Constructing A Modified Control Chart,The X-Bar And R Values
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Problem 1 (25 points)
The x-bar and R values for 20 samples of size five are shown in the following table. Specifications on this product have been established as 0.550 ± 0.02.
| Sample Number | Xbar | R |
| 1 | 0.549 | 0.0025 |
| 2 | 0.548 | 0.0021 |
| 3 | 0.548 | 0.0023 |
| 4 | 0.551 | 0.0029 |
| 5 | 0.553 | 0.0018 |
| 6 | 0.552 | 0.0017 |
| 7 | 0.55 | 0.002 |
| 8 | 0.551 | 0.0024 |
| 9 | 0.553 | 0.0022 |
| 10 | 0.556 | 0.0028 |
| 11 | 0.547 | 0.002 |
| 12 | 0.545 | 0.003 |
| 13 | 0.549 | 0.0031 |
| 14 | 0.552 | 0.0022 |
| 15 | 0.55 | 0.0023 |
| 16 | 0.548 | 0.0021 |
| 17 | 0.556 | 0.0019 |
| 18 | 0.546 | 0.0018 |
| 19 | 0.55 | 0.0021 |
| 20 | 0.551 | 0.0022 |
- Construct a modified control chart with three sigma limits, assuming that if the true process fraction non conforming is as large as 1%, the process is unacceptable.
- Suppose that if the true process fraction nonconforming is as large as 1%, we would like an acceptance control chart to detect this out of control condition with probability 0.90. Construct this acceptance control chart and compare it to the chart obtained in part
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