q2_2006 - MIT OpenCourseWare http:/ocw.mit.edu 2.830J /...

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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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Massachusetts Institute of Technology Department of Mechanical Engineering 2.830/6.780J Control of Manufacturing Processes Quiz 2 April 27, 2006 Open Book and Notes Problem 1 (45 %) You are faced with the need to model a system with three inputs but time and cost constraints limit the number of experiments that can be performed to four. Since you know that a full factorial experiment would take eight independent experiments, you have some choices to make. Starting from the following 2 2 design matrix (our X matrix in the equation y= X β ) Input 1 Input 2 1 Α Β ΑΒ 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 1 Consider the problem of using this same design for the three input problem. Notice that all row entries are unique combinations of the inputs. Thus, we could assign the AB column to the third input and run the experiment. If that were done, we would have the matrix: Input 1 Input 2 Input 3 1 A B C 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 1 Based on this approach: a) Write out the full interaction matrix for the 2 3 problem given that you have only 4
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q2_2006 - MIT OpenCourseWare http:/ocw.mit.edu 2.830J /...

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