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Chapter
12

Fundamentals of
Experimental Design

12.1 Introduction to Design of Experiments
(DOE)
Design of experiments is also called statistically designed experiments.
The purpose of the experiment and data analysis is to find the cause-
and-effect relationship between the output and experimental factors in a
process. The process model of DOE is illustrated in Fig. 12.1. This model
is essentially the same as the P-diagram model discussed in Chap. 2.

Example 12.1. Agricultural Experiment Design of experiments was first
developed as a research design tool to improve farm yields in the early
1930s. The output, or response, variable y in such an experiment was usu-
ally the yield of a certain farm crop. Controllable factors, such as x (x 1 ,
x 2 ,…, x n ), were usually the “farm variables,” such as the amount of various
fertilizers applied, watering pattern, and selection of seeds. Uncontrollable
factors, such as z (z 1 , z 2 ,…, z p ), could be soil types, weather patterns, and
so on. In early agricultural experiments, the experimenter would want to
find the cause-and-effect relationship between the yield and controllable
factors, specifically, how different types of fertilizers, application quantities,
watering patterns, and types of seeds would influence crop yield.

In any DOE project, we will deliberately change those experimental
factors and observe their effects on the output. The data obtained in
the experiment will be used to fit empirical models relating output y
with experimental factors. Mathematically, we are trying to find the
following functional relationship:
y f(x 1,x 2,…,x n) ε (12.1)

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