q5_anova_soln

q5_anova_soln - 16.881 Robust System Design Solution to...

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Solution to Quiz #5 Analysis of Variance 1) In Taguchi methods, the F value for a factor effect is defined as a) The probability that the we reject the hypothesis that the factor effect equals zero. b) The sum of squares due to a factor divided by the error variance. c) The mean square due to a factor divided by the error variance. d) The sum of squares due to a factor divided by the DOF for the factor. C is the correct answer. It is very simply the definition of the F value in Taguchi methods. Note that in traditional one-way ANOVA, the F test statistic is defined differently dfB F SSB dfW SSW Where SSB is the sum of squares within treatments and SSW is the sum of squares within treatments. A is incorrect. To compute a probability from an F test statistic, you need to integrate the F distribution over the critical region. This can be done in Mathcad with the pF function or in excel with the FDIST function. F statistics are not normally used to compute probabilities in robust design. B is incorrect. The sum of squares due to a factor divided by the DOF of the factor is the mean square due to a factor. This is the key difference. You should note the similarity in form between the F as defined in one way ANOVA and the Taguchi use of ANOVA. Both the numerator and denominator are divided by DOF. D is incorrect.
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This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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q5_anova_soln - 16.881 Robust System Design Solution to...

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