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Frequently-Asked Questions about Capability
- Are Cpk & Ppk acronyms? If so, what do they actually mean or represent?
- What is the difference between Cp and Pp?
- What is the difference in the formulas for Cpk and Ppk?
- Are there maximum values for Cp, Cpk, Pp and Ppk?
- How can I improve Cpk value, when it is less than 1.0?
- Is it possible to have a Ppk value of 10 and a Pp number of 5?
- What do the letters in Cp and Cpk stand for?
- Why do capability indices formulas divide by 3?
- What is an ideal Cpm value?
- Can I compare two processes based on only the Cpk values of each of them?
- Can the process performance index Ppk be applied on the ongoing process? If yes, how?
- Why would I have Cp and Cpk indices well over 1 when some readings are outside the specification limits?
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.
Gordon Constable Ph.D
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. The formulas for Cp and Cpk are here; formulas for Pp and Ppk are here.
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.
Gordon Constable Ph.D
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.
Gordon Constable Ph.D
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.
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 )].
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."
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.
The capability indices are designed to be applied to on going 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 or CHARTrunner will calculate these values for you if you enter the specifications. If you do not have either of these programs, the Capability Analysis article series provides information on calculating capability.
Gordon Constable Ph.D
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?
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