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- 1. Data and calculationsX-Bar and R-Chart This spreadsheet is designed for up to 50 samples, each of a constant sample size from 2 to 10. Enter the data ONLY in yellow-shaded cells.Enter the number of samples in cell E6 and the sample size in cell E7. Then enter your data in the grid below. Click on sheet tabs for a display of the control charts. Specification limits may be entered in cells N7 and N8 for process capability.Number of samples (<= 50)Sample size (2 - 10)Grand AverageERROR:#DIV/0!A2D3D4d2Average RangeERROR:#DIV/0!ERROR:#N/AERROR:#N/AERROR:#N/ AERROR:#N/ADATA1234567891011121314151617181920212 22324252627282930313233343536373839404142434445464748 495012345678910AverageERROR:#N/AERROR:#N/AERROR:# N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERR OR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/ AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERRO R:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/A ERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR: #N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AER ROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N /AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERRO R:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/A ERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR: #N/AERROR:#N/ALCLx- barERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:# DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERRO R:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ER ROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0! ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DI V/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR: #DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERR OR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!E RROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/ 0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#DIV/0!ERROR:#D
- 4. /AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERRO R:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/A ERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR: #N/AERROR:#N/AERROR:#N/AERROR:#N/AERROR:#N/AER ROR:#N/AERROR:#N/AERROR:#N/AID NOTE: This has been provided to assist the student in completing the Week 7 project. DO NOT MODIFY THIS TABLEControl Chart FactorsnA2D3D4d2A3B3B421.8803.2671.1282.65903.26731.02 302.5741.6931.95402.56840.72902.2822.0591.62802.26650.577 02.1142.3261.42702.08960.48302.0042.5341.2870.031.9770.41 90.0761.9242.7041.1820.1181.88280.3730.1361.8642.8471.099 0.1851.81590.3370.1841.8162.971.0320.2391.761100.3080.223 1.7773.0780.9750.2841.716 X-Bar Chart X-bar Chart Averages#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A# N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A# N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A# N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A# N/A#N/A#N/A#N/ALower control limit0000000000000000000000000000000000000000000000000 0Upper control limit0000000000000000000000000000000000000000000000000 0Center line0000000000000000000000000000000000000000000000000 0 Sample number Averages R-Chart R-Chart Ranges#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/ A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/
- 5. A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/ A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/ A#N/A#N/A#N/ALower control limit#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/AUpper control limit#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A #N/A#N/A#N/ACenter line0000000000000000000000000000000000000000000000000 0 Sample number Ranges The student will submit the completed case study in a Word document to the Dropbox by the end of class Week 7. The paper is worth 80 points. The students will complete and answer the following questions. 1. Calculate X-bar-bar, R-bar, and associated control limits using the data in the table above. 2. Create x̄ and R (average and range) control charts from the data in the table above. 3. Discuss notable out-of-control conditions displayed in the completed x̄ and R (average and range) control charts. Only consider points outside the control limits. Do not consider runs, set of points within certain zones, and so forth. 4. If the conditions you note could be defined as assignable conditions, and they are removed from the process, then what
- 6. will happen to the X-bar and R control chart? 1. Remove the data related to the out-of-control points you observed from the original data, and recalculate new X-bar-bar, R-bar, and associated control limits. 2. Create new X-bar and R (average and range) control charts from your updated data. 5. Discuss how the two sets of control charts are different. What has changed? The format of the case study should conform to the Publication Manual for the American Psychological Association (APA), 6th edition, for the title page and text. Citations and references are not required. A basic APA tutorial can be found in the Webliography, and a paper template can be found in Doc Sharing. The completed case study will be submitted to your Dropbox as an MS Word document. All graphics and charts will be a part of the Word document and submitted as a file. Documents authored in other applications, such as WordPerfect or MS Works, will not be accepted. Week 7 Course Project Part 2 Tutorial Note: This is a sample outline of how to proceed with this case. The data here are not the same as the data in your case. DO NOT USE THESE DATA in your case. This tutorial uses the template provide in the case. Most find using this template makes the completion of this case much easier. Scenario/Summary
- 7. 1. A transmission manufacturing company has been having process difficulties at one its assembly stations. Thirty samples of four gears (n = 4) have been selected from the process and are provided below. Observations Sample 1 2 3 4 1 4.92 4.26 4.94 4.29 2 4.65 5.54 5 5.42 3 5.77 5.26 4.76 4.79 4 6.25 4.88 5.66
- 12. 4.3 29 5.87 5.3 5.78 5.07 30 4.41 4.75 4.95 5.11 2. Calculate X-bar-bar, R-bar, and associated control limits using the data in the table above. 3. Create X-bar • R (average and range) control charts from the data in table above. 4. Discuss notable out-of-control conditions displayed in the completed X-bar • R (average and range) control charts. Only consider points outside the control limits. Do not consider runs, set of points within certain zones, and so on. 5. If the conditions you note could be defined as assignable conditions and they are removed from the process, what will happen to the X-bar • R control chart? (a) Remove the data related to the out-of-control points you observed from the original data and recalculate a new X-bar- bar, R-bar, and associated control limits. (b) Create new X-bar • R (average and range) control charts from your updated data. 6. Discuss how the two sets of control charts are different. What has changed?
- 13. Problem 1: Calculate X-bar-bar, R-bar, and associated control limits using the data in the table above and create X-bar • R (average and range) control charts. Solution : 1. Using the template provided, click on the Data and Calculation tab. In the upper left corner, enter 30 for the number of samples and enter 4 for the sample size. 2. Enter the data into the yellow data area. Note: You will have to rotate your data to fit this table. When you are done you should have 30 observations (30 columns ), each with four results.
- 14. 3. The template does all the calculations and plotting. The calculations are grouped into two parts, one for Averages (top group) and one for Ranges (bottom group). The X-bar-bar number we want in the top set of results titled Center. X-bar-bar = 5.057. The Center result the bottom set of data is R-bar. R-bar = 1.069. 3. Click on the X-bar Chart tab to view the X-bar chart; you should see a chart that looks like the one below. (It’s called an X-bar chart because you plot averages, or X-bars, on it.) We can see that one point, Point 22, is below the lower control limit (LCL). 4. Click on the R-Chart tab to view the R-chart and you should see a chart that looks like the one below. No points outside the control limits can be seen.
- 15. 5. We now have enough information to answer Questions 1, 2, and 3 in the case study. Problem 2: If the conditions you note could be defined as assignable conditions and they are removed from the process, what will happen to the X-bar • R control chart? Calculate new X-bar-bar, R-bar, and associated control limits, and create a new X-bar • R (average and range) control charts.