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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
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.
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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