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

Answer:

A) 1.111

B) 0.889

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

$Cp = \frac{USL - LSL}{6 * STANDARD DEVIATION}$ =  $\frac{1.01-0.99}{6*0.003}$ = 1.111

B) calculate Cpk

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

$Cpk = min[\frac{mean-LSL}{3* deviation} , \frac{USL- mean}{3*deviation} ]$

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

       = min [ 1.333, 0.889 ]

hence Cpk = 0.889