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1. The data shown in Table 1 are and R values for 20 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 3 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 33.8 2 15 35.6 7 6. 38.4 3 16 30.8 7 31.6 4 17 33.0 8 36.8 10 18 31.6 3 35.0 15 19 28.2 10 34.0 20 33.8

1. The data shown in Table 1 are and R values for 20 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 3 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 33.8 2 15 35.6 7 6. 38.4 3 16 30.8 7 31.6 4 17 33.0 8 36.8 10 18 31.6 3 35.0 15 19 28.2 10 34.0 20 33.8

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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**Bearing Diameter Data Analysis** **Context:** The data presented in Table 1 consists of \(\overline{x}\) (mean) and \(R\) (range) values for 20 samples, each of size \(n = 5\), taken from a bearing production process. The measurements focus on the inside diameter of the bearing, recorded to three decimal places. **Tasks:** (a) Develop \(\overline{x}\) and \(R\) control charts for this process. Assess whether the process is in statistical control. If not, adjust the trial control limits as required. (b) Considering the assumption that the diameter exhibits a normal distribution, estimate the process's standard deviation. **Data:** | Sample | \(\overline{x}\) | \(R\) | Sample | \(\overline{x}\) | \(R\) | |--------|-----------------|------|--------|-----------------|------| | 1 | 31.6 | 4 | 11 | 29.8 | 4 | | 2 | 33.0 | 3 | 12 | 34.0 | 4 | | 3 | 35.0 | 4 | 13 | 33.0 | 10 | | 4 | 32.2 | 4 | 14 | 34.8 | 4 | | 5 | 33.8 | 6 | 15 | 35.6 | 7 | | 6 | 38.4 | 10 | 16 | 30.8 | 6 | | 7 | 31.6 | 4 | 17 | 33.0 | 5 | | 8 | 36.8 | 10 | 18 | 31.6 | 6 | | 9 | 35.0 | 15 | 19 | 28.2 | 9 | | 10 | 34.0 | 6 | 20 | 33.8 | 6 | *Table 1: Bearing Diameter Data* Use these values to construct control charts, analyze stability,
Transcribed Image Text:**Bearing Diameter Data Analysis** **Context:** The data presented in Table 1 consists of \(\overline{x}\) (mean) and \(R\) (range) values for 20 samples, each of size \(n = 5\), taken from a bearing production process. The measurements focus on the inside diameter of the bearing, recorded to three decimal places. **Tasks:** (a) Develop \(\overline{x}\) and \(R\) control charts for this process. Assess whether the process is in statistical control. If not, adjust the trial control limits as required. (b) Considering the assumption that the diameter exhibits a normal distribution, estimate the process's standard deviation. **Data:** | Sample | \(\overline{x}\) | \(R\) | Sample | \(\overline{x}\) | \(R\) | |--------|-----------------|------|--------|-----------------|------| | 1 | 31.6 | 4 | 11 | 29.8 | 4 | | 2 | 33.0 | 3 | 12 | 34.0 | 4 | | 3 | 35.0 | 4 | 13 | 33.0 | 10 | | 4 | 32.2 | 4 | 14 | 34.8 | 4 | | 5 | 33.8 | 6 | 15 | 35.6 | 7 | | 6 | 38.4 | 10 | 16 | 30.8 | 6 | | 7 | 31.6 | 4 | 17 | 33.0 | 5 | | 8 | 36.8 | 10 | 18 | 31.6 | 6 | | 9 | 35.0 | 15 | 19 | 28.2 | 9 | | 10 | 34.0 | 6 | 20 | 33.8 | 6 | *Table 1: Bearing Diameter Data* Use these values to construct control charts, analyze stability,
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