Q2_2008 - MIT OpenCourseWare http/ocw.mit.edu 2.830J 6.780J ESD.63J Control of Manufacturing Processes(SMA 6303 Spring 2008 For information about

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MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Name: _____________________________________________ Massachusetts Institute of Technology Department of Mechanical Engineering Department of Electrical Engineering and Computer Science 2.830J/6.780J Control of Manufacturing Processes Spring 2008 Quiz #2 Thursday – April 24, 2008 In all problems, please show your work and explain your reasoning. Statistical tables for the cumulative standard normal distribution, percentage points of the χ 2 distribution, percentage points of the t distribution, and percentage points of the F distribution (all from Montgomery, 5 th Ed.) are provided. Problem 1 [45%] An experiment is designed and executed, in which the design or input variable is x and the output variable is y. The input range is normalized to [-1, +1]. Experiments are run in the order shown in Table 1 below, with the input setting and output result as given in the table. Table 1: Full factorial DOE experiment results Run # x y 1 -1 8 2 1 18 3 -1 9 4 1 19 5 -1 10 6 1 20 Part (a) [5%] Fit a model of the form y = β 0 + β 1 x to the data, and determine point estimates for β 0 and β 1 . 1
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[10%] Determine the standard error (std. err.) and 95% confidence intervals for the estimates of β 0 and β 1 . Are both parameters significant to 95% confidence or better? Should you include both terms in the model? Part (c) [5%] Following good practice, we next examine the residuals (differences between the model prediction values and measured values, for our data). In particular, we consider the residuals as a function of run order. What pattern in the residuals raises a concern? What modifications might you suggest to the experimental design or analysis in light of this? 2
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This note was uploaded on 09/24/2010 for the course MECHE 2.830J taught by Professor Davidhardt during the Spring '08 term at MIT.

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Q2_2008 - MIT OpenCourseWare http/ocw.mit.edu 2.830J 6.780J ESD.63J Control of Manufacturing Processes(SMA 6303 Spring 2008 For information about

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