Lecture17-3-4-2002

Lecture17-3-4-2002 - MAE 552 Heuristic Optimization...

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MAE 552 Heuristic Optimization Instructor: John Eddy Lecture #17 3/4/02 Taguchi’s Orthogonal Arrays
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S/N Ratio Why use the signal / noise ratio? Given a product or process with a target performance, deviation from that performance can typically be expressed in terms of (i.t.o) statistics (Taguchi – Quality loss). Two things you want are for your mean to be “on target” and for your variance to be low. Take the example of a machine that throws darts.
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S/N Ratio Here are the results of 4 such machines: Good Mean – Bad Var. Bad Mean – Good Var. Good Mean – Good Var. Bad Mean – Bad Var.
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S/N Ratio Noise can be interpreted as the variance observed in the process (since variance is commonly a direct result of noise). The signal can be interpreted as the desired value (the value you would like your mean to take). The S/N ratio is then 2 σ y
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S/N Ratio Another means of calculating the S/N ratio is to take -10*log(d) where d represents the mean squared deviation from the target. So in our example, the target is 0 defects, and the squared deviation for each count is the square of the count itself.
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S/N Ratio Should we always use an S/N ratio? Taguchi says yes because it accounts for both the mean and standard deviation. Will it always be a “maximize” situation? Yes it will, assuming that it is always desirable to achieve the target value with very little deviation.
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Back to our Example A B C D 1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1
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Taguchi Example Continuing with our example: Factor Levels 1 2 3 A: Temperature -20 -45 -60 B: Pressure -30 -40 -55 C: Settling Time -50 -35 -40 D: Clean Method -45 -40 -40 All the level averages for our example problem.
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Example Using the values for the level averages, we can plot the factor effects and see visually which factors have the greatest influence on the performance of our product or process.
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Example Overall Mean
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Lecture17-3-4-2002 - MAE 552 Heuristic Optimization...

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