Process Capability Index (CpK) Calculation Formula

Process capability index measures the extent of variation a process experiences relative to its specification limits. It also helps us to compare different processes with respect to the optimal situation or if they come up to our expectations.

The most common process capability index is given by Cp, which is an estimation of what the process is capable of producing if the process mean were to be centered between the specification limits, assuming that the process output is approximately normally distributed.

 

Here,

• Cp – This is how it is represented. It denotes the capability of the process that can be achieved when perfectly centered between the lower and the upper limit.
• UCL – Upper control limits
• LCL – Lower control limits
• When Cp equals 1, the process is perfectly centered. (Cp = 1, prefect process). 
• For Cp value higher than one, it means tolerance> the process.  This confirms that the process appears to be able to do this. (Cp> 1, process compatible)

We can say it (Cp) indicates how many times the tolerance zone is larger than the 6σ value of the variation.

Process Capability Index Formula

Where Cpk can be used when your process average is not perfectly centered. The formula for Cpk is as follows:

Here,

• Cpk - is the process capability index;
• USL - is the upper specification limit;
• LSL - is lower specification limit; and
• σ - is the standard deviation.

Process Capability Index Calculation Example

The process room temperature during the manufacturing must be kept between 18 degrees Celsius and 26 degrees Celsius. The process of maintaining this temperature has a standard deviation of 2 degrees Celsius. If the mean temperature is 21 degrees Celsius, find the Cpk.

Here,

USL = 18 

LSL = 26

SD = 2, 

Mean = 21

Let follow the below formulas-

Cpu = Mean – LSL / 3 X SD

Cpl = USL – Mean / (3 X SD) 

Cpk  = Minimum of (Cpu, Cpl)

Thus,

Cpu= (26 - 21)/ (3 × 2) = 5/6 = 0.8334

Cpl = (21 - 18)/ (3 × 2) = 3/6 = 0.5

Cpk = Minimum of [Cpu, Cpl]

That is Cpk = minimum of [0.8334, 0.5]

So, the process capability index Cpk is 0.5.

Read also: Sustainable Process Index (SPI) Calculation