Question

A metal fabricator produces connecting rods with an outer diameter that has a 1 ± .01 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.002 inches with a standard deviation of 0.003 inch.

Calculate the process capability index for this example. (Round your answer to 3 decimal places.)

Answer 1

Solution :

In the given example, we have upper and lower specification limits for an outer diameter of rods.

USL = Upper Specification Limit = 1 + 0.01 = 1.01 inch and

LSL = Lower Specification Limit = 1 - 0.01 = 0.99 inch.

The standard deviation for outer diamter ( σ^ ) = 0.003 inch.

The process capability index (Cp) is given by; Cp = (USL - LSL) / (6*σ^).

And hence for this example, Cp = (1.01 - 0.99) / (6*0.003) = 0.02 / 0.018 = 1.1111.

So,  Cp = 1.1111.