Problem:

Twelve samples, each containing five parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were:

SAMPLE SAMPLE MEAN (in.) RANGE (in.)

1 10.002 0.011

2 10.002 0.014

3 9.991 0.007

4 10.006 0.022

5 9.997 0.013

6 9.999 0.012

7 10.001 0.008

8 10.005 0.013

9 9.995 0.004

10 10.001 0.011

11 10.001 0.014

12 10.006 0.009

Required:

Question 1) Determine the upper and lower control limits and the overall means for x-charts and R-charts.

Question 2) Draw the charts and plot the values of the sample means and ranges.

Question 3) Do the data indicate a process that is in control?

Question 4) Why or why not?

Solve the problem and show all work.