Question
A manufacturer produces decorative wooden pieces. Each decorative wooden piece is supposed to meet company standard. To check and control the process of cutting, the company quality people randomly sampled wooden pieces varies in length from every shift and determined the number of defects on the wooden pieces. The data collected from 40 such samples are shown below:
|
Sample | Length of Wooden Piece (in inches) |
Number of Defects |
| 1 | 15 | 1 |
| 2 | 15 | 2 |
| 3 | 17 | 2 |
| 4 | 15 | 7 |
| 5 | 15 | 2 |
| 6 | 14 | 1 |
| 7 | 15 | 2 |
| 8 | 16 | 3 |
| 9 | 15 | 2 |
| 10 | 15 | 1 |
| 11 | 16 | 3 |
| 12 | 18 | 1 |
| 13 | 16 | 3 |
| 14 | 16 | 2 |
| 15 | 15 | 3 |
| 16 | 14 | 2 |
| 17 | 15 | 1 |
| 18 | 16 | 3 |
| 19 | 15 | 1 |
| 20 | 15 | 2 |
| 21 | 15 | 1 |
| 22 | 16 | 3 |
| 23 | 15 | 2 |
| 24 | 15 | 3 |
| 25 | 14 | 2 |
| 26 | 12 | 1 |
| 27 | 13 | 2 |
| 28 | 12 | 2 |
| 29 | 12 | 3 |
| 30 | 12 | 2 |
| 31 | 13 | 1 |
| 32 | 13 | 2 |
| 33 | 12 | 3 |
| 34 | 15 | 3 |
| 35 | 13 | 1 |
| 36 | 12 | 6 |
| 37 | 12 | 1 |
| 38 | 14 | 3 |
| 39 | 13 | 3 |
| 40 | 12 | 1 |
Construct a suitable control chart to check whether the process is said to be in a state of control or not using both approaches. Also construct the revised control charts, if necessary.
Answer :
Word Count : 497
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Skip in 10
First, we calculate the mean number of defects. Sum of defects from all 40 samples: 1 + 2 + 2 + 7 + 2 + 1 + 2 + 3 + 2 + 1 + 3 + 1 + 3 + 2 + 3 + 2 + 1 + 3 + 1 + 2 + 1 + 3 + 2 + 3 + 2 + 1 + 2 + 2 + 3 + 2 + 1 + 3 + 2 + 2 + 1 + 2 + 1 + 2 + 3 + 1 Let's sum in parts to avoid mistakes: * Sum of first 10: 1 + 2 + 2 + 7 + 2 + 1 + 2 + 3 + 2 + 1 = 23 * Next 10: 3 + 1 + 3 + 2 + 3 + 2 + 1 + 3 + 1 + 2 = 21 * Next 10: 1 + 3 + 2 + 3 + 2 + 1 + 2 + 2 + 3 + 2 = 21 * Last 10: 1 + 3 + 2 + 2 + 1 + 2 + 1 + 2 +
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