I will offer some further thoughts in blue, you may choose to ignore them.
For more context : we want to investigate the different quantities of various chunks in soups. There are three different flavoured soups which all have the same chunks (chicken, beans etc). We have already some chef-created versions with a certain recipe and now we want to investigate how far we can push the nutritional aspect without decreasing acceptable sensory characteristics.
I'm confused, on one hand you indicate you have already optimized ("We have already 'optimised' our recipes to a certain extent through focus groups, testing and chef creation.")....IMHO, this is why you want to evaluate multiple Y's as you iterate (multivariate). Going after different Y's sequentially can be challenging ineffective and inefficient.
1. Question the measurement systems. How precisely can they measure the nutritional values and salt? You will have sensory measures for taste and smell (ordinal data sets like some hedonic scale). How will you account for within and between assessor variation? How will you account for assessor bias?
The assessors will undergo training to reduce this bias. We will include a blocking factor for the difference between sensory sessions (days). We will accurately calculate nutritional (using an external laborotary).
IMHO, training may help consistency, however it will likely not impact sensory bias. The key to mitigating the sensory bias is to remove emotion from the evaluation. For example, don't ask which one do you like?, instead, using your expert chef's, create samples representing some ordinal scale (at least 5 categories) and ask which one does it match. Sending samples to an external lab does not guarantee the measurements will be useful. And you care more about precision than you do accuracy for experimental design purposes (you want less variation in the measurement system). I would require identical samples be tested multiple times by the lab.
2. I don't understand the 2 categorical factors? What is the factor "Texture"? Are you adding something to the batch? What? What is "Aroma"? Texture and Aroma sound like response variables, not X's. Why 3-levels for your first experiment?
Texture category refers to the fact that we will either leave one version with the the ingredients in chunks and the other version will be mixed. The content will be identical.
Aroma category - three different flavour of liquid bases (same quantity) - chicken / vegetable / coconut
OK, so the names for the factors reference what you are actually changing (chunk size and flavor). I think you might consider blocking on base (flavor) as these might create rather different sensory responses.
3. Mixture designs are what I consider to be optimization experiments. Are you ready to do this? Let's say the current process is performed in batches. Which components of variation are most significant, within batch, batch-to-batch or measurement variation? If you have significant batch-to-batch variation, you should figure out why before optimizing ingredients for 1 batch.
We have already 'optimised' our recipes to a certain extent through focus groups, testing and chef creation. We now want to optimise the nutritional component by seeing how far we can increase(protein) or decrease (salt) certain ingredients without affecting sensory characteristics.
Hind sight is 20/20. I would have recommended these be included in your initial recipe experiments.
We have 'reference' versions of these recipes which will serve as a guideline for desired level of various sensory characteristics (so we aim to investigate how much extra protein and how little salt can we use without decreasing acceptable taste and texture).
Use these "reference versions" to create your ordinal scale.
We have three categories of soup with a different liquid base and want to test how the ingredient chunks interact with the different liquids, hence the three aroma categories.
I'm not sure I understand why the consistency of the soup (chunkiness) would interact with flavor (or why you would care), but you can estimate block by factor interactions if you block on flavor. I guess I'm thinking more about what would you do with knowledge of a flavor by chunk interaction...to me you would need to have a different model for each flavor...that would be the advantage of blocking on flavor...it would be like 3 separate experiments on the same factors that can be compared.
4. I don't understand the second bullet under mixture? If there are 2 values, it can't be constant.
I have removed this element. All mixture factors are now variable (and I have also subsequently removed the linear contraint).
5. Do you understand noise in the process? For example: water quality, homogeneity of the batch, ambient conditions, lot-to-lot variation of the ingredients, day-to-day variation, etc.
We are trying to minimise noise - training sensory assesors, blocking for the variation of days, one production of all the recipes to be tested etc.
This is NOT what you should do. You want to create a design space that is representative of future conditions. Consumers' sensory perception varies, production processes vary, raw ingredients vary, etc.
The exact standardization of experimental conditions, which is often thoughtlessly advocated as a panacea, always carries with it the real disadvantage that a highly standardized experiment supplies direct information only in respect to the narrow range of conditions achieved by the standardization. Standardization, therefore, weakens rather than strengthens our ground for inferring a like result, when, as is invariably the case in practice, these conditions are somewhat varied.
R. A. Fisher (1935), Design of Experiments (p.99-100)
6. Do you understand the difference between repeats and replicates?
I didn't but I do now!!
Following your comments I have adjusted the custom DoE (in attached pdf). In the model evaluation part it states aroma 1 and aroma 2 - is this because I have three categorical levels?
I don't follow your logic here? Although I notice you use French and I don't.
"All models are wrong, some are useful" G.E.P. Box
