Problem 1

A. A bearing production shop undertook a process capability study. The following data were obtained for 15 samples of size. Based on the individual observations, management estimated the process standard deviation to be 4.21 (in thousandth of an inch) for use in the process capability analysis. The lower and upper specification limits (in thousandths of an inch) for the eccentricity of the bearing sleeves were 5 and 25.

Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Mean 11 12 8 16 13 12 17 16 13 14 17 9 15 14 9
Range 9 13 4 11 10 9 8 15 14 11 6 6 12 10 11

i. Calculate the process capability ratio and the process capability index values.
ii. What conclusions is management likely to draw from the capability analysis?

B. A clothing manufacturer produces women's clothes at four locations in Mexico. Relative locations have been determined, as shown in the table below. The location of a central shipping point for bolts of cloth must now be determined. Weekly quantities to be shipped to each location are also shown in the table. Determine the coordinates of the location that will minimize distribution costs using the rectilinear distance model

Location (x,y) Weekly
Quantity
A 5, 7 15
B 6, 9 20
C 3, 9 25
D 9, 4 30