Hi

I optimize output parameters by using RSM. it is easy, you chose your parameter and select method of optimize. that optimize output parameters are for final results in Convergence Special time. 

Good Luck!

Hi soroush

Thanks for reply.

Actually there are 3 outcomes which are simultaneously needed to be opoptimized using various input parameters.

Dear Ashutosh.

By using Central Composite Design CCD in RSM, you can design your work. There are 3 outcomes (or responses) and using many input parameters (factors). 

For example, if you use 4 factors, we have: 2^4 + 2*4 + 6 =30 runs. herein, 2^4 runs for factorial runs, 2*4 runs for axial points and 6 runs for center points. After doing 30 runs, you can have results for the optimization that you want

Good luck,

Dang 

Dear Dang,

Thanks for reply.

Ca you please mention the level of variable you took for the example you quoted. I guess it might be 2.

I was wondering if there is any method using taguchi technique for multiresponse optimization.

Dear Ashutosh,

In designing by CCD, The CCD incorporates five levels (coded –α, –1, 0, +1, +α) in which axial points (±α) for a factor and 0 for all other factors. In addition, center points were coded as 0 and used to estimate pure error.

However, if you choose Box-Behnken design. The Box-Behnken design incorporates three levels (coded –1, 0, +1). This design is the smallest classic response surface design for fewer than five factors. 

I recommend you to use CCD with 5 levels coded as above. When we split into 5 levels, I think the accuracy is higher than 3 levels.

Taguchi technique is also a solution for this problem. There had had many publications about this method before. But now, I think that RSM is maybe the best solution.

Cheers,

Dang

Thanks Dang for your guidance. It will help me a lot.

If you plan on looking for interactions among your factors, Taguchi is generally not a good idea.

How many factors do you want to test? What levels do those factors have? You might want to look into optimal response surfaces.

As far as optimization goes, when you start dealing with multiple responses, you can do many things. Some will be better than others. For example, if you say you need to maximize some things and minimize others,  you will come out with one set of factor settings. These might not work that well for what you want to do. If you go back and set some of the response such that they must be below/above a certain value will give you better results. 

An example of this, I can say, I need to minimize variance and maximize a response. The software might tell you that a point with "zero" variance and a small response is best. If you come back and say, variance needs to be below 10, then you will get a second set of factor settings that will give you a better response. 

Hi,

Taguchi based GRA Analysis or RSM based Desirability Function.

Good luck!

Thanks for reply Andrew

Infact I need to optimize these parameter within certain range. So what can be the specific method in RSM to perform the same?

Whether it must be CCD based RSM or Desirability function based on RSM?

Also which software can be used to analyse the results?

Thanks

Sorry for the delay. 

I use Design Expert software from Stat Ease. The software allows me to create a model for each factor I want to analyze. Then optimize all the responses at the same time. In general, the desirability function is what the software will use to find the best optimal solution.  The desirability function does not care what type of statistical design you use. They are separate functions.

What you are looking for is called "Multiple-Response-Optimization". First you consider each of the responses independntly and create the model for it, using the DoE. The same experiments are used for all responses, you simply work through one response after another.

Then you apply ramp-functions to project each response to a range of 0 to 1. 0 is bad, 1 is perfect. The desrability function is the product of the ramp values. In case one response is bad, the total value becomes 0. In case everything is perfect, you get 1. This way you can apply regular optimization techniques, since you collapsed the multi-dimensional problem to a one-dimensional problem.

A nice additional method to use is the Principal Component Analysis, applied on the responses. This way you can find out if the different responses are "fighting each other". More details in my script, download for free.