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Q14. The following table contains the measurements of the key length dimensions from a fuel injector.These samples of size five were taken at one -hour intervals. a. Construct a three-sigma x-chart and R-chart (use Exhibit 6.13) for the length of the fuel injector.what can you say about this process? The picture of Exhibit 6.13 is attached  The picture with the sample number and observations also attached. Thanks

Q14. The following table contains the measurements of the key length dimensions from a fuel injector.These samples of size five were taken at one -hour intervals. a. Construct a three-sigma x-chart and R-chart (use Exhibit 6.13) for the length of the fuel injector.what can you say about this process? The picture of Exhibit 6.13 is attached  The picture with the sample number and observations also attached. Thanks

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
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Q14. The following table contains the measurements of the key length dimensions from a fuel injector.These samples of size five were taken at one -hour intervals.

a. Construct a three-sigma x-chart and R-chart (use Exhibit 6.13) for the length of the fuel injector.what can you say about this process?

The picture of Exhibit 6.13 is attached 

The picture with the sample number and observations also attached. Thanks 

 

**Title: Analyzing Key Length Measurements of a Fuel Injector** **Introduction:** This section presents an analysis based on a p-chart to suggest any needed reallocation of crime protection effort. For the analysis, the selected confidence level is 95%, corresponding to Z = 1.96. **Data Overview:** The table below contains the measurements of the key length dimension from a fuel injector. These measurements were taken as samples of size five at one-hour intervals. **Table of Observations:** | Sample Number | Observation 1 | Observation 2 | Observation 3 | Observation 4 | Observation 5 | |---------------|---------------|---------------|---------------|---------------|---------------| | 1 | 0.486 | 0.493 | 0.511 | 0.481 | | 2 | 0.499 | 0.506 | 0.516 | 0.494 | 0.529 | | 3 | 0.496 | 0.506 | 0.515 | 0.488 | 0.521 | | 4 | 0.500 | 0.482 | 0.483 | 0.487 | 0.489 | | 5 | 0.472 | 0.478 | 0.475 | 0.526 | 0.469 | | 6 | 0.473 | 0.485 | 0.507 | 0.493 | 0.506 | | 7 | 0.495 | 0.498 | 0.490 | 0.471 | 0.504 | | 8 | 0.525 | 0.501 | 0.498 | 0.474 | 0.485 | | 9 | 0.497 | 0.527 | 0.535 | 0.506 | 0.516 | | 10 | 0.495 | 0.500 | 0.516 | 0.511 | 0.497 | | 11 | 0.495 | 0.489
Transcribed Image Text:**Title: Analyzing Key Length Measurements of a Fuel Injector** **Introduction:** This section presents an analysis based on a p-chart to suggest any needed reallocation of crime protection effort. For the analysis, the selected confidence level is 95%, corresponding to Z = 1.96. **Data Overview:** The table below contains the measurements of the key length dimension from a fuel injector. These measurements were taken as samples of size five at one-hour intervals. **Table of Observations:** | Sample Number | Observation 1 | Observation 2 | Observation 3 | Observation 4 | Observation 5 | |---------------|---------------|---------------|---------------|---------------|---------------| | 1 | 0.486 | 0.493 | 0.511 | 0.481 | | 2 | 0.499 | 0.506 | 0.516 | 0.494 | 0.529 | | 3 | 0.496 | 0.506 | 0.515 | 0.488 | 0.521 | | 4 | 0.500 | 0.482 | 0.483 | 0.487 | 0.489 | | 5 | 0.472 | 0.478 | 0.475 | 0.526 | 0.469 | | 6 | 0.473 | 0.485 | 0.507 | 0.493 | 0.506 | | 7 | 0.495 | 0.498 | 0.490 | 0.471 | 0.504 | | 8 | 0.525 | 0.501 | 0.498 | 0.474 | 0.485 | | 9 | 0.497 | 0.527 | 0.535 | 0.506 | 0.516 | | 10 | 0.495 | 0.500 | 0.516 | 0.511 | 0.497 | | 11 | 0.495 | 0.489
### Factors for Determining the Three-Sigma Control Limits for \(\bar{X}\)- and \(R\)-Charts #### Exhibit 6.13 This table provides factors for calculating control limits for \(\bar{X}\)-charts and \(R\)-charts, which are used in statistical process control to monitor process variation. #### Table: | Number of Observations in Subgroup (\(n\)) | Factor for \(\bar{X}\)-Chart (\(A_2\)) | Lower Control Limit (\(D_3\)) | Upper Control Limit (\(D_4\)) | |--------------------------------------------|----------------------------------------|-------------------------------|-------------------------------| | 2 | 1.88 | 0 | 3.27 | | 3 | 1.02 | 0 | 2.57 | | 4 | 0.73 | 0 | 2.28 | | 5 | 0.58 | 0 | 2.11 | | 6 | 0.48 | 0 | 2.00 | | 7 | 0.42 | 0.08 | 1.92 | | 8 | 0.37 | 0.14 | 1.86 | | 9 | 0.34 | 0.18 | 1.82 | | 10 | 0.31 | 0.22 | 1.78 | | 11 | 0.29 | 0.26 | 1.74 | | 12 | 0.27 | 0.28 | 1.72 | | 13 | 0.25 | 0.31 | 1.69 | | 14 | 0.24 | 0.33 | 1.67 | | 15 | 0.22 | 0.35 | 1.65 | | 16 | 0.21 | 0.36 | 1.64 | | 17 | 0.20 | 0.37 | 1.62 | | 18
Transcribed Image Text:### Factors for Determining the Three-Sigma Control Limits for \(\bar{X}\)- and \(R\)-Charts #### Exhibit 6.13 This table provides factors for calculating control limits for \(\bar{X}\)-charts and \(R\)-charts, which are used in statistical process control to monitor process variation. #### Table: | Number of Observations in Subgroup (\(n\)) | Factor for \(\bar{X}\)-Chart (\(A_2\)) | Lower Control Limit (\(D_3\)) | Upper Control Limit (\(D_4\)) | |--------------------------------------------|----------------------------------------|-------------------------------|-------------------------------| | 2 | 1.88 | 0 | 3.27 | | 3 | 1.02 | 0 | 2.57 | | 4 | 0.73 | 0 | 2.28 | | 5 | 0.58 | 0 | 2.11 | | 6 | 0.48 | 0 | 2.00 | | 7 | 0.42 | 0.08 | 1.92 | | 8 | 0.37 | 0.14 | 1.86 | | 9 | 0.34 | 0.18 | 1.82 | | 10 | 0.31 | 0.22 | 1.78 | | 11 | 0.29 | 0.26 | 1.74 | | 12 | 0.27 | 0.28 | 1.72 | | 13 | 0.25 | 0.31 | 1.69 | | 14 | 0.24 | 0.33 | 1.67 | | 15 | 0.22 | 0.35 | 1.65 | | 16 | 0.21 | 0.36 | 1.64 | | 17 | 0.20 | 0.37 | 1.62 | | 18
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