Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes were taken, each tube was weighed, and the weights in the table below were obtained.

view the ounces of caulking per tube data below

1 2 3 4 5 6 7 8 Sample 1 8.17 8.34 8.02 7.94 8.44 7.83 7.81 8.11 Sample 2 7.89 7.77 7.81 8.04 8.00 7.89 7.93 8.09 Sample 3 8.24 8.18 7.83 7.97 7.90 8.16 7.97 8.07 Sample 4 7.87 8.13 7.92 7.99 8.09 7.81 8.14 7.88 Sample 5 8.33 8.13 8.08 8.51 8.41 8.28 8.09 8.16 Sample 6 8.13 8.14 8.11 8.13 8.14 7.95 8.13 8.14

a. Assume that only six samples are sufficient and develop the control charts for the mean and the range.

Set up the R-chart by specifying the center line and three-sigma control limits below. (Enter your responses rounded to three decimal places.)

R-chart

UCL r = ____

R (line overtop of it) = ____

LCL r = ____