Taguchi versus fractional factorial: Can somebody check the results?

[Matt_B]

I am about to submit a short article to a foreign quality magazine and I am skeptical of my experimental conclusions. Can anybody please tell me if I goofed? It is just a small part of the article, but I don?t want to risk making a basic mistake.


I used a homemade catapult to compare a Taguchi L-8 design to a fractional factorial design; both with 8 runs and no replication. The response variable was distance traveled by a projectile and the objective was to find the optimal settings for a greater distance of travel. There is such a large difference between the results that I fear I may be misinterpreting the data.


Settings for factor A should be high according to the fractional factorial. The Taguchi design indicated factor A should be low. Factor A stretches the catapult?s rubber band so it should be high; I did five verification runs with both the fractional factorial settings and the fractional factorial setting threw the projectile just over 50% farther.



I anticipate one of two possible reasons for the discrepancy: the Taguchi design did not account for interactions; or, I made a mistake.


Can somebody clear this up?





Here is the Minitab output with the results:



[FONT=&quot]Results for: MINITAB FRACTINAL FACTROIAL 2.MTW[/FONT]
[FONT=&quot]Factorial Fit: Response versus A; B; C; D; E; F
[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Estimated Effects and Coefficients for Response (coded units)[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Term Effect Coef[/FONT]
[FONT=&quot]Constant 363,13[/FONT]
[FONT=&quot]A 168,25 84,13[/FONT]
[FONT=&quot]B -6,25 -3,13[/FONT]
[FONT=&quot]C -63,25 -31,62[/FONT]
[FONT=&quot]D -177,25 -88,63[/FONT]
[FONT=&quot]E 14,75 7,37[/FONT]
[FONT=&quot]F 17,25 8,62[/FONT]
[FONT=&quot]A*F -9,75 -4,88[/FONT]
[FONT=&quot]S = * PRESS = *[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Analysis of Variance for Response (coded units)[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Source DF Seq SS Adj SS Adj MS F P[/FONT]
[FONT=&quot]Main Effects 6 128561 128561 21426,8 * *[/FONT]
[FONT=&quot]A 1 56616 56616 56616,1 * *[/FONT]
[FONT=&quot]B 1 78 78 78,1 * *[/FONT]
[FONT=&quot]C 1 8001 8001 8001,1 * *[/FONT]
[FONT=&quot]D 1 62835 62835 62835,1 * *[/FONT]
[FONT=&quot]E 1 435 435 435,1 * *[/FONT]
[FONT=&quot]F 1 595 595 595,1 * *[/FONT]
[FONT=&quot]2-Way Interactions 1 190 190 190,1 * *[/FONT]
[FONT=&quot]A*F 1 190 190 190,1 * *[/FONT]
[FONT=&quot]Residual Error 0 * * *[/FONT]
[FONT=&quot]Total 7 128751[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Alias Structure[/FONT]
[FONT=&quot]I + A*B*D + A*C*E + B*C*F + D*E*F + A*B*E*F + A*C*D*F + B*C*D*E[/FONT]
[FONT=&quot]A + B*D + C*E + B*E*F + C*D*F + A*B*C*F + A*D*E*F + A*B*C*D*E[/FONT]
[FONT=&quot]B + A*D + C*F + A*E*F + C*D*E + A*B*C*E + B*D*E*F + A*B*C*D*F[/FONT]
[FONT=&quot]C + A*E + B*F + A*D*F + B*D*E + A*B*C*D + C*D*E*F + A*B*C*E*F[/FONT]
[FONT=&quot]D + A*B + E*F + A*C*F + B*C*E + A*C*D*E + B*C*D*F + A*B*D*E*F[/FONT]
[FONT=&quot]E + A*C + D*F + A*B*F + B*C*D + A*B*D*E + B*C*E*F + A*C*D*E*F[/FONT]
[FONT=&quot]F + B*C + D*E + A*B*E + A*C*D + A*B*D*F + A*C*E*F + B*C*D*E*F[/FONT]
[FONT=&quot]A*F + B*E + C*D + A*B*C + A*D*E + B*D*F + C*E*F + A*B*C*D*E*F[/FONT]

[FONT=&quot]Taguchi Analysis: Response versus A; B; C; D; E; F
[/FONT]


[FONT=&quot]Response Table for Signal to Noise Ratios[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Larger is better[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Level A B C D E F[/FONT]
[FONT=&quot]1 52,89 51,33 49,89 51,92 50,93 48,87[/FONT]
[FONT=&quot]2 48,23 49,79 51,22 49,20 50,19 52,25[/FONT]
[FONT=&quot]Delta 4,66 1,54 1,33 2,71 0,75 3,38[/FONT]
[FONT=&quot]Rank 1 4 5 3 6 2[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Response Table for Means[/FONT]
[FONT=&quot]
[/FONT]
[FONT=&quot]Level A B C D E F[/FONT]
[FONT=&quot]1 450,8 380,8 345,3 415,8 398,8 308,3[/FONT]
[FONT=&quot]2 275,5 345,5 381,0 310,5 327,5 418,0[/FONT]
[FONT=&quot]Delta 175,3 35,3 35,8 105,3 71,3 109,8[/FONT]
[FONT=&quot]Rank 1 6 5 3 4 2[/FONT]

 

[Matt_B]

Here are the Minitab graphs.

 

[Miner]

Please attach the raw data and design structure. You may have to zip it first.

 

[Matt_B]

I reentered the data into Minitab to post it and I found the problem. Earlier I calculated main effects by hand and it looked OK so I did not question my data; now, I have different results from Minitab. It looks like I made a mistake the when I originally entered the data. Now, the only difference I see is for factor E, which is the projectile. This makes sense as other experiments had shown the projectiles are comparable.



Now my only question is do I indeed have interactions for factors B and D, C and E, B and F as wells as E and F? I had not anticipated interactions on the catapult.