Referring to the data of Problem 1, stored in SpWater, the researchers stated, “Some of the benefits of a capable process are increased customer satisfaction, increased operating efficiencies, and reduced costs.” To illustrate this point, the authors presented a capability analysis for a spring water bottling operation. One of the CTQ variables is the amount of magnesium, measured in parts per million (ppm), in the water. The LSL and USL for the level of magnesium in a bottle are 18 ppm and 22 ppm, respectively.
a. Estimate the percentage of bottles that are within specifications.
b. Compute the Cp, CPL, CPU, and Cpk.
Problem 1: 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.
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