C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 5 ± 0.05 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 5.000 inches with a standard deviation of 0.050 inches.

Calculate the Cpk for this machine. (Round your answer to 3 decimal places.)

0.333

Explanation:

Cpk = Cpl or CPU (the lower is taken as the cpk)

Where Cpl = (USL - Mean) / 3 * standard deviation

CPU = (mean - LSL) / 3 * standard deviation

Where

The process mean = 5

Tolerance = 0.05

Sample mean = 5.000 inches

Standard deviation (sd) = 0.050 inches

Upper standard limit (USL) = 5 + 0.05 = 5.05

Lower standard limit (LSL) = 5 - 0.05 = 4.95

Cpl = (USL - Mean) / 3 * standard deviation

= (5.05 - 5) / 3 * 0.05

= 0.05/0.15

Cpl = 0.333

Cpk = Cpl = 0.333