An article in the Mid-American Journal of Business presents an analysis for a spring water bottling operation. One of the characteristics of interest is the amount of magnesium, measured in parts per million (ppm), in the water. The data in the table on the next page (stored in SpWater) represent the magnesium levels from 30 subgroups of four bottles collected over a 30-hour period:
a. Construct a control chart for the range.
b. Construct a control chart for the mean.
c. Is the process in control?
| Bottles | |||
Hour | 1 | 2 | 3 | 4 |
1 | 19.91 | 19.62 | 19.15 | 19.85 |
2 | 20.46 | 20.44 | 20.34 | 19.61 |
3 | 20.25 | 19.73 | 19.98 | 20.32 |
4 | 20.39 | 19.43 | 20.36 | 19.85 |
5 | 20.02 | 20.02 | 20.13 | 20.34 |
6 | 19.89 | 19.77 | 20.92 | 20.09 |
7 | 19.89 | 20.45 | 19.44 | 19.95 |
8 | 20.08 | 20.13 | 20.11 | 19.32 |
9 | 20.30 | 20.42 | 20.68 | 19.60 |
10 | 20.19 | 20.00 | 20.23 | 20.59 |
11 | 19.66 | 21.24 | 20.35 | 20.34 |
12 | 20.30 | 20.11 | 19.64 | 20.29 |
13 | 19.83 | 19.75 | 20.62 | 20.60 |
14 | 20.27 | 20.88 | 20.62 | 20.40 |
15 | 19.98 | 19.02 | 20.34 | 20.34 |
16 | 20.46 | 19.97 | 20.32 | 20.83 |
17 | 19.74 | 21.02 | 19.62 | 19.90 |
18 | 19.85 | 19.26 | 19.88 | 20.20 |
19 | 20.77 | 20.58 | 19.73 | 19.48 |
20 | 20.21 | 20.82 | 20.01 | 19.93 |
21 | 20.30 | 20.09 | 20.03 | 20.13 |
22 | 20.48 | 21.06 | 20.13 | 20.42 |
23 | 20.60 | 19.74 | 20.52 | 19.42 |
24 | 20.20 | 20.08 | 20.32 | 19.51 |
25 | 19.66 | 19.67 | 20.26 | 20.41 |
26 | 20.72 | 20.58 | 20.71 | 19.99 |
27 | 19.77 | 19.40 | 20.49 | 19.83 |
28 | 19.99 | 19.65 | 19.41 | 19.58 |
29 | 19.44 | 20.15 | 20.17 | 20.76 |
30 | 20.03 | 19.96 | 19.86 | 19.91 |
Source: Data extracted from Susan K. Humphrey and Timothy C. Krehbiel, “Managing Process Capability,” The Mid-American Journal of Business, 14 (Fall 1999), 7–12.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.