Design Procedure for Fractional Factorial Experiments

The following steps will allow the design of a fractional factorial experiment  

Design a full factorial experiment for the -p variables. These k-p variables are called the independent or basic variables. 

Create p new variables, which are independent combinations of some or all of the — p factors. The combinations should be determined using the above information on confounding, resolution, confounding pattern, and any additional information known about the process. 

Add p columns to the table created in Step 1, each containing one of the combinations determined above. Set each of the p variables equal to one of the new columns. Determine the appropriate level for each new colunui by considering the combination chosen for that row. It should be noted that there are many different methods to accomplish this creation of the table. 

the actual experiment will consist of runs (or treatments), where each row corresponds to a single run. For each run, the values of the factors are determined based on the corresponding column values in the table obtained in step 3. 

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