Question

A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.01 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 0.002 inch.

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

Answer 1

Question: A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.01 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 0.002 inch.

Answer: The Process Capability Index (Cpx) = 1.333

Explanation:

Given that:

Mean = 1.002

Upper Specification Limit (USL) = 1 + 0.01 = 1.01

Lower Specification Limit (LSL) = 1 - 0.01 = 0.99

Standard Deviation () = 0.002

Now:

Process Capability Index is given by:

Cpx = min{ ((M - LSL) / 3), ((USL - M) / 3) }

Therefore:

Cpx = min{ ((1.002 - 0.99) / (3 x 0.002)), ((1.01 - 1.002) / (3 x 0.002)) }

Cpx = min{ 2, 1.333 }

Hence:

The Process Capability Index (Cpx) = 1.333