MIE231 - Minitab Project Tips 2009 V2.pdf

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Department
Mechanical & Industrial Engineering
Course
MIE231H1
Professor
B B
Semester
Fall

Description
MIE231 – Tips for Term Project – 2009 The following tips may help you to complete the project. The numbers in square parentheses indicate the project question number(s) to which the tip may apply. • [1,4,6,12,13] To generate random numbers, go to Calc Æ Random data. Then, you can select the distribution that you need and specify the relevant parameters. (Note: The normal distribution does not have finite endpoints, hence, it is not the correct choice for these questions). • [2,3] To find probabilities associated with a specified value of a random variable, X, go to Calc Æ Probability Distributions. Then, select the distribution that you need and specify the relevant parameters. (Note: you may need to select the Cumulative Probability option. Also, the column with the specified X-value should be entered in the Input Column field). • [5] To calculate a confidence interval (CI) for sample means and standard deviations manually, 2 use the Z-distribution and χ -distribution equations, respectively. • [7,8] To find sample means and standard deviations, and the CI for population characteristics, use the graphical summary (i.e., go to Stat Æ Basic Statistics Æ Graphical Summary). • [9] You need to generate two separate graphs: the upper and lower CI limits (CLs) of μ vs. sample size, and the upper and lower CLs of σ vs. sample size. To plot multiple scatter-plots on one graph, go to Graph Æ Scatterplot, select the With Connect Line plot type, and click OK. Next, click on Multiple Graphs and select Overlaid on the same graph under the Multiple Variables tab. To superimpose reference lines onto the graphs, finish plotting the graphs first, and then go to Editor Æ Add Æ Reference Lines, and input the required information. • [10] The column of 100 data points does not need to be physically separated and un-stacked into 20 separate columns of 5 data points each. Instead, Minitab gives you the option to specify the subset size when determining control limits (which you will do in Point-11), and then conducts the “un-stacking” internally. To utilize this option, make sure to enter the subset size in the Subgroup Size input field when you are in the XBar-S dialog box in Point-11. • [11] Control limits can be obtained by creating an XBar-S chart. To do that, go to Stat Æ Control Charts Æ Variable Charts for Subgroups Æ XBar-S. (Note: The default control limits use ±3 σ. Also, since un-stacking of the data points is unnecessary, you may specify the input data column to be the same column that contains all your 100 data points). • [11,14] (μ,σ) values can be set manually by clicking on XBar-S Options in the XBar-S dialog box, and selecting the Parameters tab to access the Mean and Standard deviation parameter input fields. When trying to establish the control limits based on a set of sample data (i.e., Point-11), no parameters should be specified. Once the process has been established, these limits should remain the same as new data samples are used on the control chart (i.e., Point- 14). To do that, the unbiased estimators of μ and σ should be entered into the Mean and Standard deviation input fields, respectively. You will need to use the sample mean and standard deviation values from Point-11 to calculate these estimators. The unbiased estimator of μ is the mean of the sample means and the unbiased estimator of σ is the mean of sample standard deviations/c 4, where c4depends on the size of the data subsets. (Note: The control limits in Point-14 should remain the same as the ones in Point-11). Page 1 of 3   Sample Graphs Graphical Summary of a set of data Summary for n = 100 A nderson-Darling Normality Test A-Squared 0.21 P-Value 0.866 Mean 9.9821 StDev 1.0926 V ariance 1.1937 Skewness 0.153096 Kurtosis -0.387835 0 0 N 1 Minimum 7.6058 1st Q uartile 9.2420 Median 9.9444 3rd Quartile 10.7409 8 9 10 11 12 Maximum 12.5279
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