In designing an experiment, the researcher can often choose many different levels of the various factors in order to try to find the best combination at which to operate. As an illustration, suppose the researcher is studying a certain chemical reaction an can choose four levels of temperature, five different pressures, and two different catalysts

a- To consider all possible cam binations. How many experiments would need to be conducted?
b- Often in preliminary experimentation each factor is restricted to two levels. With the three factors noted. How many experiments would need to be ran to cover all possible combination with each of the three factors at two levels/ (Not’s, this is often called a 23 design)

Multiplication principle If one event can occur in m ways AND a second event can occur in n ways, then the number of ways that the two events can occur in sequence is then m • n.

SOLUTION

(a)

Temperature: 4 ways

Pressure: 5 ways

Catalysts: 2 ways

Use the multiplication principle:

4*5*2 = 40

(b)

Temperature: 2 ways

Pressure: 2 ways

Catalysts: 2 ways

Use the multiplication principle:

2*2*2=2^3 = 8

(a) 40 combinations (b) 8 combinations