Sample Size, n 2 3 4 6 8 9 10 12 Mean Factor, A₂ 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 Lower Control Limit (LCL) = b) The control limits for the 3-sigma Upper Control Limit (UCLR) Lower Control Limit (LCLR)= Lower Range, D3 0 0 0 0 0 0.076 0.136 0.184 0.223 0.284 Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.; Average range R = 1.78 lb. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCL;)=Ib. (round your response to three decimal places). lb. (round your response to three decimal places). R-chart are: Ib. (round your response to three decimal places). Ib. (round your response to three decimal places).
Sample Size, n 2 3 4 6 8 9 10 12 Mean Factor, A₂ 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 Lower Control Limit (LCL) = b) The control limits for the 3-sigma Upper Control Limit (UCLR) Lower Control Limit (LCLR)= Lower Range, D3 0 0 0 0 0 0.076 0.136 0.184 0.223 0.284 Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.; Average range R = 1.78 lb. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCL;)=Ib. (round your response to three decimal places). lb. (round your response to three decimal places). R-chart are: Ib. (round your response to three decimal places). Ib. (round your response to three decimal places).
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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Question

Transcribed Image Text:### Transcription for Educational Website:
#### Table of Control Chart Factors
| Sample Size, n | Mean Factor, \( A_2 \) | Upper Range, \( D_4 \) | Lower Range, \( D_3 \) |
|----------------|-----------------------|---------------------|---------------------|
| 2 | 1.880 | 3.268 | 0 |
| 3 | 1.023 | 2.574 | 0 |
| 4 | 0.729 | 2.282 | 0 |
| 5 | 0.577 | 2.115 | 0 |
| 6 | 0.483 | 2.004 | 0 |
| 7 | 0.419 | 1.924 | 0.076 |
| 8 | 0.373 | 1.864 | 0.136 |
| 9 | 0.337 | 1.816 | 0.184 |
| 10 | 0.308 | 1.777 | 0.223 |
| 12 | 0.266 | 1.716 | 0.284 |
#### Description of Sample Data:
Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were:
- Overall mean = 60.75 lb.
- Average range \( \overline{R} \) = 1.78 lb.
#### Control Limits Calculations:
**a) For the given sample size, the control limits for the 3-sigma \( \bar{x} \) chart are:**
- Upper Control Limit (UCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places).
- Lower Control Limit (LCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places).
**b) The control limits for the 3-sigma R-chart are:**
- Upper Control Limit (UCL\(_R
Expert Solution
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Step 1: Determine the given variables
Overall mean (X-double bar) = 60.75 lb
Average range (R-bar) = 1.78 lb
Sample size (n) = 7
Step by step
Solved in 3 steps
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