Bottles of aspirin tablets typically have labels indicating that each tablet contains 325 mg of aspirin, but the actual amounts can vary between 315 mg and 335 mg. A tablet is defective if it has less than 315 mg of aspirin or more than 335 mg of aspirin. Listed below are numbers of defects found in batches of 1000 tablets. Use the given process data to construct a control chart for p. Use the three out-of-control criteria to determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply. 13 11 8 6 5 6 4 17 O A. 17 Construct a control chart for p. Choose the correct graph below. Proportion 0.02 0.01- 10 0 2 4 6 8 10 Sample Q Q B. Proportion 0.03 0.02- 0.01- 0 2 4 6 8 10 Sample Q C. Proportion 0.02 Um 0 2 4 6 8 10 Sample D. Proportion 0.03 0.02- 0.01- 0 2 4 6 8 10 Sample Use the three out-of-control criteria to determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply. Select all that apply. A. The process is out of statistical control because there is a pattern, trend, or cycle that is obviously not random. B. The process is out of statistical control because there are at least eight consecutive points all above or all below the centerline. C. The process is out of statistical control because there is at least one point above the upper control limit or at least one point below the lower control limits. D. The process is within statistical control because none of the out-of-control criteria are satisfied.

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### Control Charts in Quality Control

Bottles of aspirin tablets typically have labels claiming each tablet contains 325 mg of aspirin. However, the actual amounts can vary between 315 mg and 335 mg. A tablet is deemed defective if it contains less than 315 mg or more than 335 mg of aspirin. Below are the number of defects found in batches of 1000 tablets:

**Defects per Batch:** 17, 17, 13, 10, 11, 8, 6, 6, 5, 6, 4

The objective is to construct a control chart for the proportion (p) of defects and determine if the process is within statistical control. If not, identify which of the three out-of-control criteria are applicable.

#### Control Charts

Four options (A, B, C, D) of control charts are provided:

- **Graph A:** Display a downward trend in the proportion of defects from sample 0 to 10.
- **Graph B:** Also shows a downward trend but starts from a higher proportion, crossing control limits.
- **Graph C:** Exhibits fluctuations within a stable range.
- **Graph D:** Represents a consistent downward trend but within broader control limits.

#### Out-of-Control Criteria

Use the following criteria to decide if the process is out of control:

- **A.** Out of control due to an obvious non-random pattern, trend, or cycle.
- **B.** Out of control as there are at least eight consecutive points all above or all below the centerline.
- **C.** Out of control because there is at least one point above the upper control limit or at least one point below the lower control limit.
- **D.** Within control as none of the above out-of-control criteria are met.

Identifying whether the process is under statistical control helps maintain quality and consistency in production.
Transcribed Image Text:### Control Charts in Quality Control Bottles of aspirin tablets typically have labels claiming each tablet contains 325 mg of aspirin. However, the actual amounts can vary between 315 mg and 335 mg. A tablet is deemed defective if it contains less than 315 mg or more than 335 mg of aspirin. Below are the number of defects found in batches of 1000 tablets: **Defects per Batch:** 17, 17, 13, 10, 11, 8, 6, 6, 5, 6, 4 The objective is to construct a control chart for the proportion (p) of defects and determine if the process is within statistical control. If not, identify which of the three out-of-control criteria are applicable. #### Control Charts Four options (A, B, C, D) of control charts are provided: - **Graph A:** Display a downward trend in the proportion of defects from sample 0 to 10. - **Graph B:** Also shows a downward trend but starts from a higher proportion, crossing control limits. - **Graph C:** Exhibits fluctuations within a stable range. - **Graph D:** Represents a consistent downward trend but within broader control limits. #### Out-of-Control Criteria Use the following criteria to decide if the process is out of control: - **A.** Out of control due to an obvious non-random pattern, trend, or cycle. - **B.** Out of control as there are at least eight consecutive points all above or all below the centerline. - **C.** Out of control because there is at least one point above the upper control limit or at least one point below the lower control limit. - **D.** Within control as none of the above out-of-control criteria are met. Identifying whether the process is under statistical control helps maintain quality and consistency in production.
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