Hi

Fist of all, why do you want to do a RSM (response surface design) ? being a central composite design, composite design in general, Box-Behken design?

- with this question I mean what do you want to achieve as a result from your experimental work:

A process/synthesis/unit operation optimization should be conducted by some steps

(1) Identify a procedure / method that operate

(2) Conduct a parameterization of the procedure, that is to identify the experimental variables that are possible to variety and the responses that can be measured (yield, selectivity, ….)

(3) Conduct an introductory screening design. In this you commonly identify the solvent, catalyst etc. that you should use. In your case you should consult. the paper by Rolf Carlson and collaborators: Strategies for solvent selection. Acta Chem Scand 1985 B39, 79-91 (and the book by Carlson see below).

When you have performed a screening design, where you should include as many variables as possible. Type of design for this purpose: I suggest you to use a fractional factorial design. By such a design you can identify which variables that are the more important and identify a preliminary optimum.

(4) The preliminary identified optimum might subsequently operate as the centre of a new design that allow you to create a predictive model that allow you to estimate: (a) coefficients for single variables, (b) coefficients for the square of each of the single variables and (c) the coefficients for two-factor interactions of the single variables. I strongly recommend to you to use a response surface design of the type central composite design. This allow you to estimate a model:

y(x1, x2, …, xk) = b0 + b1x1 + b2x2 + … + bkxk + b12x1x2 + b13x1x3 + … + b11x12 + b22x22 + … bkkxk2

Be aware that sometimes, the star points of the central composite design cannot be created; e.g. reaction time -1 (10 min)  0 (25 min) +1 (40 min) will result in that “-2” become a negative time:  -5 min.  In such cases you can solve this by change either the value of (-1) increase the reaction time, shorten the step, i.e. the (0) will be at a smaller value. You can also change the value of the star point.

Introduction of the categorical variables such as: “type of solvents”, “type of catalyst”, “type of reactor”, “type of base”,  etc. should not, from my point of view” be included in a response surface design. In fact, such variables shall be investigated by means of a screening design, where all such parameters (variables) is investigated/compared and decided before you do the response surface deign (a composite design).

Some “bibles” for statistical experimental design, screening and response surface modelling and more:

Design:

Box, G. E. P.; Hunter, J.; Hunter, W. G. Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed.; 390 Wiley: New York, 2005.

Box, G. E. P.; Draper, N. R. Empirical Model-Building and Response Surfaces; Wiley: New York, 1987.

Model building – regression:

Montgomery, D. C.; Peck, E. A. Introduction to Linear Regression Analysis; Wiley: New York, 1982.

Draper, N. R.; Smith, H. Applied Regression Analysis, 3rd ed.; Wiley: New York, 1998.

Optimization in synthesis:

Design and Optimization in Organic Synthesis, Second Revised and Enlarged Edition

Rolf Carlson Johan Carlson

ISBN: 9780444515278, Elsevier Science, 8th April 2005

Normally central composite design has more features as compared to box behnken, but the selection of an appropriate design depends upon the nature of parameters and preliminary information about parameters, I can help you to select best one if you share the nature and possible range of reaction parameters. The link below would also help you to discuss various parameters regarding such designs 

https://www.researchgate.net/publication/266910524_RSM_based_optimized_enzyme-assisted_extraction_of_antioxidant_phenolics_from_underutilized_watermelon_Citrullus_lanatus_Thunb_rind?_iepl%5BviewId%5D=YQLaW01bk0UBPLXiXBEaOH5rHAQjOpgsQy1u&_iepl%5Bcontexts%5D%5B0%5D=prfhpi&_iepl%5Bdata%5D%5BstandardItemCount%5D=3&_iepl%5Bdata%5D%5BuserSelectedItemCount%5D=4&_iepl%5Bdata%5D%5BtopHighlightCount%5D=2&_iepl%5Bdata%5D%5BtopHighlightIndex%5D=1&_iepl%5Bdata%5D%5BfeaturedItem1of2%5D=1&_iepl%5BtargetEntityId%5D=PB%3A266910524&_iepl%5BinteractionType%5D=publicationTitle

Article RSM based optimized enzyme-assisted extraction of antioxidan...

Dear,

If you are not sure about the range of the process parameter in your study then go for CCD approach.

CCD is the widely accepted approach because it can give you the idea about the optimised condition if it lies beyond the chosen range. So if you have a basic rough idea of your process and the range of process parameters but not sure about the probable optimised condition then go for CCD. 

You can opt for BBD only if you are sure about the optimised condition will lie within the chosen range, because in BBD approach it will not consider the values of +-alpha of the individual parameter. Thus if you are sure about the probable optimised condition will lie in the chosen range then go for BBD approach because it will give optimised condition in a minimum number of experimental runs as compared to CCD. 

I hope it will help you to understand the selection protocol for both the approaches. for further help, you can contact me or go through my papers.

Thanks and Regards

Sumit

Hi professor Muhammad, 

Thanks for your answer.  I have the next factors and levels:

*Amount of catalyst: between 5 and 25 mg (Level -1: 5 mg, Level 0: 15 mg and Level 1: 25 mg)

*Kind of solvent: Toluene, Ethyl acetate and ethanol. (-1,0 and 1 respectively)

*Temperarture: 50, 60 and 70 (-1, 0 and 1 respectively)

*Reaction time: 0,5-1,5 and 2,5 h. (-1, 0 and 1 respectively)

As I said in my message, I chose the Box-Behken model, but I created the central-composite design, but with this the value of alpha (star point) are not in the range of my parameters (for me is so strange).

I hope that you can help me.

On the other hand, professor Summit I will contact after read your articles if exist other possibility.

Thanks a lot,

Julián Sánchez.

In my understanding solvent type should be taken as categoric parameter rather than numeric, still I will check and share with you design tomorrow for these values and let see it is acceptable for you or not 

Hi Porfessor,

I am waiting for your answer!!

Best regards,

Julián.

Hi

Fist of all, why do you want to do a RSM (response surface design) ? being a central composite design, composite design in general, Box-Behken design?

- with this question I mean what do you want to achieve as a result from your experimental work:

A process/synthesis/unit operation optimization should be conducted by some steps

(1) Identify a procedure / method that operate

(2) Conduct a parameterization of the procedure, that is to identify the experimental variables that are possible to variety and the responses that can be measured (yield, selectivity, ….)

(3) Conduct an introductory screening design. In this you commonly identify the solvent, catalyst etc. that you should use. In your case you should consult. the paper by Rolf Carlson and collaborators: Strategies for solvent selection. Acta Chem Scand 1985 B39, 79-91 (and the book by Carlson see below).

When you have performed a screening design, where you should include as many variables as possible. Type of design for this purpose: I suggest you to use a fractional factorial design. By such a design you can identify which variables that are the more important and identify a preliminary optimum.

(4) The preliminary identified optimum might subsequently operate as the centre of a new design that allow you to create a predictive model that allow you to estimate: (a) coefficients for single variables, (b) coefficients for the square of each of the single variables and (c) the coefficients for two-factor interactions of the single variables. I strongly recommend to you to use a response surface design of the type central composite design. This allow you to estimate a model:

y(x1, x2, …, xk) = b0 + b1x1 + b2x2 + … + bkxk + b12x1x2 + b13x1x3 + … + b11x12 + b22x22 + … bkkxk2

Be aware that sometimes, the star points of the central composite design cannot be created; e.g. reaction time -1 (10 min)  0 (25 min) +1 (40 min) will result in that “-2” become a negative time:  -5 min.  In such cases you can solve this by change either the value of (-1) increase the reaction time, shorten the step, i.e. the (0) will be at a smaller value. You can also change the value of the star point.

Introduction of the categorical variables such as: “type of solvents”, “type of catalyst”, “type of reactor”, “type of base”,  etc. should not, from my point of view” be included in a response surface design. In fact, such variables shall be investigated by means of a screening design, where all such parameters (variables) is investigated/compared and decided before you do the response surface deign (a composite design).

Some “bibles” for statistical experimental design, screening and response surface modelling and more:

Design:

Box, G. E. P.; Hunter, J.; Hunter, W. G. Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed.; 390 Wiley: New York, 2005.

Box, G. E. P.; Draper, N. R. Empirical Model-Building and Response Surfaces; Wiley: New York, 1987.

Model building – regression:

Montgomery, D. C.; Peck, E. A. Introduction to Linear Regression Analysis; Wiley: New York, 1982.

Draper, N. R.; Smith, H. Applied Regression Analysis, 3rd ed.; Wiley: New York, 1998.

Optimization in synthesis:

Design and Optimization in Organic Synthesis, Second Revised and Enlarged Edition

Rolf Carlson Johan Carlson

ISBN: 9780444515278, Elsevier Science, 8th April 2005

Dear Sanchez,

Really sorry, I have tried a lot but could not find your question during last couple of days, Now I have noted it and I will attach you design and word file in private text

One is the selection of experimental points (plan of experiment) and the other is the mathematical model. Usually, the plan of the experiment imposes the form of the equation - in this case the power polynomial of first degree with interactions (ie y = ao + a1x1 +... + a12 x1x2......). The problem is the way of determining the coefficients. Of course, you can use -1, +1, and central point 0 (chacking of variance homogeneity), and you can use real values. In this first (orthogonal plan) calculations are simplified (no inversion of the matrix in the least squares method). There is also no numerical correlation between coefficients of equation. However, it is important to remember that the design of the experiment takes into account the physical quantities that can be assigned a value.

It is also important to remember that the orthogonal plan usually describes the surface of the response as a hyperplane. So in the case of optimization, it is only possible to determine the value of the empirical gradient (Box and Wilson method).

Regards,

Dear Julian,

I have a published article on RSM with Box-Behnken Experimental Design (BBD). The detailed procedure of BBD design involving four variables. I hope it might be helpful to you. Let me know if you have any specific questions.

Article Optimization by Box-Behnken Experimental Design for synthesi...