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# 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.

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1. robert says:

Hi Ron. I love the analogy to golf. Great minds think alike as I was busy developing my own posts on process capability, you can read me efforts here (http://tinyurl.com/2eya72) and here (http://tinyurl.com/ytbokf). Are you planning on some more posts on for example, Pp, Ppk? As a separate topic I’m also thinking about explaining statistical power and how it relates to data sensitivity, significance and population size difference.

Keep up the good work!

Rob

2. Gary says:

The analogy I was taught dealt with a car and a roadway. The left and right sides of the roadway are upper and lower control limits. As your car gets more and more narrow, it becomes easier to keep it in the roadway (good Cp). But you might be driving a narrow car in the ditch (outside of process limits). Having good Cpk requires that the car be narrow and driving in the road, preferably near the middle.

Thanks for the post and the analogy.

3. Ron Pereira says:

Hi Rob – Thank for the links.

Hi Gary – Thanks for the great analogy. I like it a lot and hope you don’t mind me stealing it from you for future training purposes. I get tired of talking golf all the time!

4. chinmaya says:

piease tell me about cp &cpk and also about 6sigma

5. hanuaar says:

as

6. Rahul R Deshpande says:

Please explain for me the process of Cp & Cpk

7. chittaranjan says:

ok, but not give 100% information about cp & cpk.
yes, pls tell me what is sigma & what is 1s, 2s, 3s, 4s, 5s, & 6sigma. and also tell me about cp & cpk with help of production process not golf. just u take 20 boring jobs.u check the dia then u get 5 jobs comes in mean, 5 jobs comes in usl but within tolerance, 5jobs also comes in the side of lsl but within tolerance, but 3 jobs comes over size and 2 jobs comes undersize. ok this is question. now u solve how to calaculate cp & cpk?

8. rajbir says:

Its a graet example for explaining the importance of Cpk & Cp. i like this style of explaining & its more practical than other examples which i learn earlier. Thanks
Rajbir

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