Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Help on Problem 8

## 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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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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