q4_additivity_soln

q4_additivity_soln - 16.881 Robust System Design Solution...

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Unformatted text preview: 16.881 Robust System Design Solution to Quiz #4 S/N Ratios & Additivity 1) (25%) An increase in 6dB in the nominal-the-best S/N ratio always indicates a) A reduction by about 50% in the standard deviation of the response. b) A reduction by about 50% in the variance of the response. c) An increase by about 400% in the mean of the response. d) An approximate four fold increase in the ratio of mean squared and variance. d is the correct answer. The nominal the best signal to noise ratio is defined as = 10log 10 2 2 where is the mean of the response and is the standard deviation of the response. Lets say we have a product with a signal to noise ratio of 1 a mean of 1 and a standard deviation on 1 . Lets also say that, through robust design, the signal to noise ratio was increased by 6dB and that this robust product has a mean of 2 and a standard deviation on 2 . 1 = 10log 10 1 2 2 1 + 6 = 10log 10 2 2 2 1 2 Subtracting the first equation from the second gives 2 6 = 10log 10 2 2 2 10log 10 1 2 2 = 10log 10 2 2 2 2 1 1 2 1 2 Therefore 2 2 6 2 2 2 2 = 10 10 4 1 1 So, the ratio of mean squared and variance must increase by a factor of approximately...
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q4_additivity_soln - 16.881 Robust System Design Solution...

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