Homework SoursePlease show all your work to all parts of the problem 5 Th
**** Please show all your work to all parts of the problem ****
5- The data given below contains the number of defective products found in a sample of 25 randomly selected from each hour’s production for 20 hours.
a- Construct a control chart for the proportion of defective products.
b- Is the process in control?
c- Conduct a runs analysis for this control chart.
DATA:-
| 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
First find mean and std dev for the sample
Control means within 3 sigma times from the mean
mu-3sigma = 0.078032
mu+3 sigma = 0.201968
Comparing with our sample chart,
0.04 is below control level and
0.24, 0.28, 0.32 are above contol level.
Here is the 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 |
| Mean | 0.14 |
| Std dev | 0.092376 |
| Std error | 0.020656 |
