# Fractional Factorial Experiments

Half fraction of a fractional factorial experiment

Half fraction of a 2k experiment of the highest resolution, can be constructed by writing a basic design that consists of runs for a 2k-1 full factorial type and then, adding the kth factor, identifying it with the plus and minus, that represent the levels of interaction of higher order ABC...(K-1). So, the  fractional factorial can be obtained by a 22 full factorial and then, equating the interactions of second order AB with C. The alternative fraction, this way, -AB with C.

Example: An investigator wants to evaluate the behavior of a cane harvester pinion wear, in relation to four factors: chassis side opening, window mug, disk format and roll format. The objective is to determine which configuration establishes a lower pinion wear. Using 8 machines of the same model, same manufacturing year and using the same work force, we performed a 24-1 fractional factorial experiment with two replicates. The experimental unities were 250 hour of work by replicate.

Then, for the example, we will make the Design of Experiment

To use the tool Design of Experiments, the user must follow these steps:

Action → DOE Design of Experiments

2. The following screen will be shown:

3. In the field Type of Experiment select one of the 3 options: Full Factorial, Factorial in Blocks and Fractional Factorial, in this case, Fractional Factorial;

4. In the field Factors, click in Num. Factors and select the number of factors of the experiment, in this case, 4;

If the number of factors is higher than 8, click in Factors and in the blank field select in the sheet the number of factors of the experiment.

5. In the field Runs, select the number of runs of the experiment, in this case, 8;

6. In the field Replicates, select the number of replicates of the experiment, in this case, 3;

7. In the board Show Results, choose one of the option. We suggest the option New Sheet becuase Action does not have the undo command;

When choosing the option Current Cell, the results will be printed from the cell where the cursor is. In this case, the user must put the cursor in an appropriate position previously (before step 1);

8. To finish, click Ok.

Results and Interpretation

Once the process is finished, the following results will be shown: