Which DoE modeling technique to use when there are Edge of Failure conditions?

[#1]

Hello,

I have performed a two-parameter full factorial DoE to optimize process conditions. The DoE was composed of 12 runs.

Prior modelling I verified the normality of the distribution of my responses and my distributions do not pass the Goodness-of-Fit test. There are 2/12 conditions which are clear Edge of Failure conditions (they performed from a scientific point of view very poorly) and are making the distribution drift (see in attachment).

What would you recommend to use as a modeling technique? How could I best model my data without repeating my experiment?

Thank you in advance for the support!

Claire

[#2 · Accepted solution]

Do you mean to say that you analyzed the normality of the responses? There is no assumption about the distribution of the responses. The assumption is that the statistical errors of the model are normally distributed. The errors are estimated by the residuals. The residual plots are available within the Fit Least Squares platform via the red triangle menu, or you can say the residuals and then use other platforms such as Distribution or Graph Builder to assess them separately from the fitting process.

[#3]

Many thanks for your prompt reply! Yes, I analyzed the normality of the responses and I realize now with your answer that I should have checked the normality of the residuals instead.

Thanks for re-directing me in the right direction!

[#4]

I have now performed distributions on the residuals and one of my distributions is not passing the goodness of fit (see attachment).

This is the residuals distribution from a time-dependent Standard Least Squares model; There are multiple time-course samples per condition.

Is another modeling technique or a transformation on the data necessary?

[#5]

I suggest that you read this JMP Technical Note about repeated measures ands see if it suits your study.

[#6 · Accepted solution]

Regarding your example, I would not worry about it from the standpoint of the assumption of normally distributed errors. First, if you were to generate a random sample of the same size from the assumed distribution, you will find, not infrequently, 'patterns' in the normal quantile plot. Second, the large sample size will likely mitigate the departure from ideal normality. Third, goodness of fit tests will be significant α proportion of the time under the null hypothesis (fit is good). If you perform many such tests and the fit is always good, you will still get some that reject a good fit.

See my previous reply about time-dependent responses to see if it addresses the other issue.

[#7]

To add a bit to the questions and counsel posed by @Mark_Bailey , when I counted the 'dots' in the normal probability plot I count 11, not 12, unless maybe you got identical responses for one of the treatment combinations? And 12 is kind of an unusual number of runs for a 'full factorial design.' If you have 2 levels specified for each factor, then the number of runs has to equal a power of 2. 12 is not a power of 2. 3 levels per factor, the number of runs has to equal a power of 3 and so on. Maybe you can share the specific design?

And when you say 'two parameter' do you mean 'two factors'? Parameters in a DOE context are usually a word used for describing coefficient estimates for terms in a model. So depending on the structure of your model you could have no parameters (ie, predict y as the grand mean of your responses with just an intercept term or main effects, interaction effects etc.) where each of these effects has their own unique 'parameter estimate'. Maybe you could share your design and responses?

And a bit about your specific experimental goals and objectives? For example, if one of your goals is to ultimately find a robust operating position for the factors that minimizes the risk of 'failure', whatever that means practically or physically, then if you have 2 of 12 responses near the edge of that 'failure' space...well you may really be onto something wrt to your overall problem in terms of where to avoid 'failure' within the factor space.

[#8]

The DoE is composed of 11 points and among these 3 are centerpoints. There is also 1 point to check if the model is valid and is excluded from the model.

Yes, I meant 2 factors.

The goal is to maximize one response. Identifying edge of failure conditions is also useful information for process understanding and for later development.