Answer:
4.00
Explanation:
Given:
Upper Specification Limit, USL = 27
Lower Specification Limit, LSL = 21
Mean = 22
Standard deviation,
= 0.25
Required:
Find the process capability index
First center the mean by taking the average of the LSL and USL.



Use formula below to find process capability index:
![C_p_i = min [(\frac{USL - X}{3*\sigma}), (\frac{X - LSL}{3*\sigma})]](https://tex.z-dn.net/?f=%20C_p_i%20%3D%20min%20%5B%28%5Cfrac%7BUSL%20-%20X%7D%7B3%2A%5Csigma%7D%29%2C%20%28%5Cfrac%7BX%20-%20LSL%7D%7B3%2A%5Csigma%7D%29%5D%20)
![C_p_i = min [(\frac{27 - 24}{3*0.25}), (\frac{24 - 21}{3*0.25})]](https://tex.z-dn.net/?f=%20C_p_i%20%3D%20min%20%5B%28%5Cfrac%7B27%20-%2024%7D%7B3%2A0.25%7D%29%2C%20%28%5Cfrac%7B24%20-%2021%7D%7B3%2A0.25%7D%29%5D%20)
![= min [(\frac{3}{0.75}), (\frac{3}{0.75})]](https://tex.z-dn.net/?f=%20%3D%20min%20%5B%28%5Cfrac%7B3%7D%7B0.75%7D%29%2C%20%28%5Cfrac%7B3%7D%7B0.75%7D%29%5D%20)
![min [ (4.00), (4.00)]](https://tex.z-dn.net/?f=%20min%20%5B%20%284.00%29%2C%20%284.00%29%5D%20)
We are sullosed to take the minimum value, but since both values are equal, our process capability index will be 4.00
Therefore, the process capability index = 4.00