Temperature is used to measure the output of a production process. When the process is in control, the mean of the process is u = 128.5 and the standard deviation is o = .4. a. Construct the X control chart and upper control limit and lower control limit for this process if samples of size 6 are used. (to 2 decimals). UCL LCL b. Determine if the process is in control for a sample with data 128.6, 128.0, 129.2, 128.8, 128.5, and 129.0. What is the value of X (to 2 decimals)? What is your conclusion? Select C. Determine if the process is in control for a sample with data 129.0, 128.8, 128.4, 129.0, 129.5, and 129.4. What is the value of x (to 2 decimals)? What is your conclusion? Select

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**Temperature Monitoring in Production Process**

Temperature is crucial for monitoring the output of a production process. When the process operates under control, the mean (μ) is 128.5 with a standard deviation (σ) of 0.4. Below are the tasks and calculations for determining the control limits and assessing process control status using sample data.

### a. Constructing Control Limits

To construct the \( \bar{X} \) control chart with an upper control limit (UCL) and lower control limit (LCL) for samples of size 6:
- **UCL**: [Input Box]
- **LCL**: [Input Box]

### b. Sample Analysis: Data Set 1

*Evaluate if the process is in control using the sample data: 128.6, 128.0, 129.2, 128.8, 128.5, 129.0.*

- **Calculate \( \bar{X} \)** (to 2 decimals): [Input Box]
- **Conclusion**: [Dropdown Menu: "In Control"/"Out of Control"]

### c. Sample Analysis: Data Set 2

*Evaluate if the process is in control using the sample data: 129.0, 128.8, 128.4, 129.0, 129.5, 129.4.*

- **Calculate \( \bar{X} \)** (to 2 decimals): [Input Box]
- **Conclusion**: [Dropdown Menu: "In Control"/"Out of Control"]

Use this guide to evaluate and ensure that the production process maintains the desired output quality.
Transcribed Image Text:**Temperature Monitoring in Production Process** Temperature is crucial for monitoring the output of a production process. When the process operates under control, the mean (μ) is 128.5 with a standard deviation (σ) of 0.4. Below are the tasks and calculations for determining the control limits and assessing process control status using sample data. ### a. Constructing Control Limits To construct the \( \bar{X} \) control chart with an upper control limit (UCL) and lower control limit (LCL) for samples of size 6: - **UCL**: [Input Box] - **LCL**: [Input Box] ### b. Sample Analysis: Data Set 1 *Evaluate if the process is in control using the sample data: 128.6, 128.0, 129.2, 128.8, 128.5, 129.0.* - **Calculate \( \bar{X} \)** (to 2 decimals): [Input Box] - **Conclusion**: [Dropdown Menu: "In Control"/"Out of Control"] ### c. Sample Analysis: Data Set 2 *Evaluate if the process is in control using the sample data: 129.0, 128.8, 128.4, 129.0, 129.5, 129.4.* - **Calculate \( \bar{X} \)** (to 2 decimals): [Input Box] - **Conclusion**: [Dropdown Menu: "In Control"/"Out of Control"] Use this guide to evaluate and ensure that the production process maintains the desired output quality.
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