Design Of Experiments
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May 2, 2003 at 5:21 am #32139
Dear Friends
My problem is related DOE
i need clarification
Suppose i have 7 factors each at 2 level i want to go for design at resolution 4 so i will require minimum 16 runs of experiments.
what extra information will i get if i do 32 experiments?
ankur0May 2, 2003 at 1:34 pm #85489
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.For a 16 run res IV design with 7 factors at 2 levels you will have all main effects clear of all twoway interactions and at most seven specific twoway interactions clear of one another. All other twoway interactions will be confounded with one another. If you choose to go for a 32 run res IV design with 7 factors at two levels you will have all main effects clear of all twoway interactions and 15 of the 21 possible twoway interactions clear of one another. The other six twoway interactions will be confounded with each other. Thus, increasing your runs from 16 to 32 will increase the number of twoway interactions that you can examine.
0May 2, 2003 at 1:50 pm #85490How do I know which 2 way interactions to examine?
0May 2, 2003 at 2:31 pm #85492If you use a statistical package such as Minitab it will generate the DOE spreadsheet for you. (This is the easiest way to determine which interactions will be confounded). By running the DOE at res IV / 32 runs you can have most two way interactions freed of confounding. Without knowing the process that is being DOE’ed it is difficult to recommend which method to use – cost is one factor (as always) but can you reduce the KPIV’s ?
The following lists the deault generators for a 32 run DOE / 7 factors / 1/8th fraction / res IV. In this case only three two interactions are confounded with other two way interactions.
Fractional Factorial Design
Factors: 7 Base Design: 7, 32 Resolution: IV
Runs: 32 Replicates: 1 Fraction: 1/4
Blocks: none Center pts (total): 0
Design Generators: F = ABCD G = ABDE
Alias Structure
I + CEFG + ABCDF + ABDEG
A + BCDF + BDEG + ACEFG
B + ACDF + ADEG + BCEFG
C + EFG + ABDF + ABCDEG
D + ABCF + ABEG + CDEFG
E + CFG + ABDG + ABCDEF
F + CEG + ABCD + ABDEFG
G + CEF + ABDE + ABCDFG
AB + CDF + DEG + ABCEFG
AC + BDF + AEFG + BCDEG
AD + BCF + BEG + ACDEFG
AE + BDG + ACFG + BCDEF
AF + BCD + ACEG + BDEFG
AG + BDE + ACEF + BCDFG
BC + ADF + BEFG + ACDEG
BD + ACF + AEG + BCDEFG
BE + ADG + BCFG + ACDEF
BF + ACD + BCEG + ADEFG
BG + ADE + BCEF + ACDFG
CD + ABF + DEFG + ABCEG
CE + FG + ABCDG + ABDEF
CF + EG + ABD + ABCDEFG
CG + EF + ABCDE + ABDFG
DE + ABG + CDFG + ABCEF
DF + ABC + CDEG + ABEFG
DG + ABE + CDEF + ABCFG
ACE + AFG + BCDG + BDEF
ACG + AEF + BCDE + BDFG
BCE + BFG + ACDG + ADEF
BCG + BEF + ACDE + ADFG
CDE + DFG + ABCG + ABEF
CDG + DEF + ABCE + ABFG
The following lists the default generators for a 16 run DOE / 7 facots / 1/4 fraction/ res IV. In this case all two way interactions are confounded with at least one other two way interaction.
Fractional Factorial Design
Factors: 7 Base Design: 7, 16 Resolution: IV
Runs: 16 Replicates: 1 Fraction: 1/8
Blocks: none Center pts (total): 0
Design Generators: E = ABC F = BCD G = ACD
Alias Structure
I + ABCE + ABFG + ACDG + ADEF + BCDF + BDEG + CEFG
A + BCE + BFG + CDG + DEF + ABCDF + ABDEG + ACEFG
B + ACE + AFG + CDF + DEG + ABCDG + ABDEF + BCEFG
C + ABE + ADG + BDF + EFG + ABCFG + ACDEF + BCDEG
D + ACG + AEF + BCF + BEG + ABCDE + ABDFG + CDEFG
E + ABC + ADF + BDG + CFG + ABEFG + ACDEG + BCDEF
F + ABG + ADE + BCD + CEG + ABCEF + ACDFG + BDEFG
G + ABF + ACD + BDE + CEF + ABCEG + ADEFG + BCDFG
AB + CE + FG + ACDF + ADEG + BCDG + BDEF + ABCEFG
AC + BE + DG + ABDF + AEFG + BCFG + CDEF + ABCDEG
AD + CG + EF + ABCF + ABEG + BCDE + BDFG + ACDEFG
AE + BC + DF + ABDG + ACFG + BEFG + CDEG + ABCDEF
AF + BG + DE + ABCD + ACEG + BCEF + CDFG + ABDEFG
AG + BF + CD + ABDE + ACEF + BCEG + DEFG + ABCDFG
BD + CF + EG + ABCG + ABEF + ACDE + ADFG + BCDEFG
ABD + ACF + AEG + BCG + BEF + CDE + DFG + ABCDEFG
0May 2, 2003 at 2:37 pm #85493Thanks, but I know that.
What I am interested in is a discussion of first how does one choose which interactions to study if I must choose a subset of those possible; and second, now that I have chosen, how do I get the right design?0May 2, 2003 at 2:40 pm #85494
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.If we call the seven factors A,B,C,D,E,F,G then for a 16 point design the alias structure for the two way interactions is:
AB + CE + FG + ACDF + ADEG + BCDG + BDEF + ABCEFG
AC + BE + DG + ABDF + AEFG + BCFG + CDEF + ABCDEG
AD + CG + EF + ABCF + ABEG + BCDE + BDFG + ACDEFG
AE + BC + DF + ABDG + ACFG + BEFG + CDEG + ABCDEF
AF + BG + DE + ABCD + ACEG + BCEF + CDFG + ABDEFG
AG + BF + CD + ABDE + ACEF + BCEG + DEFG + ABCDFG
BD + CF + EG + ABCG + ABEF + ACDE + ADFG + BCDEFG
so AB,AC,AD,AE,AF,AG,and BD are clear of one another.
For a res IV 32 point design the alias structure for the two way interactions is:
AB + CDF + DEG + ABCEFG
AC + BDF + AEFG + BCDEG
AD + BCF + BEG + ACDEFG
AE + BDG + ACFG + BCDEF
AF + BCD + ACEG + BDEFG
AG + BDE + ACEF + BCDFG
BC + ADF + BEFG + ACDEG
BD + ACF + AEG + BCDEFG
BE + ADG + BCFG + ACDEF
BF + ACD + BCEG + ADEFG
BG + ADE + BCEF + ACDFG
CD + ABF + DEFG + ABCEG
CE + FG + ABCDG + ABDEF
CF + EG + ABD + ABCDEFG
CG + EF + ABCDE + ABDFG
DE + ABG + CDFG + ABCEF
DF + ABC + CDEG + ABEFG
DG + ABE + CDEF + ABCFG
So the six two way interactions that are not clear of each other are CE, CF, CG, FG, EG, EF. However, CE, CF, and CG (or FG, EG, and EF,) are clear of all of the other two way interactions so the number of two way interactions that are actually clear of one another (as defined for the 16 point design) should be 18 and not 15 as I stated in my first post.
Since you can assign any variable you want to the coded letters “A”, “B”, etc. you do have some latitude with respect to defining the interactions that you wish to examine.0May 2, 2003 at 2:44 pm #85495Robert,
What about using Linear Graphs to choose the design to give the interactions you want?0May 2, 2003 at 3:47 pm #85498
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Stan,
I’ve heard of the method but I don’t know anything about it. If you could either provide a “howto” description of the technique or recommend a good paper/reference I would be interested in learning more.0May 2, 2003 at 4:02 pm #85501Minitab will lay this out for you automatically if you go to DOE > Taguchi.
I would use this to tailor any design where you knew which interactions you should worry about and more importantly which ones you don’t need to look at. I, personally, would not use the analysis here. I would redefine the experiment under DOE > Factorial and do the analysis there.
If you want to know the logic and the mechanics behind this after looking at it, give me an email address and I will explain.0May 2, 2003 at 4:14 pm #85502
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Thanks for the tip Stan. I’ll check it out.
0May 2, 2003 at 9:18 pm #85515One thing to note, since the Taguchi designs are primarily for studying main effects, all the possible confounding relationships are not identifed in the linear graphs and interaction tables. They are only good if you want to study the interactions between a few selected factors.
In Minitab, if you go into the Taguchi designs and choose 7 factors at 2 levels, you can find all 21 of the possible 2 factor interactions. If you select all 21 and ask for the design, you will get an error message that a design cannot be located for your selections.
If you want to know all of the possible interactions and study them, stick with the Western or classical designs.0May 2, 2003 at 9:51 pm #85517You do not understand Linear Graphs – bad advice
0May 3, 2003 at 8:54 pm #85524If you have Minitab version 13 or higher (I believe 14 is just about to be released) then you can specify which factors you want. Generate the spreadsheet and if the factors that you want are not the ones listed for interactions tudy you can change the factor names easily. I would also investigate the correlation levels between the factors and look at the variance impact of the factors on the process to determine which factors should be studied for interaction.
0May 5, 2003 at 2:53 pm #85554Stan,Do the linear graphs show all possible 2 factor interactions and confounding relationships so that you can study all of them in the same experimental run? If so, where can I locate them?Thanks for your help.
0May 6, 2003 at 12:38 am #85569You can’t study more things than the experimental design allows.
For example, the sixteen treatment combination experiment that was first proposed will allow for studying 15 things. If you want 7 factors, this allows for, at most, 9 two way interactions. Since there are a possibility of 21 two way interactions, you can’t look at them all.
BUT, if yoiu have real process knowledge and know which interactions you should look for and more importantly which ones you can discount, you can get the same knowledge out a greatly reduced experiment.
You just need real knowledge. There are Taguchi practitioners that do this daily.0May 6, 2003 at 2:32 pm #85584Stan,
I appreciate your response and explanation.
In a previous post I basically stated that if one wanted to know all the possible confounding relationships of 2 factor interactions for 7 factors at 2 levels, the Taguchi linear graphs would not show them all. I probably should not have included “…and study them…” in my closing sentence. Obviously, I assumed that if the effect of an interaction column was significant, the individual would perform further investigations/experiments to determine which of the factor interactions the effect was due to. Your response to my post was, “You do not understand linear graphs – bad advice”.
If I understand your most recent post correctly, you say that of the 21 possible 2 factor interactions, the linear graphs will allow (at most) 9 interactions. If this is the case, maybe I understand linear graphs more than you think.
Without getting into a debate of Taguchi versus Western techniques, for individuals who want to see all possible confounding or aliasing involved in a particular design, the linear graphs will not provide this information. If you don’t care what all of the interactions are and want to study only specific ones, the linear graphs are fine.
I would appreciate if you would refrain from using derogatory remarks in the future, when you have no knowledge of someone’s background and experience.
Thank you
0May 6, 2003 at 9:05 pm #85598All I said is that you don’t understand Linear Graphs and I still think thats true. If you have process knowledge, you will not want to include all possible interactions, if for no other reason, it is too complex and too costly. As you well know, most interactions drop out of the analysis immediately.
Don’t be so touchy, I’ll say what I believe to be true. It should not be an issue.0 
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