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Cpk Formula
Cpk formula helps in calculating the process capability index (cpk), which is the measure of process capability. This value depicts how closely a process is able to produce the output to its overall specifications. Thus, deciding how consistent we are with our average performance. The development of any product or service must follow a wellstructured process. The ability of this course of action will decide the successful outcome. Cpk formula helps in confirming this successful outcome of a process.
What is Cpk Formula?
Cpk is an important statistical tool. Process capability refers to the arithmetical study of the natural process variability of the given responsibilities in consideration. Process capability index(cpk) is used for calculating the ability of the process. The cpk formula is given as,
Cpk = min[(USL−mean)/3σ, (mean−LSL)/3σ]
where,
 Cpk = Process capability index
 mean = mean value
 σ is a standard deviation
 USL is the upper specification limit
 LSL is the lower specification limit
Let us have a look at a few solved examples on the Cpk formula to understand the concept better.
Solved Examples Using Cpk Formula

Example 1: Food at a restaurant, when delivered to a customer, should be served between 40ºC and 50ºC. The standard deviation of the process used to keep the food at the correct temperature is 2ºC and the mean value for these temperatures is 41ºC. Find out the process capability index of the process?
Solution:
To find: Process capability index of the given process
USL (Upper Specification Limit) = 50ºC
LSL (Lower Specification Limit) = 40ºC
Standard Deviation = 2ºC
Mean = 41ºC
Cpk formula is:
\(Cpk = min(\dfrac{USL−mean}{3 \sigma},\dfrac{mean−LSL}{3 \sigma})\)
\(= min \left (\dfrac{5041}{3 \times 2},\dfrac{41 – 40}{3\times 2} \right) \\ = min (\frac {9}{6} , \frac {1}{6})\\ = \frac {1}{6} \\ = 0.166\)
Therefore, the process capability index i.e. Cpk is 0.166.
Answer: The process capability index i.e. Cpk is 0.166.

Example 2: The room temperature during the training must be kept between 19 degrees Celsius and 27 degrees Celsius. The process of maintaining this temperature has standard deviation of 2 degrees Celsius. If the mean temperature is 22 degrees Celsius, find the PCI using cpk formula.
Solution:
To find: PCI using cpk formula
Here USL is 27 and LSL is 19 and the Standard deviation is 2, and the mean is 22.
Cpu= (27  22)/ (3 × 2) = 5/6 = 0.8334
Cpl = (21  18)/ (3 × 2) = 3/6 = 0.5
Cpk = Minimum of [ Cpu, Cpl]
Cpk = minimum of [0.8334, 0.5]
The process capability index, Cpk is 0.5
Answer: The process capability index Cpk is 0.5
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