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# Variable responses analysis (DOE)

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Hello colleagues,

“When running an analysis of influences experiment, the number of experiments required using the basic methodology increases on the order 2**x, where x = number of input variables”. This is text from Help.

In full factor experiment requires:

- 8 runs for 3 factors,

- 16 runs for 4 factors,

- 32 runs for 5 factors,

- 64 runs for 6 factors,

- 128 runs for 7 factors.

In Variable responses analysis of ASMI requires:

- 15 runs for 3 factors,

- 25 runs for 4 factors,

- 43 runs for 5 factors,

- 77 runs for 6 factors,

- 143 runs for 7 factors.

What type of DOE is used in ASMI? And why do we need so many runs, if full factor experiment includes all combinations?

# Re: Variable responses analysis (DOE)

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Hi, Barvinsky.

The 2^N full factorial experiments are used to provide linear models like

Y=A0+A1*X1+A2*X2+...AN*XN+A12*X1*X2+A13*X1*X3...+A

Those models are usable if you want to evaluate the influence of a factor or a combination of factors to the responce: whether increasing of a factor increases the responce or decreases it. By the nature of the linear model it does not predict any minima or maxima of the responce.

Often the molder expects to have a minimum or a maximum of the responce: e.g. Minimum of the warpage, minimum of injection pressure, etc. For the model to have minimum or maximum it must have at least quadratic terms. For a full factorial experimant to produce quadratic terms we must have at least three levels for each input variable. This gives 3^N experimants for each variable. That is 3 experiments for 1 variable, 9 for 2 variables, 27 for 3 variables, 81 for 4 variables, 243 for 5 variables, etc.

Moldflow uses a lmore economic method named Central_composite_design. It requres 2^N+2*N+1 experiments and still work pretty well.

# Re: Variable responses analysis (DOE)

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Hi Alexander,

Thank you very much!