Optimizing Multiple Response Variables Using Taguchi Signal-to-Noise ratios

[TaguchiNovice]

Hi All,

I am trying to optimize a system using Taguchi's Signal-to-Noise ratios. This is a larger-the-better kind of optimization and it involves 2 response variables that need to be optimized at the same time - i.e. I want to maximize the value of both these response variables at the same time using the same experiment.

Now, this presents a problem because in many situations, choosing one level of a control factor in my experiment might maximize one of the response variables, but choosing another level of the same factor will maximize the other response variable. In that situation, it is unclear to me as to which factor level should be chosen.

The way I have thought of resolving this is to use an equation that combines the 2 response variables, and weights are attached to each response variable in the equation representing the value of the 2 variables to me.

For instance, if R1 and R2 are the 2 response variables, and if the R1 variable is thrice as important to me as the R2 variable, then instead of trying to maximize R1 or R2 separately, I would maximize the equation 3R1 + R2.

So, in this case, I will find out the value of this equation 3R1 + R2 for each of my test cells and then use the standard Larger-is-Better Signal to Noise Ratio to find out which factor levels will maximize the value of this equation for me and at the same time will minimize noise.

My question is - is this a statistically valid way of approaching the issue? Is there a better way of doing this?

 

[Marc]

This is above me - Any statistical gurus out there that can comment?

 

[Barbara B]

Just for clarification: You want to optimize a process with two response variables and several (how much?) factors. Are the factors qualitative or quantitative?

You want to achieve the best factor levels for optimal results. On the other hand you have a preferred response variable R1 and a less preferred R2, but nevertheless R1 and R2 are both important for the process. Is this correct so far?

Barbara

 

[TaguchiNovice]

Hi Barbara

Thanks for responding.

You are absolutely correct. I am trying to optimize 8 factors using Taguchi's L18 array (i.e. 7 three level factors and 1 two level factor). The factors are all qualitative.

Let me know if you have any other questions.

Thanks.