Regression model based on DOE with many repetitions

[#1]

Hi community,

I've received a data set from an experiment where a product was dropped from a certain height and its performance tested afterwards, resulting in a pass/fail response.

There were six different configurations of the device, and 16 specimens of each configuration. All 96 specimens were drop tested in random order.

The main reason for the many repetitions for each configuration is that the failure rate is known to be around 1/10 for the base configuration and it was a wish to have some certainty of seeing devices that fail in all configurations in order to compare them. If we had done e.g. only 3 repetitions for each configuration we might have seen no or very few failures and would probably have learned nothing.

My question is, how do I best model this?

- If I use all 96 pass/fail results as a nominal response in a logistic model, the model effect values are identical in groups of 16, since all configuration A rows have the same model effects values, all configuration B rows have the same model effect values, etc. (Inside each group the response varies of course: some pass, some fail.) Is this acceptable? I've not tried doing a model like this before, where the input variables have been so homogeneous in groups.

- If I calculate a fail percentage (no. of failed divided by 16) for each of the 6 configurations and use that as a continuous response in a standard least squares model, I get a very poor model because of the low sample size (6). And I'm not sure if that setup really represents what was done experimentally (96 independent runs).

Hope somebody can help!

Kind regards,

Morten

[#2 · Accepted solution]

I will first say that it is unwise to perform an experiment before you select the model or analysis. The data might not support what you want to know. The analysis and model come first, not last.

There are several types of analysis for a binary response that might satisfy you. You could use a logistic regression model, a binomial generalized linear model with a logit link function, or a Probit analysis. All of these analyses would use the same linear predictor.

[#3]

Hi Mark,

Thanks for you answer, and sorry for the late reply.

I agree with you that the model should have come first, unfortunately the testing had already been carried out.

I've created a logistic model and it seems to work; I guess all the "repeated rows" (all factors at the same levels for multiple rows) just provide more confidence that that configuration passes, for instance. So I think I'll continue with this logistic model. 

Thanks for your help!