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Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? x= 156.76 mm (round your response to two decimal places). b) What is the value of R? R= 4.40 mm (round your response to two decimal places). c) What are the UCL; and LCL using 3-sigma? Upper Control Limit (UCL)= 158.12 mm (round your response to two decimal places). Lower Control Limit (LCL) = 155.40 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= mm (round your response to two decimal places). Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 Range R (mm) 4.2 4.4 4.3 4.8 4.3

Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? x= 156.76 mm (round your response to two decimal places). b) What is the value of R? R= 4.40 mm (round your response to two decimal places). c) What are the UCL; and LCL using 3-sigma? Upper Control Limit (UCL)= 158.12 mm (round your response to two decimal places). Lower Control Limit (LCL) = 155.40 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= mm (round your response to two decimal places). Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 Range R (mm) 4.2 4.4 4.3 4.8 4.3

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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please provide upper and lower limit

**Auto Pistons Diameter Control at Wemming Chung's Shanghai Plant** The diameters of auto pistons produced at Wemming Chung's plant in Shanghai are critical and controlled factors in the forging process. Sample measurements of 10 pistons produced each day have been recorded, with the daily mean and range of this diameter shown in the table below: | Day | Mean \( \bar{x} \) (mm) | Range \( R \) (mm) | |-----|------------------------|------------------| | 1 | 158.9 | 4.2 | | 2 | 155.2 | 4.4 | | 3 | 155.6 | 4.3 | | 4 | 157.5 | 4.8 | | 5 | 156.6 | 4.3 | **Calculations:** a) **What is the value of \( \bar{\bar{x}} \)?** \(\bar{\bar{x}} = \text{156.76 mm (round your response to two decimal places).}\) b) **What is the value of \( \bar{R} \)?** \(\bar{R} = \text{4.40 mm (round your response to two decimal places).}\) c) **What are the \( UCL_x \) and \( LCL_x \) using 3-sigma?** - Upper Control Limit (\( UCL_x \)) = **158.12 mm (round your response to two decimal places).** - Lower Control Limit (\( LCL_x \)) = **155.40 mm (round your response to two decimal places).** d) **What are the \( UCL_R \) and \( LCL_R \) using 3-sigma?** - Upper Control Limit (\( UCL_R \)) = **[Not specified, fill in based on context and calculation requirements] mm (round your response to two decimal places).**
Transcribed Image Text:**Auto Pistons Diameter Control at Wemming Chung's Shanghai Plant** The diameters of auto pistons produced at Wemming Chung's plant in Shanghai are critical and controlled factors in the forging process. Sample measurements of 10 pistons produced each day have been recorded, with the daily mean and range of this diameter shown in the table below: | Day | Mean \( \bar{x} \) (mm) | Range \( R \) (mm) | |-----|------------------------|------------------| | 1 | 158.9 | 4.2 | | 2 | 155.2 | 4.4 | | 3 | 155.6 | 4.3 | | 4 | 157.5 | 4.8 | | 5 | 156.6 | 4.3 | **Calculations:** a) **What is the value of \( \bar{\bar{x}} \)?** \(\bar{\bar{x}} = \text{156.76 mm (round your response to two decimal places).}\) b) **What is the value of \( \bar{R} \)?** \(\bar{R} = \text{4.40 mm (round your response to two decimal places).}\) c) **What are the \( UCL_x \) and \( LCL_x \) using 3-sigma?** - Upper Control Limit (\( UCL_x \)) = **158.12 mm (round your response to two decimal places).** - Lower Control Limit (\( LCL_x \)) = **155.40 mm (round your response to two decimal places).** d) **What are the \( UCL_R \) and \( LCL_R \) using 3-sigma?** - Upper Control Limit (\( UCL_R \)) = **[Not specified, fill in based on context and calculation requirements] mm (round your response to two decimal places).**
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