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Analyzing Variance in a DOE

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  • #40764

    Nats
    Participant

    I have been given training to analyze variance or standard deviation by simple taking replicates, getting their standard deviation and treating it as a response. Now I am being told it that is wrong and violates the assumptions of ANOVA. What is right?

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    #127233

    FTSBB
    Participant

    Which assumption(s) do you feel are violated?  Or, which assumptions are people telling you are violated?  Any of the assumptions (normality, stability & homogeneous variance) can be checked quickly & easily – only thing that may be suspect is sample size, but it’s probably moot.

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    #127445

    Kim Niles
    Participant

    Nats:
    ANOVA is in essence a signal to noise measurement used to provide confidence (variation based) in factor effect (factor means) measurements.  It doesn’t compare variation relative to the factors to that end.  I believe it was Taguchi who outlined using run related signal to noise measurements and or standard deviation / variation as you stated you’ve been taught.
     
    ANOVA assumes that the data comes from a normal distribution.  Multiple samples are taken per run in order to utilize the central limit theorem and assure that the data follows a normal distribution.
     
    I hope that helps.
     
    Sincerely,
    http://www.KimNiles.com

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    #127447

    Kim Niles
    Participant

    Nats:
    I just want to be clear that “replicates” are defined as repeat experiments whereas “repeat measures” are defined as multiple samples per run.  Perhaps you’re just getting caught up in definitions. 
    In this case, you need to measure variation in the “repeat measures” in order to compare variation in the factors.
    KN

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    #127449

    Robert Butler
    Participant

      If you have a design you could go out and replicate each of the design points, get a two or three sample estimate of the variance at each design point and then build a regression model using these estimate of variance as a response.  This method is very cumbersome and really not terribly efficient for the simple reason that variance estimates based on only two or three points will be very crude.  If variance as a response from a DOE is your concern then the most efficient approach to the problem would be the Box-Meyers method.
    1. Use a resolution 4 or higher design to avoid confounding interaction and dispersion effects.
    2. Fit the best model to the data (that is Y = f(X1, X2, X3, etc)
    3. Compute the residuals
    4. For each level of each factor, compute the standard deviation of the residuals.
    5. Compute the difference between the two standard deviations for each factor (that is the standard deviation for all of the + levels and the standard deviation of all of the – levels)
    6. Rank the differences in #5
    7. Use a Pareto chart, a normal probability plot, or the ratio of the log of the variance of the + to the variance of the – for each factor to determine the important dispersion effects.
    For purposes of control
    1. For factors with important dispersion effects, determine the settings for least variation. and set location effect factors to optimize the response average.
    2. If a factor for minimizing variance is in conflict with a factor for optimizing location use a trade-off study to determine which setting is most crucial to product quality.
    From – Understanding Industrial Designed Experiments -Schmidt and Launsby – 1997

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    #127866

    ade supriatna
    Participant

    tolong kirimkan artikel ini

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    #127870

    Ron
    Member

    ANOVA is a technique whereby the total variation present in a set of data is partitioned into several components.Associated with each of these components is a specific source of variation, so that, in the analysis,it is possible to ascertain the magnitude of the contribution of each of these sources to the total variation.
     
    If you do not take replicates you cannot calculate the ANOVA calculations.

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    #127882

    Bill Craig
    Participant

    Nats,
    I think Kim made a good point about the distinction between replicates and repeat measures. You perform replicates for each treatment combination in order to estimate “noise” or MSE for the F-ratio. Your response is the characteristic being measured, not the variance of what is measured.  If you have a situation where you need to take multiple readings across one experimental unit, then you can use the average of these readings or the std deviation of these readings as a response. Multiple readings across one experimental unit are not independent, so collectively they should represent one run from your DOE.  Keep a close watch on the normality assumption if you use standard deviation across-part as a response. To add even more confusion, you don’t need replicates in screening DOEs in order to estimate error. As you build the model from your data, those terms which are dropped are included in the error.
    A good example to answer your question is cooking pizza.
    Factor A:Temp (-level 350, +level 450) Factor B:Time (-level 30min,+level 45 min)
    Experimental unit: The smallest item to which you can apply a treatment(in this case,a Pizza). To obtain replicates, you have to run the treament combination multiple times, rather than taking a measurement on each slice. With a Pizza you might want to use an average of some characteristic or a variablilty of some characteristic as a response. Especially if you get the burnt piece next time!
    Treatment combination: One combination of factor levels (i.e. temp 350, time 45 min)
    Hope this helps!

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    #127916

    CT
    Participant

    In agreiance with what Bill has stated, except if you use the coefficient of variance which is the STD DEV/Average*100 (expressed as %) then you will have a spread in your data that will lend itself to better interpretation from a response point of view.
    CT

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    #127927

    Mikel
    Member

    Nonsense – whoever taught you that is wrong.

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    #127930

    Darth
    Participant

    SEE, DEEP WAS WRONG.  YOU DO KNOW A LOT ABOUT DOE  :-).  Couldn’t resist, sorry.

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    #127932

    Joe BB
    Participant

    How can you tell that he knows something, he is always in denial. he never says anything positive, he only refutes without any explanation. I think that he is a big ignorant!
    Joe The Third

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    #127934

    Mikel
    Member

    Joe honey the third (or is that turd?),
    Say something positive yourself.
    The advice of using COV is dumb because it can mask exactly what you are looking for. It’s bad advice.

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    #127937

    GomezAdams
    Participant

    ps homey!
    What’s the “BB” stand for?
    “Billy Bob”?

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    #127939

    Mikel
    Member

    I am pretty sure it stands for bloated brain.

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    #127940

    CT
    Participant

    Stan I understand that it can mask what you are looking for, I just think it depends on the application and when the responses are not easily distinguishable, and is a calculation  that is easy enough to maybe shed light on certain factors of the DOE. But I could be wrong and usually am some how.
    CT

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    #127955

    Vicky
    Member

    Summing up, there are 2 views expressed in the entire discussion.
    1. Use repeat experiments2. Use COV
    I dont think, as do some others, that COV is a good idea. You should take repeat measurements of the response. Repeat means taking multiple readings without changing the setting (i.e., at the same treatment combination). Once you change the settings before running the same combination again, it is termed as a replicate.
    So once you take multiple measurements, take the Std Dev for all the measurements per treatment combination and use this as a response in analysis. Alternatively, use the option of Analyse Variability in Minitab, which also works on the same principle as mentioned above.
    Hope this will help.
    Rgds

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    #128951

    Craig
    Participant

    For those of you who have not had the pleasure of dealing with COV in the real world, think twice about ruling it out!
    It is a valuable indicator in fields such as plating, semicondcutor manufacturing, etching.  These processes can cause havoc when you have to hit thicker targets, or etch through thicker films.  The varation across piece will become unacceptably large if you do not optimize your process.  You have to take multiple readings within a part and use COV as ONE of your responses. 

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    #134449

    fsamyn
    Participant

    I greatly appreciate the response; a new way to enhance my knowledge.
    I would like to point out that the method that I did suggest uses 5-10 replicates not 2 or 3. Agreed this is more cumbersome. I will share my thoughts when I have had a chance to look at the referenced material.
    Again many thanks for the reply.

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