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Cp

Cpk

Cp and Cpk are measurements of process capabilities. They are used in studies such as process capability and can be used to monitor a process similar to how X-Bar and Range charts are used.

Cp – Inherent Process Capability

Note: in some industries this calculation is called pk.
This is the ratio of the Upper Specification Limit minus the Lower Specification Limit to six sigma. It is denoted by the symbol Cp.

Cp  =  (Upper Spec Limit – Lower Spec Limit) 

6s Actual

Note: s = Sigma

You cannot calculate Cp if your specifications are one sided. In other words, if you specification only has an upper parameter specification limit or a lower specification limit. In these cases, Cp is ignored and only Cpk can be used.

There is some confusion about the difference between Cp and Pk along with Cpk and Ppk. The difference is in how you calculate the actual sigma, or standard deviation, either using an estimate, or the actual calculations. These terms are tossed around a lot and are sometimes used interchangeable, even though they are not. For details see the Sigma/Standard Deviation explanation.

We have made calls out for scientific proof that has been reviewed by peers as to the validity of the estimated way and have as of yet to seen the data. Statistics IS a science, and as such, all theory should be able to be validated by such peer reviews.

 

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If a processes mean, or average, is shifted with respect to the design or specification mean, the inherent process capability is adjusted with a factor k, and becomes Cpk.

k Factor

k  = Process Shift

Design Specification Width / 2

Cpk – Process Capability

Note: in some industries this calculation is called Ppk.
This is the capability of the process expressed in relation to a worse case scenario view of the data. It is denoted by the symbol Cpk.

Use it to determine if a process or service, is within the normal variation, and is capable of meeting specifications.

Cpk = the lesser of …

Cpk  = (Upper Spec Limit – Mean) (Mean – Lower Spec Limit )

 or 
3s Actual 3s Actual

Note: s = Sigma

For an example of a distribution, X Bar, and R Bar charts see our ZeroRejects features page. It makes doing statistical process control charts easy. And at only $150.00, (USD), our software can get you going quickly.

Also see Cpk vs PPM, Common cause. Our free software can do Cpk, along with PPM and yields, for you.

We have a free and commercial product to aid you in these calculations for discrete data types. See the free Cpk calculator and the commercial Cpk calculator for more details.

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Last Updated: Saturday, 10-Jun-06 15:50:57 PDT

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