Catapult Fractional Factorial Experiment

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:

Factor	Level I	Level II	Level III
Elevation -	Low	Medium	High
Stationary Arm	Low	Medium	High
Upright Arm Tension Location	Low	Medium	High
Pivot Arm Tension Location	Low	Medium	High
Ball Seat Position	Low	Medium	High
Turn Table Position	Low	Medium	High
Ball Type	Foam	Whiffle	Ping Pong

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.

Order	Elevation	Upright	Pivot Arm	Ball Seat	Turn Table	Ball Type	Dist
1	Lowest	Low	High	Highest	Lowest	Foam	120
2	Lowest	High	High	Lowest	Lowest	Ping Pong	95
3	Highest	High	Low	Highest	Lowest	Foam	81
4	Highest	Low	High	Lowest	Highest	Foam	44
5	Lowest	Low	Low	Highest	Highest	Ping Pong	39
6	Lowest	High	Low	Lowest	Highest	Foam	41
7	Highest	Low	Low	Lowest	Lowest	Ping Pong	37
8	Highest	High	Low	Highest	Lowest	Foam	79
9	Highest	Low	Low	Lowest	Lowest	Ping Pong	31
10	Lowest	High	High	Lowest	Lowest	Ping Pong	96
11	Lowest	Low	High	Highest	Lowest	Foam	125
12	Lowest	Low	Low	Highest	Highest	Ping Pong	36
13	Highest	Low	High	Lowest	Highest	Foam	52
14	Highest	High	High	Highest	Highest	Ping Pong	88
15	Lowest	High	Low	Lowest	Highest	Foam	42
16	Highest	High	High	Highest	Highest	Ping Pong	95

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