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Upper Control Limit (UCLR) = inches (round your response to three decimal places).

Upper Control Limit (UCLR) = inches (round your response to three decimal places).

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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**Control Chart Factors for Different Sample Sizes** This table provides key factors for creating control charts, specifically used in process control and quality management. The factors adjust according to the sample size (n) to help determine control limits for mean and range charts. | Sample Size, n | Mean Factor, A₂ | Upper Range, D₄ | Lower Range, D₃ | |----------------|-----------------|-----------------|-----------------| | 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 | **Explanation of Columns:** - **Sample Size, n**: This denotes the number of samples taken (e.g., 2, 3, 4, etc.). - **Mean Factor, A₂**: This factor is used in the calculation of control limits for the average (mean) chart. It helps determine how much the average should deviate. - **Upper Range, D₄**: This is a multiplicative factor used to calculate the upper control limit for a range chart. It helps ensure variations are kept within acceptable limits. - **Lower Range, D₃**: This factor is used to calculate the lower control limit for a range chart. When D₃ is zero, it means there is no lower control limit applicable for those sample sizes. These factors are essential for maintaining quality control in manufacturing and other industries that require precise process monitoring.
Transcribed Image Text:**Control Chart Factors for Different Sample Sizes** This table provides key factors for creating control charts, specifically used in process control and quality management. The factors adjust according to the sample size (n) to help determine control limits for mean and range charts. | Sample Size, n | Mean Factor, A₂ | Upper Range, D₄ | Lower Range, D₃ | |----------------|-----------------|-----------------|-----------------| | 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 | **Explanation of Columns:** - **Sample Size, n**: This denotes the number of samples taken (e.g., 2, 3, 4, etc.). - **Mean Factor, A₂**: This factor is used in the calculation of control limits for the average (mean) chart. It helps determine how much the average should deviate. - **Upper Range, D₄**: This is a multiplicative factor used to calculate the upper control limit for a range chart. It helps ensure variations are kept within acceptable limits. - **Lower Range, D₃**: This factor is used to calculate the lower control limit for a range chart. When D₃ is zero, it means there is no lower control limit applicable for those sample sizes. These factors are essential for maintaining quality control in manufacturing and other industries that require precise process monitoring.
Refer to [Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)] for this problem. Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | |------|-------------|-----|------|-------------|-----|------|-------------|-----|------|-------------|-----| | 1 | 3.25" | 0.71"| 7 | 3.05" | 0.58"| 13 | 3.21" | 0.85"| 19 | 3.31" | 1.66"| | 2 | 3.20" | 1.18"| 8 | 2.65" | 1.13"| 14 | 2.93" | 1.31"| 20 | 2.79" | 1.09"| | 3 | 3.12" | 0.71"| 9 | 3.12" | 0.71"| 15 | 3.22" | 1.01"| 21 | 2.75" | 1.13"| | 4 | 3.29" | 1.26"| 10 | 2.95" | 1.38"| 16 | 2.94" | 0.45"| 22 | 3.28" | 0.51"| | 5 | 3.17" | 1.17"| 11 | 2.93" | 1.17"| 17 | 2.96" | 1.48"| 23 | 3.04" | 1.53"| | 6 | 2.86" | 0.42"| 12 | 2.97" | 0.35"| 18 | 2.64"
Transcribed Image Text:Refer to [Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)] for this problem. Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | Hour | \(\bar{x}\) | R | |------|-------------|-----|------|-------------|-----|------|-------------|-----|------|-------------|-----| | 1 | 3.25" | 0.71"| 7 | 3.05" | 0.58"| 13 | 3.21" | 0.85"| 19 | 3.31" | 1.66"| | 2 | 3.20" | 1.18"| 8 | 2.65" | 1.13"| 14 | 2.93" | 1.31"| 20 | 2.79" | 1.09"| | 3 | 3.12" | 0.71"| 9 | 3.12" | 0.71"| 15 | 3.22" | 1.01"| 21 | 2.75" | 1.13"| | 4 | 3.29" | 1.26"| 10 | 2.95" | 1.38"| 16 | 2.94" | 0.45"| 22 | 3.28" | 0.51"| | 5 | 3.17" | 1.17"| 11 | 2.93" | 1.17"| 17 | 2.96" | 1.48"| 23 | 3.04" | 1.53"| | 6 | 2.86" | 0.42"| 12 | 2.97" | 0.35"| 18 | 2.64"
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