Monitoring and change-point estimation for spline-modeled non-linear profiles in phase II

Abstract

In some applications of statistical quality control, quality of a process or a product is best characterized by a functional relationship between a response variable and one or more explanatory variables. This relationship is referred to as a profile. In certain cases, the quality of a process or a product is better described by a non-linear profile which does not follow a specific parametric model. In these circumstances, nonparametric approaches with greater flexibility in modeling the complicated profiles are adopted. In this research, the spline smoothing method is used to model a complicated non-linear profile and the Hotelling T² control chart based on the spline coefficients is used to monitor the process. After receiving an out-of-control signal, a maximum likelihood estimator is employed for change point estimation. The simulation studies, which include both global and local shifts, provide appropriate evaluation of the performance of the proposed estimation and monitoring procedure. The results indicate that the proposed method detects large global shifts while it is very sensitive in detecting local shifts.

Keywords:

• B-spline smoothing method
• change-point estimation
• Hotelling T² chart
• non-linear profile
• profile monitoring

Acknowledgements

The authors are grateful to the respected editor and the two anonymous reviewers for their comments and suggestions which made this work more valuable.

Disclosure statement

No potential conflict of interest was reported by the authors.