a. Develop a p-chart with a z = 3. b. Suppose that the next four samples selected had 5, 2, 4, and 1 defects. What conclusion can you make?
a. Develop a p-chart with a z = 3. b. Suppose that the next four samples selected had 5, 2, 4, and 1 defects. What conclusion can you make?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![## Tire Manufacturer Quality Control
A tire manufacturer has been concerned about the number of defective tires found recently. To evaluate the true magnitude of the problem, a production manager selected 10 random samples of 20 units each for inspection. The number of defective tires found in each sample are as follows:
### Data Table
| Sample | Number Defective |
|--------|------------------|
| 1 | 0 |
| 2 | 2 |
| 3 | 3 |
| 4 | 2 |
| 5 | 5 |
| 6 | 2 |
| 7 | 1 |
| 8 | 1 |
| 9 | 2 |
| 10 | 3 |
### Exercises
**a.** Develop a p-chart with a z = 3.
**b.** Suppose that the next four samples selected had 5, 2, 4, and 1 defects. What conclusion can you make?
### Explanation
**a. p-chart Development**: A p-chart (proportion chart) is a type of control chart used to monitor the proportion of defective items in a process. To construct the p-chart, calculate the center line (average proportion defective), and the upper and lower control limits using the given z-value.
**b. Conclusion Analysis**: Analyze whether the new sample values fall within the control limits of the p-chart to determine if the process is still in control or if there are indications of a change in the process quality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ea8fc0c-7d56-44c0-aa3c-420ce6cba61f%2F4d1aee51-4ffa-44a7-95d9-0dbec5283b93%2Fln36fsp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Tire Manufacturer Quality Control
A tire manufacturer has been concerned about the number of defective tires found recently. To evaluate the true magnitude of the problem, a production manager selected 10 random samples of 20 units each for inspection. The number of defective tires found in each sample are as follows:
### Data Table
| Sample | Number Defective |
|--------|------------------|
| 1 | 0 |
| 2 | 2 |
| 3 | 3 |
| 4 | 2 |
| 5 | 5 |
| 6 | 2 |
| 7 | 1 |
| 8 | 1 |
| 9 | 2 |
| 10 | 3 |
### Exercises
**a.** Develop a p-chart with a z = 3.
**b.** Suppose that the next four samples selected had 5, 2, 4, and 1 defects. What conclusion can you make?
### Explanation
**a. p-chart Development**: A p-chart (proportion chart) is a type of control chart used to monitor the proportion of defective items in a process. To construct the p-chart, calculate the center line (average proportion defective), and the upper and lower control limits using the given z-value.
**b. Conclusion Analysis**: Analyze whether the new sample values fall within the control limits of the p-chart to determine if the process is still in control or if there are indications of a change in the process quality.
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