1. Assume you have seven factors , , , , , , and two different levels of each factor L1 and L2.

a) How many experiments are necessary in full factorial design? Try to show all possible experiments without writing all of them.

b) How many experiments are necessary in fractional factorial design? What is your aim in making fractional factorial design?

c) Show the necessary experiments in fractional factorial design in a tabular form using the symbols above. What is the principal to determine the number of these experiments?