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Double Mixture with Process variables

Muralidhara

Hi Team,

A professor (of Agriculture and Food Tech) is going through a challenge. Here is the inputs. Please advice.

Production of a Cream biscuit

Response = Texture (Match Target)

Factors

The cream biscuit product has two mixtures,

Mixture1: Biscuit component = 60% (0.6)

Wheat = 0.05 - 0.26

Sorgham = 0.1 - 0.31

Sugar = 0.2 - 0.41

Mixture 2 : Cream = 40% (0.4)

water = 0.2 - 0.36

Butter = 0.08 - 0.28

Oil = 0.16 - 0.32

Process Variables:

Process variables related to Mixture 1:

Temperature = 160-180

Viscosity = 100-150

Baking Time = 2 - 20

Airflow rate = 100-150

cooling temperature 1 = 5-20

Process variables related to Mixture 2:

Mixing rate = 500-1200

cooling temperature 2 = 5-20

___________

I tried using custom design. but when i add process variables, i am unable to add constraints of mixture1 = 60%

The professor also asked me about feasibility of Kowalski, Cornell, and Vining (KCV) model.

Looking for your inputs and thoughts on this

Thanks

Accepted answers

Ryan_Lekivetz

Mixture-of-mixture with process is possible, but with linear constraints only (see code below for an example). I was also able to add interactions, and remove the singular effects after the first Make Design. However, we cannot currently accommodate any mixture factors with disallowed combinations. You would need to use a candidate set approach for something more complex involving mixture factors.

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Mixture, 0, 1, "X1", 0 ),
	Add Factor( Mixture, 0, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),
	Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),
	Add Factor( Mixture, 0, 1, "X6", 0 ), Add Factor(
		Categorical,
		{"L1", "L2"},
		"X7",
		0
	), Add Factor( Continuous, -1, 1, "X8", 0 ), Set Random Seed( 54230280 ),
	Add Constraint( [1 1 1 0 0 0 0 0.4, -1 -1 -1 0 0 0 0 -0.4] ), Add Term( {2, 1} ),
	Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ), Add Term( {6, 1} ),
	Add Term( {7, 1} ), Add Term( {8, 1} ), Set Sample Size( 21 ), Simulate Responses( 0 ),
	Save X Matrix( 0 )}
);

All comments

Ryan_Lekivetz

I can't speak to the KCV model, but I'm guessing they are trying to add all two-factor interactions? We've discussed how to better handle this in future, but if you setup as a mixture-of-mixture, when JMP fails the first time, it should highlight the effects identified as singular - hitting the "Remove Term" button and Make Design again should work. Heading out to a conference, so not sure when I can check back.

Chris_Kirchberg

Hi @Muralidhara ,

I think you posted on a similar topic:

https://community.jmp.com/t5/JMP-SE-Discussions/Mixture-Design-with-2-Mixtures-and-Process-Variables/m-p/556315

Is this the same people?

Muralidhara

Hi Chris,

This was an old request from IIT Madras Professor. The new request came from Food tech professor.

Thanks

murali

Muralidhara

@Ryan_Lekivetz : I could do the mixture with mixture with custom design. however when i add the process variables, i am unable to add constraints.

looking for your inputs

thanks

murali

Chandramouli_R

Hi @Muralidhara :

This seems to an intresting problem.

The abstract of the Kowalski, Cornell, and Vining (KCV) model paper reads as follows: "Experiments that involve the blending of several components are known as mixture experiments. In some mixture experiments, the response depends not only on the proportion of the mixture components, but also on the processing conditions, A new combined model is proposed which is based on Taylor series approximation and is intended to be a compromise between standard mixture models and standard response surface models. Cost and/or time constraints often limit the size of industrial experiments. With this in mind, we present a new class of designs that will accommodate the fitting of the new combined model". However, this is a feature in Design-Expert (DX), and it is unclear if it is licensed to them.

Based on my understanding of kneading processes in the context, the cream layer is typically sandwiched between the biscuit layers, with each component processed independently. Specifically, the upper and lower biscuit layers are kneaded and baked separately, while the cream layer is blended independently before being deposited as a sandwiched layer in a separate batch process at all production scales. I am uncertain if this is the correct approach being employed, as these represent two mutually exclusive process steps. There is no need to complicate the problem; even if there are certain dietary restriction limitations in mind, this approach seems counterintuitive.

Furthermore, even if the response of the experiment is texture—which can be measured on a scale of hardness or brittleness of the biscuit layer, along with the mouthfeel of the cream and biscuits—this assessment would be highly subjective. It would necessitate a different DOE approach that takes into account the complexities of sensory evaluation.

Muralidhara

Hi Chandra,

Thanks for your input. My example of biscuit was similar to one which i heard from a professor. It was just an example of the Process. Please ignore my knowledge of the process.

The question was how to do Mixture of Mixture with Process variables? This question came from Chemical Professor also earlier. i just gave an example with some random values for factors and responses.

Irrespective of domain, I understand two things.

1. As per my learning Mixture of Mixture is possible in JMP through Custom Design.

2. We can also do a mixture with process variables through custom design.

Now my question is that can we add a process variable to Mixture of Mixture. If yes, how?

I hope this clarifies

thanks

murali

Ryan_Lekivetz

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Mixture, 0, 1, "X1", 0 ),
	Add Factor( Mixture, 0, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),
	Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),
	Add Factor( Mixture, 0, 1, "X6", 0 ), Add Factor(
		Categorical,
		{"L1", "L2"},
		"X7",
		0
	), Add Factor( Continuous, -1, 1, "X8", 0 ), Set Random Seed( 54230280 ),
	Add Constraint( [1 1 1 0 0 0 0 0.4, -1 -1 -1 0 0 0 0 -0.4] ), Add Term( {2, 1} ),
	Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ), Add Term( {6, 1} ),
	Add Term( {7, 1} ), Add Term( {8, 1} ), Set Sample Size( 21 ), Simulate Responses( 0 ),
	Save X Matrix( 0 )}
);