# Lesson 12: Robust Parameter Designs

### Introduction

In what we have discussed so far in the context of optimization only the average location of the response variable has been taken into account. However, from another perspective the variation of the response variable could be of major importance as well. This variation could be due to either usual noise of the process or randomness in the nature of one or more controllable factors of the process.

The Robust Parameter Design (RPD) approach initially proposed by Japanese engineer, Genichi Taguchi, seeks a combination of controllable factors such that two main objectives are achieved:

- The mean or average location of the response is at the desired level, and
- The variation or dispersion of the response is as small as possible.

Taguchi proposed that only some of the variables cause the variability of the process, which he named noise variables or uncontrollable variables. Please note that noise variables may be controllable in the laboratory, while in general they are a noise factor, and uncontrollable. An important contribution of RPD efforts is to identify both the controllable variables and the noise variables and find settings for the controllable variable such that the variation of response due to noise factors is minimized.

The general ideas of Taguchi widely spread throughout the world; however, his philosophy and methodology to handle RPD problems caused lots of controversy among statisticians. With the emergence of Response Surface Methodology (RSM), many efficient approaches were proposed which could nicely handle RPD problems. In what follows, RSM approaches for Robust Parameter Design will be discussed.

### Learning Objectives and Outcomes

- Understanding the general idea of Robust Parameter Design approaches
- Getting familiar with Taguchi’s crossed array design and its relative weaknesses
- Understanding combined array design and response model approach to RPD