# Conduct a fractional factorial 2^13-5 experiment with Minitab

T

#### thunderspeed

Hi ,
I want to conduct a fractional factorial 2^13-5 experiment with minitab , I mean its a 2^13 and i want to make it a fractional factorial of V resolution so it will be 2^13-5 = 2^8 ,,,, can this ever be done with minitab ?
if not can you recommend another software name that can do such experiment ?

#### v9991

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Yes it is possible, Minitab offers Res-IV, fractional factorial designs for 13 factors., with options for 32, 64 & 128 runs.

BUT, why dont you consider using other screening designs such as Placket burman or Definitive screening designs, to be more manageable runs of < 16-17 runs. (inlcuding center points) even fractional factorial with res-III gives us 16 runs.!!!

T

#### thunderspeed

dear v9991 ,

I want to explain the situation I have so you can get idea of what I'm facing . I have an analytical equation for a thermal system . To answer this equation and come out with this single response of interest , one must solve a long series of equations , conducting a long process of iterations and given some boundary conditions . My goal is to come out with a linear equation to resemble this system and give the closest response possible to the real response.And finding out the percent of contribution of each parameter to the response . This is for making the design and sizing process easier for engineers on site .
What I just said was made in a paper written by a researcher in this field using the fractional factorial method of a 2^13-5 V resolution .
I myself want to try to do the same except I want to find the linear equation from the taguchi method instead . I believe it might give a more precise linear equation since the one predicted from mentioned factorial method returned a response sometimes not very close to the real one .

Up till now , I've written a python code conducting the analytical equations solutions and iterations to give the response and defined boundary conditions . Know I have no other way to make sure the code I've written is all ok except by conducting the same fractional factorial procedure as this researcher , if the results (percent of contribution or linear equation constants ) were the same , then my code now is verified to be right and I can proceed to answer with taguchi method and come up with a new linear equation .

#### v9991

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thank you for explaining the background., but couple of queries.
1. you mentioned about 'linear' equation couple of times, hope you are sure that there are no interactions! and it is not any other model!
2. when compared with res-V design (256 runs) or res-IV design ( 128 runs); optimal design offers 105 runs. can think about it.

T

#### thunderspeed

1- It has only one factor and some 2 factor interaction considered
all main factors were as I mentioned before 13 - 5 = 8 , and the number of two factor interactions of interest are 11 . The rest of 2 factors interactions and all 3 factor interactions and above are negligible .
2- You appear to be right , but as I told you before , my concern is to follow the same method exactly as the one in the researcher's paper so I can check the validity of my analytical equation .
3- The result equation is something like :

a = (alpha0) + (alpha1 * r )+ (alpha2 * t )+ (alpha3 * y )+ (alpha1 * u)+ (alpha1 * p)+.............+ (alpha1 * ry )+ (alpha1 * ru )+ (alpha1 * pz )+.....

my goal is to come out with the constants alpha0 , alpha 1 , ... till alpha 19
using the same method (fractional factorial of 2^13-5 = 2^8 , V resolution) using minitab .

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