas for calculating Cp and Cpk.

Cp = (USL – LSL) / 6*Standard Deviation (within)

Cpk = Min (Cpl, Cpu); where:

Cpl = (mu – LSL) / 3*Standard Deviation (within)

Cpu = (USL – mu) / 3*Standard Deviation (within)
 

Golf Analogy

For the rest of us here is a nice golf analogy to help differentiate between Cp and Cpk.

OK, I admit I don’t play golf but work with me here.  For grins, let’s say you want to learn how to drive a golf ball like Tiger does.  Even I, a non golfer, would love to be able to do this!

Step 1: Hit it Consistently

Your first mission is to learn how to hit the ball consistently and to the same spot. When you have learned this fine art and are indeed able to hit the ball to the same spot over and over again you may say you have good Cp. This is to say that you have a very capable golf swing.

Step 2: Get it to the Hole!

This is all well and good. But there is one big issue. You now need to learn how to aim since you have not paid any attention to where the pin was when learning how to hit the ball to the same spot. You may say your process is “shifted” away from the target (i.e. the golf pin which is the center of the process). So your over paid golf instructor now teaches you how to shift your body and aim your now capable shot.

Assuming this process is successful you are now able to hit the ball to the same spot (good Cp) and you are now able to aim the ball toward the hole (good Cpk). Life is good… Tiger watch out!

Summary

In summary, Cp tells us how capable our process is. If there is tons of variation your process may not be very capable at all. In this case you will want to reduce variation which will improve your Cp.

When you are happy with Cp you can move onto to Cpk which tells us how centered our process is. If your process is capable (good Cp) but is hugging the upper customer specification limit your Cpk will be poor. In order to improve Cpk you will need to work on “shifting” the process back towards the mean of the process.

There are some rules to all this Cp and Cpk fun. One giant rule is that your data must follow the normal distribution.  Here is an excellent article from Keith Bower on this very topic.

Subscribe to LSS Academy

If you enjoyed this article please consider subscribing to our full feed RSS. You can also subscribe by email and have new articles sent directly to your inbox.

---