Phase I Monitoring of Polynomial Profiles

Abstract

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. In many practical situations, a profile can be modeled as a polynomial regression. In this article, three methods are developed for monitoring polynomial profiles in Phase I. Their performance is evaluated using power criterion. Furthermore, a method based on likelihood ratio test is developed to identify the location of shifts. Numerical simulation is used to evaluate the performance of the developed method.

Keywords:

• Change point
• Phase I and II
• Polynomial profile
• Statistical process control

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62P30

Acknowledgments

The authors gratefully acknowledge the insightful and valuable comments of the anonymous reviewer which led to improvement in this article. Dr. Kazemzadeh's research is partially supported by a financial help from Tarbiat Modares University and Dr. Noorossana's research is partially supported by a grant from Iran National Science Foundation.