**1.1 Objective of the chapter**

The objective of this chapter is to provide an in-depth understanding of DOE and its applications in quality control and assurance. We will explore various

**Figure 1.** *Design of Experiment (DOE).*

experimental designs, statistical techniques, and methodologies that are commonly used in DOE. Additionally, we will discuss its practical applications across various fields and the benefits and advantages that DOE offers in ensuring and improving quality standards.

#### **1.2 An overview and definitions of design of experiments (DOE)**

Definitions of Design of Experiments (DOE): DOE is a statistical methodology used to systematically plan, conduct, analyze, and interpret experiments to obtain valid and reliable results. It allows researchers to efficiently explore and identify the significant factors influencing a process or product's performance. DOE is an important statistical method used in controlling input factors or variables in order to ascertain the level of relationships with the output (responses) according to **Figure 1**, so as to ensure product or process quality. DOEs are usually carried out in five stages [7, 8] as shown in **Figure 2**. They are:

#### **1.3 History of DOE**

DOE has its roots in the work of Sir Ronald Fisher, who developed the basic principles of DOE in the early twentieth century. Fisher's work was initially applied to agricultural research, but it was soon adapted for use in other fields, including manufacturing, engineering, and medicine [9]. Since then, many scientists and statisticians have contributed to DOE development and its application in different fields [9–12].

#### **1.4 Types of DOE**

There are many different types of DOE, each with its own strengths and weaknesses [8, 13]. The best type of DOE to use will depend on the specific situation. Factors to consider include the number of factors, the number of levels for each factor, the desired level of confidence, and the time and budget constraints (**Figure 3**) [10, 14–16].

The most common types of DOE are:

#### *1.4.1 Full factorial designs*

These designs involve testing all possible combinations of factors. For example, if there are two factors with two levels each, there would be four possible combinations (2 × 2 = 4). Full factorial designs are the most comprehensive, but they can also be the most time-consuming and expensive.

**Figure 2.** *Five stages of DOE.*

#### *Quality Control and Quality Assurance – Techniques and Applications*

