DOE (Design of Experiment) with Several Output Variables




I'm recently tasked to do a Design of Experiment to optimise several press parameters. I have a few questions

1. We have identified several input variables to test. However the tricky part is we also have several (about 3-4) output variables (all measureable variables) that we need to optimise simultaneously. Is it possible to conduct one single set of DOE with where several output variables are tested simultaneously against our input variables? If yes , what if the optimum setting for one output variable may not be the same as the optimum setting for another output variable.
2. Or do I need to do some preliminary analysis to see if the output variables are related? If so what tools should we use? Multivariate analysis? Can a multi vari chart do the trick?
3. One prerequisite of DOE is to ensure the process is stable before attempting DOE. This is a fairly new process and we do not have enough data to run Xbar R charts. Will it suffice to plot individual chart (vs time) to see if there is any time related trends on the output parameters instead?

Thanks in advance
S Lim
Elsmar Forum Sponsor

David DeLong

Re: DOE with several output variables

I will assume that you are going to use a Taguch Array with 2 levels. If so the L4 can take 3 factors, L8 7 factors and and L16 15 factors. The factors may be either variable or attribute in nature.

All are tested simultaneously in a balanced manner.


Forum Moderator
Re: DOE with several output variables

Simultaneous optimization of multiple input factors will require Response Surface Methodology.

Do not start this process thinking that you can optimize your process after a single designed experiment. It typically will take a screening experiment to isolate significant factors and interactions. This may or may not take a follow-up experiment to isolate confounded/aliased factors/interactions. Once these are isolated, another experiment with multiple levels is required to determine whether curvature exists and how to best optimize. Finally a confirmation experiment must be run to validate the final model.

Tim Folkerts

Trusted Information Resource
Re: DOE with several output variables

I agree with Miner - you will probably need more that a single experiment to achieve your goals.

Let me address what I consider to be the main question. Assuming you have selected important input variables (perhaps from a screening experiment) and that you have run the appropriate trials for a response surface experiment, it is possible to use that information to optimize several output variables.
  • If all the output variables are optimized with the same values of the input variables, then when you have analyzed the experiments, you are basically done.
  • If the output variables are optimized with different values of the input variables, then you typically create a composite variable and optimize that single variable. As a simple example, if you want to maximize all the variables, you could create a new variable by adding together all the outputs. Then you would optimize this new variable.
Deciding how to combine the variables would take a bit of judgment. Minitab has this process of creating a composite variable built in.

You might want to consider EVOP (Evolutionary Operation) as an alternative to standard response surface designs. EVOP is more of a continuous improvement approach - making minor changes to an existing process.
Classic experimental design and Taguchi methods are revolutionary methodologies which help us to establish an optimum combination of the design factors and their proper levels for the manufacturing process. They are very powerful tools; but they cost money, time, manpower and require special training to conduct the experiments. In most cases, they interrupt production. Experimental design should be used in the design stage and trouble shooting to solve specific quality problem. It cannot be a routine operation. EVOP is a tool in which a continuous investigative routine becomes the basic mode of operation for the plant and replaces normal static operation.
This is from Another link that looks promising is at (I have no connection to either of them - they came up in Google searches and looked pretty good first glance).

Tim Folkerts
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