The amount of a preservative added to dairy products should not exceed certain levels of 23 ±6 mg (set by the Food and Drug Administration). Samples of size 5 of processed cheese produced the values of the average and range shown in given Table.
(a) Construct appropriate control charts and determine stability of the process.
(b) If the process is out of control, assuming remedial actions will be taken, estimate the process mean and standard deviation.
(c) Assuming normality and a target value of 23 mg, determine the indices Cp, Cpk, Cpm, and Cpmk.
(d) What proportion of the dairy products meets government standards, assuming normality?
(e) Find a 95% confidence interval for Cpk, assuming normality.
(f) Can we conclude that Cpk is less than 1? Use α =0.05.
| Observation |
Average Level of Preservative (mg) |
Range |
Observation |
Average Level of Preservative (mg) |
Range |
| 1 |
22 |
5 |
14 |
22 |
7 |
| 2 |
26 |
4 |
15 |
20 |
5 |
| 3 |
26 |
6 |
16 |
24 |
8 |
| 4 |
24 |
7 |
17 |
25 |
6 |
| 5 |
22 |
3 |
18 |
23 |
8 |
| 6 |
21 |
5 |
19 |
20 |
5 |
| 7 |
29 |
7 |
20 |
22 |
4 |
| 8 |
25 |
8 |
21 |
22 |
6 |
| 9 |
22 |
4 |
22 |
23 |
7 |
| 10 |
25 |
6 |
23 |
24 |
5 |
| 11 |
25 |
9 |
24 |
22 |
6 |
| 12 |
22 |
3 |
25 |
25 |
5 |
| 13 |
21 |
5 |
|
|
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