Frequently-asked questions about capability

1. Are Cpk & Ppk acronyms? If so, what do they actually mean or represent?
2. What is the difference between Cp and Pp?
3. What is the difference in the formulas for Cpk and Ppk?
4. Are there maximum values for Cp, Cpk, Pp and Ppk?
5. How can I improve Cpk value, when it is less than 1.0?
6. Is it possible to have a Ppk value of 10 and a Pp number of 5?
7. What do the letters in Cp and Cpk stand for?
8. Why do capability indices formulas divide by 3?
9. What is an ideal Cpm value?
10. Can I compare two processes based on only the Cpk values of each of them?
11. Can the process performance index Ppk be applied on the ongoing process? If yes, how?
12. Why would I have Cp and Cpk indices well over 1 when some readings are outside the specification limits?

Are Cpk & Ppk acronyms? If so, what do they actually mean or represent?

Since their introduction, there has been a lot of speculation as to meaning. Here is my two cents worth.

Cp has always been know as capability of the process since I became aware of it and it has been around for some time. My connection with Cpk came through the Ford "Continuous Process Control and Process Capability Improvement Manual" probably more than 20 years ago. In the Ford manual, a k value was used to represent the number of standard deviations between the Target and the . I would assume that the Cpk came literally from Cp with a k factor adjustment. In reference to the Pp and Ppk, the reference from the beginning has been to Process Performance as opposed to Process Capability.

What is the difference between Cp and Pp?

The technical difference is that the 6 sigma used for the Cp calculation (or the 3 sigma used for the Cpk calculation) comes from the estimate of sigma based on the average range, and the 6 sigma used for Pp calculation (or 3 sigma used for the Ppk calculation) comes from the estimate of sigma based on using all the data and the classical formula for the standard deviation. View the formulas for Cp and Cpk; view the formulas for Pp and Ppk.

In general, if the process is in control and normally distributed (standard assumptions when doing capability analysis), both values should be close. However, since most processes wander around a little bit (and are in control), an intuitive interpretation is that the Cpk is what you could be doing and Ppk is what you are doing.

What is the difference in the formulas for Cpk and Ppk? The only difference I see is the i and r after the sigma symbol. What are these referring to?

The six sigma used for the Cpk calculation comes from the estimate of sigma based on the average range (r). The six sigma used for the Ppk calculation comes from the estimate of sigma based on using all the Individual data (i) and the classical formula.

In general, if the process is in control and normally distributed (standard assumptions when doing capability analysis), both values should be close. However, since most processes wander around a little bit (and are still in control), an intuitive interpretation is that the Cpk is what you could be doing and Ppk is what you are doing.

Are there maximum values for Cp, Cpk, Pp and Ppk?

No. As long as the spec range does not change and you continually reduce the variation, you will increase these indices. I have seen as high as 36 and have heard of higher.

How can I improve Cpk value, when it is less than 1.0?

First, compare Cpk to Cp. If Cpk is less than Cp and Cp is greater than one, center the process in the specification. This should make Cpk comparable to Cp. If Cp and Cpk are less than one, there are two actions you can take. The first (an unadvisable one) is to widen the specification particularly on the side that has the spec limit closest to the center of the process (). The second and more advisable answer is to improve the process by reducing variation in the process. If the process is off-center, it would be advisable to try to center it as you try to improve it.

Is it possible to have a Ppk value of 10 and a Pp number of 5?

This should not occur. You might have a negative number for the Ppk that is larger in absolute value then the Pp number. This implies that the process mean lies outside the specification limits.

What do the letters in Cp and Cpk stand for?

There is no authoritative answer. Cp has been around for a long time and many believe it stands for Capability of the Process. Others say Process Capability, but that would reverse the letters.

As for Cpk, in the literature that I first saw about Cpk, k was the amount of the difference in the target value and in standard deviations (the number of standard deviations that the process is off target). Before you ask, Pp generally is said to be Process Performance.

Why do capability indices formulas divide by 3?

When calculating Cp you divide the specification range by six sigma. This is plus and minus three sigma on each side of the mean of the process which would include about 99.7% of the distribution of output if the process is normal. Cp considers only the spread and not the centering of the process. Consequently, you can have a capable process (Cp > 1) and not be making any good product. Cpk considers the mean of the process and calculates two values ([Cp-usl = (USL - )/3] and [Cp-lsl = (- LSL)/3]). Since the specification has been split into two pieces, the process spread is split into two as well [(6 )/2 = (3 )].

What is an ideal Cpm value?

Generally there is no "ideal." Bigger is always better. The difference in Cpm as defined in SQCpack is in the calculation of the stand deviation or variance term. The standard deviation for Cpm is based on using the target value rather than the mean which will make sigma(pm) larger and Cpm smaller when the process is not centered on the target value. You could say "ideally" the process should be centered in the specification making Cpm = Cp. However, Cp might only be 0.80 which clearly is not "ideal."

Can I compare two processes based on only the Cpk values of each of them? Is there any other tool by which I can say that one process is better than other?

It depends on what you mean by better. If the processes are producing the same product dimension, then you can compare them more or less directly.

Cpk includes a centering factor as well as the variation factor. Unless you want to compare centering as part of the two processes, use Cp.

Can the process performance index Ppk be applied on the ongoing process? If yes, how?

The capability indices are designed to be applied to ongoing processes. They are an indication of what a customer can expect in terms of quality from a particular process.

If you have a control chart on a characteristic for a process, SQCpack will calculate these values for you if you enter the specifications. If you do not have the software, the capability analysis article series provides information on calculating capability.

Why would I have Cp and Cpk indices well over 1 when some readings are outside the specification limits?

My first guess would be that if you look at a control chart of the data, it is out of control. Before you can do capability analysis, the process should be predictable and that requires that it be stable (in-control). For a more detailed discussion, see How can Cpk be good with data outside the specification?