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Process Capability – Cp, Cpk, Pp, Ppk.

Process Capability is a relatively simple statistical measure which provides an estimate on the level of process outputs which will be within permitted specification limits.

It provides a comparison between the output of a process versus the process specifications.

The process capability measure therefore allows comparison between desired levels of process capability and the actual performance levels of a process. Where a process is “acceptable as is”, then controls methods such as Statistical Process Control can be applied to monitor the process, where the process is not capable and not meeting desired levels of performance, then action can be taken to investigate and have process improvements implemented to achieve the desired capability levels.



Process capability is a measure obtained by taking a representative sample of process output, performing a statistical analysis and using the results obtained to determine future expected process yields.

Process Capability will provide a single number which details the ability of a process to consistently provide output that will be within required specifications.

In order to measure process capability a process must be “stable”, i.e. there can only be common cause variation present within the process. Common cause variation is variation around the process mean (average), arising from variation which is naturally inherent within the process, it is not caused by some special causes.



 

 

Capability versus Stability:

A process is Capable if the outputs produced are predictable to be within specification.

A process is stable if it is only influenced by common causes of variation.

You don’t actually need to know the process specifications to determine process stability but you must know the specifications to determine capability.

 

The Capability Index, Cpk.

What a process would be capable of, if it were stable.

The outcome of a Process Capability study is a single metric, which provides an indication of the ability of a process to consistently provide output which is within required specifications.

CPK <1.00 (Poor, incapable)

1.00< CPK <1.67 (Fair)

CPK >1.67 (Excellent, Capable)

CPK = 2 for a 6δ process (i.e. a 6 sigma process)

 

Formulae for Cp, Cpk, Pp and Ppk.




What is Cpk?

Cpk is the “Capability Index”. It is a measure of the capability of a process to provide output that is within the process specification limits. The Cpk formula, applies an estimate of sigma, which details the potential of a process to meet specifications. The Cpk formula, includes reference to the process mean.

Where Cpk = 1, then 99.73% of all data points will reside within the specification limits, i.e. 99.73% of outputs from a process will be within specification.

The meaning of Cpk =1.



 

What is Cp?

Cp is a measure of the potential of a process to provide output which is within upper and lower specification limits. The Cp measure does not take into account the centering of the process, so while Cp may indicate a potential to operate within the specifications, due to poor centering, the actual output may be skewed with resultant outputs outside of specification. Using Cp alone can therefore be misleading, but it does give a good indication of process potential.

As the Cp measure increases, the spread of the process output decreases, which is normally seen as positive. With variation decrease, the process output becomes increasingly homogeneous.

Cp will normally be used in conjunction with the Cpk measure, so that both centering and spread can be understood.

Where the Cp and Cpk values are equal, then the process is centered between the specifications, where not equal, then the greater the gap between the two values, the greater the shift in the process mean from the nominal mean.

 

Process capability (CPK).  Assume worst case.

Cpk measures how much a process is in control by measuring its spread / dispersion within the specification limits.

In metric terms:

Cpk = {USL – Mean}/3σshort or {Mean – LSL}/3σshort

We take the worst case of either Cpk = {USL – Mean}/3σshort or {Mean – LSL}/3σshort

If the mean is centred, either approach gives the same result. If the mean is (say) closer to the Upper Specification Limit (USL), then we use USL – Mean, to get the worst case result, i.e. result which will generate the higher level of outputs outside of specification.


What is Ppk?

The Ppk measure provides information on how well a process is actually performing versus the process specifications. The Ppk measure also includes the centering of the process outputs versus specifications.

Note: The Ppk uses the actual process sigma, rather than an estimate of sigma, which is used for Cpk, therefore Ppk is used to measure actual past performance, whereas Cpk is used to measure future performance, future process capability.

As per Cpk, if Ppk = 1, then 99.73% of all data points will reside within the specification limits.

 

What is Pp?

Pp is a measure of the actual performance of a process in providing output which is within upper and lower specification limits.

(As per Cp).
The Pp measure does not take into account the centering of the process and only provides a measure of the level of process spread or variation within the process

The Pp measure should be used in conjunction with the Ppk measure in order to understand how a process is performing in terms of spread / variation and how well the process is centered between specification limits.

As the Pp measure increases, the spread of the process output decreases.

Where the Pp and Ppk values are equal, then the process is centered between the specifications, where not equal, then the greater the gap between the two values, the greater the shift in the process mean from the nominal mean.

 

Differences between Cpk and Ppk.

Cpk informs the user about the future capability of a process.

Ppk informs the user of how the process has performed in the past.

The Cpk and Ppk measures will be very close when the process remains in a state of consistent statistical control, as both the actual sigma and estimated sigma will be similar. If a process is not in statistical control, then the measures will diverge from each other

Comparison between Cpk and Ppk can be used to help identify special cause variation.

 

Advantages of a capable process.

i) A process must provide outputs which are within specifications. A capable process will consistently and reliably deliver to specification requirements.

ii) A capable process with a low level of spread, will produce highly uniform outputs.

iii) With a stable, low variability process, in-process and final inspection and testing can be reduced, resulting in lead-time and costs savings.

iv) Defect rates will be low or may even be eliminated. There will be low levels of scrap, rework, repair associated with a capable process.

v) A capable process, well centered and with a low spread, will provide opportunity to revise specification limits.

Note: The specifications must relate to customer requirements and customer expectations. This will involve a continuous communication with the customer.

 

Interpreting the capability index.

Capability index  > 2.0                “Excellent”. At “6 sigma” level.

Capability index  of 1.34 – 2.0    “Good”

Capability index of 1.00-1.33   “Need Control”

Capability index < 1.00             “Not Capable”

 

 

Statistical Process Control, Statistical Process Improvement. “Delivering Improved Processes”. >>>