Discussion:
Q: Plastics food containers that can be baked in ovens must be able to withstand certain temperatures without melting. One such container, which is 4 inches deep, is designed for use at oven temperatures of 325°F. To monitor the quality of these containers, a subgroup of 5 finished containers is taken every hour and subjected to oven baking for one hour at 325°F. Since defective containers will tend to deform under heating, the height of each container is used as an indicator of the quality of the product. The table below shows these measurements (in inches) for the most recent 20 subgroups of data:
1. Complete the table with the ranges for the last four subgroups (from 17 to 20), and plot them on the R chart.
2. Plot the centerline, upper control limit (UCL), and lower control limit (LCL) for the R chart.
| Subgroup number |
Measurement |
Range |
| 1 |
3.88 |
3.78 |
4.12 |
3.63 |
4.22 |
0.59 |
| 2 |
3.56 |
3.63 |
4.1 |
3.47 |
4.05 |
0.63 |
| 3 |
4.25 |
3.97 |
4.26 |
3.82 |
4.35 |
0.53 |
| 4 |
4.2 |
3.41 |
3.42 |
4.09 |
4.3 |
0.89 |
| 5 |
3.47 |
3.94 |
3.48 |
4.34 |
4.11 |
0.87 |
| 6 |
4.04 |
4.38 |
3.98 |
3.64 |
4.09 |
0.74 |
| 7 |
3.93 |
4.14 |
3.99 |
4.17 |
4.22 |
0.29 |
| 8 |
4.35 |
3.85 |
3.52 |
3.8 |
4.07 |
0.83 |
| 9 |
3.95 |
3.82 |
3.51 |
4.54 |
3.63 |
1.03 |
| 10 |
4.28 |
4.14 |
3.77 |
4.2 |
3.5 |
0.78 |
| 11 |
3.7 |
4.01 |
4.38 |
3.53 |
4.51 |
0.98 |
| 12 |
4.57 |
3.84 |
3.74 |
4.42 |
3.92 |
0.83 |
| 13 |
4.24 |
4.53 |
3.84 |
4.5 |
3.91 |
0.69 |
| 14 |
4.26 |
4.53 |
4.29 |
4.53 |
4.08 |
0.45 |
| 15 |
4.45 |
4.43 |
3.69 |
3.7 |
4.25 |
0.76 |
| 16 |
3.57 |
4.12 |
3.78 |
4.23 |
4.42 |
0.85 |
| 17 |
4.5 |
3.67 |
4.25 |
3.46 |
4.08 |
|
| 18 |
3.91 |
3.48 |
3.86 |
4.46 |
4.08 |
|
| 19 |
3.79 |
4.16 |
4.23 |
3.53 |
4.57 |
|
| 20 |
3.61 |
4.19 |
4.19 |
3.57 |
3.77 |
|