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 .003 inch.

a. Calculate the Cp of the process. (Round your answer to 3 decimal places.)
Cp =
b. Calculate the Cpk of the process. (Round your answer to 3 decimal places.)
Cpk =

Answer 1

A) 1.111

B) 0.889

Step-by-step explanation:

given data :

outer diameter of connecting rods = 1 ± 0.01 inch

sample mean outer diameter = 1.002 inches

standard deviation = 0.003 inches

A) Calculating the Cp of the process

mean = 1.002

Standard deviation = 0.003

LSL = 1 - 0.01 = 0.99

USL = 1 + 0.01 = 1.01

`Cp = (USL - LSL)/(6 * STANDARD DEVIATION)` =
`(1.01-0.99)/(6*0.003)` = 1.111

B) calculate Cpk

mean = 1.002, LSL = 0.99, USL = 1.01 , deviation = 0.003

`Cpk = min[(mean-LSL)/(3* deviation) , (USL- mean)/(3*deviation) ]`

= min [(0.012/0.009) , (0.008/0.009) ]

= min [ 1.333, 0.889 ]

hence Cpk = 0.889