16.881 – Robust System Design
Solution to Quiz #2
Matrix Experiments
1) Does the following matrix experiment have the balancing property with respect to
control factors A and B?
Yes. All levels of B are equally represented at each level of A.
2)
Does the following matrix experiment have the balancing property with respect to
control factors B and C?
Yes. This one is slightly harder to see right away, but all levels of B are equally
represented at each level of C.
3)
Does the following matrix experiment have the balancing property with respect to
control factors A and D?
NO. All levels of D are not equally represented at each level of A. For example,
rows 46 are all the rows with level A2. In these rows we have D2 twice, D1 once and
no instance of D3.
4) Is the matrix an orthogonal array?
NO. If any pair of columns in a matrix experiment are not orthogonal, then the
matrix is not orthogonal. Columns A and D have neither the balancing property nor
proportional balancing. Hence they are not orthogonal. Also, we can check the inner
product of the contrast of the two columns directly. Since the inner product is non
zero, the matrix is not orthogonal
−
1
−
1
−
1
0
−
1
1
0
0
0
⋅
−
1
=
1
+
0
−
1
+
0
+
0
+
0
+
1
+
1
−
1
= −
1
0
0
1
1
1
1
1
−
1
Control Factors
Expt.
No.
A
B
C
D
1
1
1
1
1
2
1
2
2
2
3
1
3
3
3
4
2
1
2
2
5
2
2
3
1
6
2
3
1
2
7
3
1
3
3
8
3
2
1
3
9
3
3
2
1
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After completing a matrix experiment, if an additive (factors separable) model holds,
and one wishes to maximize the S/N ratio, one should
a)
Select the control factor settings in the row of the array corresponding to the
experiment with the highest response.
b) Select the noise factor levels that maximize the inner product of the array.
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 Fall '03
 lDavidMiller
 Statistics, Standard Deviation, Signaltonoise ratio, matrix experiment

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