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I am very new to design of experiments concept. I would like to design an experiment to understand the relationship between input parameters like amount of various ingredients, cooking temperature, time of cooking, etc. vs. the quality of a cake to be baked.

Assuming that all input parameters are continuous and range bounded, and the quality of the cake to be assessed by an expert from a scale of 1-5 stars, is the best sampling strategy for input parameters uniform over their ranges?

My understanding is that the uniform sampling helps us collect information regarding the entire function space. However in this experiment I am interested in figuring out the best inputs in order to achieve 5-star quality cakes. Therefore is there a better sampling strategy than uniform?

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    $\begingroup$ +1 It's a good question. The literature suggests there is no universal answer, because different optimal designs have been found depending on one's specific objectives as well as assumptions about the response surface, measurement errors, etc. If you're asking this question in order to understand DOE better, it might help to make it more specific so the scope of answers can be narrowed--and if you're asking in order to actually design an experiment, then you had better make it more specific so that the responses are helpful! $\endgroup$ – whuber Aug 28 '17 at 20:48
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    $\begingroup$ @whuber actually both. Believe it or not somebody asked me to crunch the math for a cooking machine they are building and they want to know the optimal settings for the device. I am trying to understand why factorial design is the standard way to go because it implies uniform distribution over the ranges which sounds like a heuristic. $\endgroup$ – Cagdas Ozgenc Aug 29 '17 at 17:20
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You should not sample points, you should design an experiment, that is, choosing values of the input variables so as to maximize the information gain. In your case you could start with factorial design, possibly fraccionated. And maybe adding center points.

You mention the variables temperature, cooking time, amount of different ingredients, ... . With say five ingredient that would make for 5+2 variables, so maybe a fractional factorial experiment. You should have a look at the excellent book https://www.amazon.com/Statistics-Experimenters-Design-Innovation-Discovery/dp/0471718130. Also look into response surface designs, see Regression analysis and response surface analysis.

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  • $\begingroup$ Well I call it sampling because the strategy to pick the design points correspond to covariate distributions. $\endgroup$ – Cagdas Ozgenc Aug 8 '17 at 15:22
  • $\begingroup$ I don't understand that comment. If you did'nt like my answer, can you explain why it will not work for you? $\endgroup$ – kjetil b halvorsen Aug 8 '17 at 16:05
  • $\begingroup$ I was looking for some fast practical suggestions. Obviously I can take a book and read. $\endgroup$ – Cagdas Ozgenc Aug 9 '17 at 6:02
  • $\begingroup$ Well, the practical suggestion is to use a fractional factorial design. Choosethevariables, choose amax and a min for each, maube add a centerpoint. $\endgroup$ – kjetil b halvorsen Aug 9 '17 at 7:30

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