Cpk Formula

About Cpk Formula

The processing capability index (cpk), it is a measure of process capability, is calculated using the Cpk formula. This number indicates how closely a process can create output that meets its overall parameters. As a result, determining how constant our average performance is. Any product or service must go through a systematic development process. The success of this line of action will be determined by its ability. The Cpk formula aids in certifying a process's effective outcome.

Define Cpk Formula

Cpk is a very useful statistical tool. The arithmetical analysis of the inherent process variability of the assigned duties in question is referred to as process capacity. The process capability index (cpk) is used to determine the process's capabilities. The cpk formula is as follows:

Cpk = min[(USL−mean)/3σ, (mean−LSL)/3σ]

Here,

Cpk = Process capability index

mean= mean value

σ is the standard deviation

USL is upper specification limit

LSL is a lower specification limit

Solved examples based on Cpk Formula

Example: When food is brought to a customer, it should be served between 40oC and 50oC. The procedure utilised to keep the food at the proper temperature has a standard deviation of 2oC, and the mean value for these values is 41oC. How can I find out the process capability index?

Sol:

To find: Process-capability index of the given process

USL = 50ºC

LSL = 40ºC

Standard Deviation = 2ºC

Mean = 41ºC

Cpk formula is:

Cpk=min(USL−mean3σ,mean−LSL3σ)Cpk=min(USL−mean3σ,mean−LSL3σ)

=min(50−413×2,41–403×2)=min(96,16)=16=0.166=min(50−413×2,41–403×2)=min(96,16)=16=0.166

Therefore, the process capability index i.e. Cpk is 0.166.

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Cpk Formula

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