The specifications for a product are 6 mm ± 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the Cpk for this process?

1.67

Step-by-step explanation:

In the above question, we are given our Specification limit as :

6mm ± 0.1 mm

Lower limit = 6 - 0.1 = 5.9mm

Upper limit = 6 + 0.1 = 6.1mm

Mean = 6.05mm

Standard deviation = 0.01mm

The formula for Cpk = Min [(USL – mean/3 × standard deviation),(mean-LSL/3 × standard deviation)]

Cpk = Min [(6.1 – 6.05/3 × 0.01),(6.05 - 5.9/3 × 0.01)]

Cpk = Min [ (0.05/0.03),(0.15/0.03)]

Cpk = Min[ 1.6666666667 , 5]

Therefore,

Cpk = 1.6666666667

Approximately = 1.67