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I have to design an experiment where tool wear is a factor (not a response). I'm not trying to study tool wear minimizing. I'm trying to study the effect of tool wear along with 3 other factors on the number of a certain defect type.

What kind of design should I use? I considered dividing the tool wear into 3 conditions (low, med, high) and then running each treatment within the conditions. But I'm not sure that is a correct method. Tool wear is considered to be a highly significant contributor to the defect rate. Interactions are also important here.

This is a forging operation. The other factors are billet temp, spotting location and pancake height. I have plenty of replication opportunities and plan at least 10 parts for each treatment.

Many Thanks - Kelly

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You want to look into ANCOVA, where tool wear is your covariate (in this terminology), and the effects of your factors are what you care about. You could randomly assign your cases to the levels of your factors, & the levels of tool wear should be equal, on average, between the conditions. On a different note, can there be >1 defect per case? If so, I think your response is a count variable, & you want Poisson regression, if each case can either have a defect or not, you will want logistic regression. –  gung Nov 15 '12 at 3:19
    
Thank you @gung. I think I am on the right track. As long as I am running all tests of the IVs with the dependent low/med/high tool wear categories, I should be ok and still be able to measure variation attributable to tool wear. The part can either have the defect or not (logistic reg. scenario). I realize this is not ideal and considered assigning a rank to the severity of the defect where 0=no defect/5=severe defect. I'm looking for a crack in a certain location. Sometimes the crack is short and shallow, other times long and deep. Do you think assigning a severity rank would be helpful? –  user16877 Nov 15 '12 at 13:10
    
Thanks for your note, @KellyKane. As for the substance of your response, I would call tool wear a covariate or an independent variable, rather than a 'dependent' one. In addition, if you have a good measurement of tool wear, I would use it, rather than categorizing it into low / med / high. In fact, if you only have those categories, I would encourage you to come up w/ reasonable numbers, and use those numbers instead of the categories. –  gung Nov 15 '12 at 14:16
    
Sorry about commenting in the wrong place. Live and learn. –  Kelly Kane Nov 18 '12 at 21:42

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