ASSIGNMENT2

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Conestoga College *

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8091

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Statistics

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Feb 20, 2024

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Uploaded by DeanCaterpillar3662

1(a). Choose the correct location and variation chart for the data analysis. Explain in the Word file the reason behind your choice. [1 mark] Here takes a closer look at why the X-bar chart for location and the R chart for variation are acceptable in this situation. 1. Location (Central Tendency) X-Bar Chart:  The X-bar chart is used to track the average or central tendency of a process across time.  In your situation, each sample (Sample Number 1 through 5) has numerous measurements (X1 through X7). The X-bar chart computes the average (X-bar) for each sample, indicating the process's center of gravity.  Plotting the X-bar values across time allows you to discover shifts or patterns in the process's central tendency. 2. R Variation Chart:  The R chart is used to track the variability or dispersion of a process across time.  You have several measurements (X1 through X7) for each sample in your data. The R chart computes the range (R) for each sample, which represents the dispersion or variability within each sample.  Monitoring R values can assist identify changes in process variance, such as an increase in variability or the appearance of outliers. Why are X-bar and R charts used? Efficiency: For low sample sets, X-bar and R charts provide a reasonable blend of sensitivity to process changes and practicality. full Monitoring: By addressing both central tendency and variance, these charts provide a full perspective of the process. Ease of Interpretation: Because X-bar and R charts are reasonably simple to understand, they are commonly employed in statistical process control.

Using the Charts:  X-bar Chart: Look for spots that exceed the estimated control boundaries. This signals a dramatic shift in the process's primary tendency.  R Chart: Look for spots that are outside the control boundaries. Outliers in the R chart may suggest unusual reasons of variance, such as measurement mistakes or process modifications. Using X-bar and R charts, you may methodically evaluate the data, notice any changes in the process, and take relevant steps to maintain or improve process performance. These charts are useful in quality control and process improvement programs. 1(d). Is the process in statistical control? Explain why or why not in the Word file. [1 mark] According to the data in the table, the procedure is not under statistical control. The following are the reasons: X-bar Out-of-Control Points: There are FALSE values in the "Out control of X-bar" column, indicating that the X-bar chart has no out-of-control points. This corresponds to the X-bar chart's control boundaries being inside the predicted range. R's Out-of-Control Points: There are TRUE values in the "Out control of R-bar" column, suggesting that the R chart has out-of-control points. This implies that there are samples with ranges that exceed the computed R chart control limits. Trends and Patterns: Examine the X-bar and R charts for any patterns, trends, or spots that are outside of the control bounds. Out-of-control points on the R chart show higher process variance in this example.

1(e). Use the trial control limits from part 1.(b) to identify all the out-of- control sample points in Excel. [2 marks] The out-of-control sample points, as indicated by TRUE values in the "Out control of R-bar" column, are: Sample 2, Sample 3, Sample 4, Sample 5, Sample 6, and Sample 7 The ranges of these samples exceed the computed control limits for the R chart. 1(f). If the process is out of control, revise your control limits for location and variation charts in Excel, assuming that any samples that plot outside of the control limits can be eliminated. Find the revised UCL, CL, LCL for the location chart [0.75 x 3 = 2.25 marks] Find the revised UCL, CL, LCL for the variation chart [0.75 x 3 = 2.25 marks] For the Location Diagram (X-bar): If any samples were found to be out of control for X-bar, you can remove them and recalculate the X-bar, R, and control limits. However, based on the information supplied, there are no out-of-control spots for X-bar. For Chart Variation (R): Because the R chart contains out-of-control points, consider modifying control limits by eliminating those points and recalculating R-bar, UCL_R, and LCL_R. R-chart UCL, CL, and LCL revisions: R-bar should be recalculated (average range eliminating out-of-control points).

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Use the following formulas: UCL_R Revised = D4 * R-bar Revised CL_R Revised = R-bar has been updated. LCL_R Revised = D3 * R-bar Revised

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