Dear Jyotsna,

If you want to reduce the number of experiments, you will have to go for a sequential approach.

First, using a screening design, identify which factors are important.

Second, using important factors in a full or fractional factorial with center point, verify whether curvature is present or not.

Third, using method of steep accent/ decent, identify the region of maxima/ minima as the case may be.

Fourth, apply DOE in the region of maxima/ minima to find the optimum point.

Dear Jyotsna,

If you want to reduce the number of experiments, you will have to go for a sequential approach.

First, using a screening design, identify which factors are important.

Second, using important factors in a full or fractional factorial with center point, verify whether curvature is present or not.

Third, using method of steep accent/ decent, identify the region of maxima/ minima as the case may be.

Fourth, apply DOE in the region of maxima/ minima to find the optimum point.

Minitab is excellent for this purpose. I agree with Divyang and I would suggest you do two or three experiments, to successively approach the optimum.

Begin with a crude 2-level design (2^p). For each factor, you just have one 'low' and one 'high' level. This will tell you which factors are the most important, the size of their effect.

You can then exclude a couple of factors that are not very important, to get a smaller number of factors. These you can use in a response surface optimization. The design should be such that the optimum is located somewhere within the parameter space. Use a central composite design. You then have three levels, 'low', 'middle' and 'high'. This will allow you to fit a quadratic response surface and it will approximately locate the optimum. Use a resolution 4 or better design.

Then you make a third experiment, close to the optimum you found in the second experiment. Now you can also include the less important factors and perhaps increase the number of replicates to get more confidence in your results. Use a rotatable central composite response surface design with resolution 4 or better.

Dear  Nyman n Divyang 

Thank you very much.

According to your suggestion, the factors are reduced to 3.In minitab when I design the experiments with  "create response surface design" it gives only 2 level option (high and low).  With "create factorial design" I got 54 runs and with " create response surface design" I got 40 runs. However, the second option (RS) fixes the numeric value of the level on its own. in some run the value also goes -Ve which can't b controlled in my system. Is it fine to follow the first option?  A column appears as "BLOCKS".What is it's significance? For all the run it appears to be 1. I am using this for the first time. So please let me know if I am missing something and need to take care of.

Dear Jyotsna,

Something goes wrong if MiniTab doesn't give other than 2 level designs in creating response surface designs. See e.g. section 11.2 in the link below:

https://onlinecourses.science.psu.edu/stat503/book/export/html/57

If you have already chosen 4 variables of interest, there is no need for screening designs, nor need for reducing the number of variables, unless your experiments are terrible expensive or time consuming. A central composite design with 4 variables creates 2^4+2*4+1 = 25 experiments (plus few replicates at the center point which is a reasonable number. I wouldn’t, at least not before getting an estimate of the mean experimental error, replicate all experiments; just the center point for 3 to 5 times depending on the cost.

Actually you could get one more variable almost at the same cost because a central composite design with a 2^(5-1) fractional factorial part (half fraction) has resolution V, and you could still fit a quadratic RSM model. This design gives 2^4+2*5+1 = 27 experiments (plus the replicates).  

Blocks are for block variables (noise factors). For example, if two work shifts carry out the experiments, the shifts creates a block variable whose unwanted contribution is made uncorrelated with the design variables by the blocking scheme. If you don't have obvious noise factors, use unblocked designs.

In MiniTab, choose either a full central composite design with 4 variables or a half fraction central composite design with 5 variables. The first alternative suggests you 31, and the second 32 experiments. You can reduce the number of center point experiments if you don't choose the default option, but don't go below 3, and if you can afford it, use the default. 

The link below may give you some new ideas:

http://cdn.intechopen.com/pdfs-wm/33609.pdf

Good Luck!

Veli-Matti

Dear Veli-Matti,

Thank you so much for such  a clear and elaborate explanation. Hope this time I'll be able to do the task.

Thank you,

Jyotsna 

Are your 4 factors continuous or categorical? If they are continuous, you can use a 6-factor Definitive Screening Design, which should use 13 runs. This will test your 4 factors at 3 levels and allow you to have some extra df to test interactions. Definitive Screening Designs are a new way to screen factors. 

You only need 3-levels to find a quadratic effect.

If you have 4-levels per factor and you can't use a 3-level design, you can check out the L-16 Taguchi Designs. You'll test your 4 factors at 4 levels each in a screening design. You'll need to remove a factor from the design. You should have several df left over for an error term and look at some interactions.   

you can use taghuchi method!

surf the net for more information

To minimized the experimental runs depends on the factors you are considering, 1. if you are using four factors the runs no will be different from two factors runs no.

2. when you are looking at interactions in the parameters you are considering in your experiment this will also after the no of runs.

3. if using 2 or 3 factors you can employ taghuchi method, but if is more than 3, please make use of other method, in RSM. it will give more accurate result.