Homework SourseThe data given in worksheet Problem 5 in the Test 4 Data fil
The data given in worksheet “Problem 5” in the “Test 4 Data” file contains the number of defective products found in a sample of 25 randomly selected from each hour’s production for 20 hours.
- Construct a control chart for the proportion of defective products.
- Is the process in control?
- Conduct a runs analysis for this control chart.
| Sample | Proportion Defective |
| 1 | 0.2 |
| 2 | 0.24 |
| 3 | 0.16 |
| 4 | 0.28 |
| 5 | 0.04 |
| 6 | 0.12 |
| 7 | 0.24 |
| 8 | 0.2 |
| 9 | 0.16 |
| 10 | 0.2 |
| 11 | 0.32 |
| 12 | 0.12 |
| 13 | 0.08 |
| 14 | 0.04 |
| 15 | 0 |
| 16 | 0.04 |
| 17 | 0.04 |
| 18 | 0.08 |
| 19 | 0.12 |
| 20 | 0.12 |
Solution
Thus control chart has lower limit as 0.086334, middle line as 0.14 and higher line as 0.193666
Comparing with the table and analyse each entry whether it falls within this limit.
0.04, 0.08, 0 are outside this control limit.
| Sample | Proportion Defective |
| 1 | 0.2 |
| 2 | 0.24 |
| 3 | 0.16 |
| 4 | 0.28 |
| 5 | 0.04 |
| 6 | 0.12 |
| 7 | 0.24 |
| 8 | 0.2 |
| 9 | 0.16 |
| 10 | 0.2 |
| 11 | 0.32 |
| 12 | 0.12 |
| 13 | 0.08 |
| 14 | 0.04 |
| 15 | 0 |
| 16 | 0.04 |
| 17 | 0.04 |
| 18 | 0.08 |
| 19 | 0.12 |
| 20 | 0.12 |
| Mean | 0.14 |
| Std dev | 0.089443 |
| n | 25 |
| Std error | 0.017889 |
| Mean-3 se | 0.086334 |
| Mean+3se | 0.193666 |
