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ISYE 3039 hw3

# ISYE 3039 hw3 - y = 9 x 1 z 1 x 2 5 z 1 x 3 z 2 where z 1...

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ISyE 3039 A Homework 3 Due March 6, 2008 1. An experiment using a 2 7 - 4 design crossed with a 2 1 design was conducted using 7 control factors and one noise factor in an electro-plating process. One measurement of the plated thickness was taken for each run under each noise level. The data are given below. A B C D E F G Z=- Z=+ 1 1 1 1 1 1 1 1 29 21 2 1 1 1 2 2 2 2 35 27 3 1 2 2 1 1 2 2 31 30 4 1 2 2 2 2 1 1 25 26 5 2 1 2 1 2 1 2 33 25 6 2 1 2 2 1 2 1 40 31 7 2 2 1 1 2 2 1 35 36 8 2 2 1 2 1 1 2 30 29 The target thickness is 25 microns. Find the robust parameter design using (a) performance measure modeling. (b) response modeling. (Assume z N (0 , 1)). 2. Suppose in a system, there are 3 control factors ( x 1 , x 2 , and x 3 ) and 2 noise factors ( z 1 and z 2 ). From an experiment, the following response model is obtained.
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Unformatted text preview: y = 9 + x 1 z 1 + x 2-. 5 z 1 + x 3 z 2 , where z 1 and z 2 have means 0 and variances 2 and 1 respectively. Suppose 10 is the target value of the response, then ﬁnd the robust setting for the control factors. 3. (a) In the problem above, suppose the response model is y = 9 + x 1 z 1 + 2 x 2 z 1-. 5 z 1 + 2 x 3 + 2 x 1 z 2 + x 2 z 2-z 2 . Find the robust setting for the control factors. (b) Suppose in the above problem, the response model were y = 9 + x 1 z 1-. 5 z 1 + x 2 + x 1 z 2-z 2 , then what would be the robust setting for the control factors. 4. Solve Exercise 13.3 from the textbook. 1...
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