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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