A metal fabricator produces connecting rods with an outer di

A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.02 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 0.008 inch.

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

Solution

a)
USL = 1+0.02 =1.02
LSL = 1-0.02 = 0.98
Mean=xbar = 1.002
sigma= 0.008
The process capability index is
Cpk = min {(xbar-LSL)/3sigma, (USL-xbar)/3sigma}
= min {(1.002-0.98)/(3*0.008), (1.02-1.002)/(3*0.008)}
Process capability index = min{0.9167, 0.75} = 0.75
b)
As the Cpk < 1, the process is not capable of producing the desired quality.