# Cpk Formula

Process capability index (cpk) is the measure of process capability. It shows how closely a process is able to produce the output to its overall specifications. It decides how consistent we are to our average performance.

A person may perform with minimum variation, but he can be away from his target towards one of the specification limits that indicates the Cpk will be lower, but Cp will be high.

$\large Cpk=min \left (\frac{USL-mean}{3\sigma},\frac{mean-LSL}{3\sigma} \right)$

Where,
$\sigma$ is standard deviation,
USL is the upper specification limit,
LSL is the lower specification limit.

### Solved Examples

Question 1: Food served at a restaurant should be between 38°C and 49°C when it is delivered to the customer. The process used to keep the food at the correct temperature has a process standard deviation of 2°C and the mean value for these temperature is 40. What is the process capability of the process?
Solution:

USL (Upper Specification Limit) =49°C
LSL (Lower Specification Limit) =39°C
Standard Deviation =2°C
Mean = 40

Cpk is given by,

$Cpk=min \left (\frac{USL-mean}{3\sigma},\frac{mean-LSL}{3\sigma} \right)$
$=min \left (\frac{40-39}{3\sigma}\right)$
= $0.166$