Assignment:
No matter how closely the production process is monitored, some chips will work faster than others and be worth more in the marketplace. The goal is to make this number as high as possible, and improvements are being implemented continually. Consider the data set shown in Table, summarizing the number of memory chips that worked properly at the highest speed for each of 25 batches of 1,000 chips.
a. Find the center line for the percentage chart.
b. Find the control limits for the percentage chart.
c. Draw the percentage chart.
d. Comment on what you see in the percentage chart. In particular, is this process in control? How do you know?
e. For the particular case of high-speed memory chips here, does the control chart show good or bad news?
f. Write a paragraph, as if to your supervisor, summarizing the situation.
| Number of Highest-Speed Memory Chips for 25 Batches of 1,000 Chips Each |
| Batch Identification Number |
Number of Highest-Speed Chips, X |
Proportion of Highest-Speed Chips, p |
| 1 |
75 |
0.075 |
| 2 |
61 |
0.061 |
| 3 |
62 |
0.062 |
| 4 |
70 |
0.07 |
| 5 |
60 |
0.06 |
| 6 |
56 |
0.056 |
| 7 |
61 |
0.061 |
| 8 |
65 |
0.065 |
| 9 |
54 |
0.054 |
| 10 |
71 |
0.071 |
| 11 |
84 |
0.084 |
| 12 |
84 |
0.084 |
| 13 |
110 |
0.11 |
| 14 |
71 |
0.071 |
| 15 |
103 |
0.103 |
| 16 |
103 |
0.103 |
| 17 |
80 |
0.08 |
| 18 |
90 |
0.09 |
| 19 |
84 |
0.084 |
| 20 |
88 |
0.088 |
| 21 |
111 |
0.111 |
| 22 |
118 |
0.118 |
| 23 |
147 |
0.147 |
| 24 |
136 |
0.136 |
| 25 |
123 |
0.123 |
| Average |
86.68 |
0.08668 |
Provide complete and step by step solution for the question and show calculations and use formulas.