MIE364S_T_7_11 - MIE364H1S Methods of Quality Control and...

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MIE364H1S Methods of Quality Control and Improvement Course Instructor: Prof. V. Makis Tutorial #7 1. An engineer is trying to improve the life of a battery for use in a device that will be subjected to some extreme variations in temperature. He knows from experience that temperature will probably impact the effective battery life. The only design parameter that he can select at this point is the plate material for the battery, and he has three possible choices. The engineer decides to test all three plate materials at three temperature levels – 15˚F, 70˚F, and 125˚F – as these temperatures levels are consistent with the product end-use environment. Four batteries are tested at each combination of plate material and temperature, and all 36 tests are run in random order. The experiment and the resulting observed battery life data are given below. Temperature Material type 15 70 125 1 130 155 34 40 20 70 74 180 80 75 82 58 2 150 188 136 122 25 70 159 126 106 115 58 45 3 138 110 174 120 96 104 168 160 150 139 82 60 a. Analyze the data and draw conclusions. b. Analyze the residuals from this experiment and comment on your findings. 2. An automobile manufacturer wanted to examine the effect of three welding rod variables: maker, diameter, and chromium content, on the strength of spot welds made by assembly line robots. He selected two makers: M 1 , M 2 ; three rod diameters: D 1 = 30 mm, D 2 = 60 mm, D 3 = 90 mm; and three chromium contents: C 1 = 1.00%, C 2 = 1.5%, C 3 = 2.00%. He decided to use a 2 x 3 x 3 factorial set of treatments (M x D x C). He randomly assigned the treatments to 18 robots on each of two assembly lines, which he treated as blocks in a randomized block design. The assignment of treatments and tensile strength of welds (psi x 10 -3 ) were as shown below.
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Assembly Line 1: Chrome Maker Diameter C1 C2 C3 M1 D1 76.2 79.2 80.7 D2 75 77.8 80.4 D3 76.7 78.3 80.6 M2 D1 75.1 76 78.8 D2 74 76.2 79.8 D3 72.2 74.8 77.8 Assembly Line 2: Chrome Maker Diameter C1 C2 C3 M1 D1 77.6 78.8 81.8 D2 75.7 78.2 80.6 D3 76.5 79 81.6 M2 D1 75.8 76.4 79.4 D2 74.4 77.1 79.2 D3 73 74.8 78.1 Analyze the data and draw conclusions.
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Solutions Solution to 1 (a) 2 11 :, ~ ( 0 , ) 1,. .., 3 1,. .., 3 1,. .., 4 Reparameterization : ,3 6 .. .. . .. ˆ ... 105.5278 1 ˆ .. ijk ij ijk ijk ijk i j ij ijk ii jj ij ij i j bn i ijk jk Model Y where N ia jb kn Y N abn Y YY bn == =µ +ε ε σ =µ+α +β +γ +ε = = µ=µ α=µ−µ β=µ .−µ γ=µ− µ −α− β µ= = α= ∑∑ 1 . .. ... 1 ˆ ... . . ... 1 ˆ ... .. ... . . ... . .. . . ... i an ji j k j ik n ij ijk i j ij i j k YY Y Y an YYYYYYYYYY n = =− β= = γ= + + = + 1 2 3 ˆ 22.3611 ˆ 2.8056 ˆ 19.5556 α=− 1 2 3 ˆ 39.3056 ˆ 2.0556 ˆ 41.3611 β=−
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11 12 13 21 ˆ 12.2778 ˆ 27.9722 ˆ 15.6944 ˆ 8.1111 γ= 22 23 31 32 33 ˆ 9.3611 ˆ 17.4722 ˆ 20.3889 ˆ 18.6111 ˆ 1.7778
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2 2 111 2 2 ..
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This note was uploaded on 03/31/2012 for the course MIE 364 taught by Professor Makis during the Spring '12 term at University of Toronto.

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MIE364S_T_7_11 - MIE364H1S Methods of Quality Control and...

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