Math
CPK Formula & CP Formula with Problem Solution & Solved Example
Table of Contents
Cpk Formula
CpK means Process Capability Index that could be defined as the statistical measure of process capability. It shows how closely a process is able to compute output based on the given specifications. It will show how consistent we are in delivering performance. A person can work to its level best to achieve the maximum accuracy but he could be away from achieving the target that shows the value of CpK will be lower but the value of Cp will be higher in that case.
Cpk Formula
\[\ Cpk=min \left (\frac{USLmean}{3\sigma},\frac{meanLSL}{3\sigma} \right)\]
USL is the upper specification limit,
LSL is the lower specification limit.
Here, sigma is the standard deviation, USL is the upper specification limit and LSL is the lower specification limit. As we know that capability statistics work wonderful. These statistics shows how well the process is meeting your specifications. This is generally difficult understanding these statistics and it may take some time too.
Two most common capability statistics that are used frequently in mathematics are Cp and CpK. There is the difference of only one alphabet in both terms. The CpK equation is tough to understand when compared to the Cp and it defines how well the process are aligned within specification limits. And the term CpK defines how well the mean is aligned among specification limits.
The smaller the standard deviation, greater would be the value of both statistics measures. Under certain conditions, both statistical measures could have the same outcome values. The application of CpK is not just limited to the mathematical applications only but it could be used for multiple realtime examples too.
Cp Formula
Cp or process capability is defined as the technique to find out the measurable property of a process to a specification. In practice, the final output for the process capability technique is either defined in the form of histograms or calculations. The Cp formula is mathematics could be written as –
Where USL is the upper specification limit, LSL is the lower specification limit and sigma is the standard deviation. This is one of the popular statistical measures that compared the outcomes of an uncontrolled process to limits. Here, the capable word signifies that all processes lie within defined limits only. Many other options to measure the process quality capability are Cpk, Pp and Ppk etc.
Cp Formula
\[\ Cp=\frac{USLLSL}{6\sigma}\]
USL is the upper specification limit,
LSL is the lower specification limit.
A few manufacturing segments have defined only a limited requirement for these parameters and they could further help in advanced quality planning too. Six Sigma however suggests a different process for evaluation of process capability against the defined sigma level that is named as the sigma capability.
Incorporating these quality measuring techniques in traditional manufacturing approaches may sound tough and makes adoption of these metrices little difficult. Here you should understand the sigma level capabilities and once the process is under statistical control, it goes predictable. This approach helps in meeting current expectations of customers and requirements too.
The most interesting step here is to analyze data that occurs outside customers’ expectations. It lies below LSL or above USL and usually tough in understanding. A normal distribution of data makes it possible to estimate the accurate probability of any given dataset.

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