Response surface methodology (RSM) which is a useful tool for the statistical modeling and analysis of experimental design, has been extensively applied in many situations,
especially in the engineering, chemical and manufacturing areas. Canonical analysis in RSM not only help us to find the stationary point, but also to determine the type of fitted model.
However, such analysis can be affected by influential points/outliers. In this thesis, our aim is to study the influence analysis on the response surface methodology.

1 Introduction

2 Response Surface

2.1 Canonical Analysis

2.2 The A canonical form

2.3 The Stationary Point in RSM

3 Influence Functions for RSM

3.1 Influence Functions for the Matrix B

3.2 Empirical Influence Function for the Matrix B

3.3 Deleted Empirical Influence Function for the Matrix B

3.4 Sample Influence Function for the Matrix B

3.5 Pair-Perturbations Influence Functions

3.6 Pair-Perturbations Influence Function for the Matrix B

3.7 Influence Function for Stationary Point

3.8 Pair-Perturbations Influence Function for xS

3.9 Cut Points Selection of Influence Functions

4 Examples

4.1 A Simulation Study

4.2 Real Data Example

4.2.1 Raw Wool Data

4.2.2 Chemical Process Data

5 Conclusions

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