CAT-100 Fractional Factorial Experiment

The CAT-100 catapult has six different factors, each of which can be set at three different levels. They are:  

To test each factor at each level would require a full factorial experiment consisting of 729 different treatment combinations (3 6 = 729). If the experiment is conducted only using the Level I and II the experiment is reduced to 2 6 = 64 treatment combinations. This is still a large experiment, hence the need to develop some sort of fractional experiment or Taguchi orthogonal array.

Different types of fractional factorials can be developed based on the instructors preferences. The following example is for a one-eighth fractional factorial with two replications of each treatment. The response variable is the distance the ball is thrown in inches.

This data has been analyzed by Stat Ease Design Ease Software. The results are shown on the following pages. The most significant factors according to the analysis are Pivot Arm Location, Ball Seat Position, and Turn Table Position.

   ANOVA for Selected Factorial Model
   Analysis of variance table [Partial sum of squares]
                       Sum of                             Mean          F                 
   Source         Squares       DF               Square        Value          Prob > F

   Model               15211.94                  7       2173.13         183.97      < 0.0001                    significant

                     A         473.06                  1         473.06           40.05         0.0002
                     B       1105.56                  1       1105.56           93.59     < 0.0001
                    C       6765.06                  1       6765.06         572.70     < 0.0001
                    D       3164.06                  1       3164.06         267.86     < 0.0001
                     E       3220.56                  1       3220.56         272.64     < 0.0001
                     F         280.56                  1         280.56           23.75         0.0012
                  AF         203.06                  1         203.06           17.19         0.0032
       Pure Error           94.50                  8           11.81
        Cor Total     15306.44                15

The Model F-value of 183.97 implies the model is significant.  There is only
a 0.01% chance that a "Model F-Value" this large could occur due to noise.

Values of "Prob > F" less than 0.0500 indicate model terms are significant. 
In this case A, B, C, D, E, F, AF are significant model terms. 
Values greater than 0.1000 indicate the model terms are not significant. 
If there are many insignificant model terms (not counting those required to support hierarchy),    model reduction may improve your model.

   Std. Dev.                   3.44                                           R-Squared         0.9938
   Mean                      68.81                                     Adj R-Squared         0.9884
   C.V.                          4.99                                   Pred R-Squared         0.9753

   PRESS                  378.00                                     Adeq Precision         36.416

   The "Pred R-Squared" of 0.9753 is in reasonable agreement with the "Adj R-Squared" of 0.9884.

   In this case A, B, C, D, E, F, AF are significant model terms. 
   Values greater than 0.1000 indicate the model terms are not significant. 

   "Adeq Precision" measures the signal to noise ratio.  A ratio greater than 4 is desirable.  Your
   ratio of 36.416 indicates an adequate signal.  This model can be used to navigate the design space.

    Final Equation in Terms of Coded Factors:

                              Distance                 =
                                +68.81
                                   -5.44              * A
                                  +8.31               * B
                                +20.56              * C
                                +14.06              * D
                                 -14.19               * E
                                   -4.19               * F
                                  +3.56        * A * F