Statistical Monitoring of Autocorrelated Simple Linear Profiles Based on Principal Components Analysis

Abstract

In this article, a transformation method using the principal component analysis approach is first applied to remove the existing autocorrelation within each profile in Phase I monitoring of autocorrelated simple linear profiles. This easy-to-use approach is independent of the autocorrelation coefficient. Moreover, since it is a model-free method, it can be used for Phase I monitoring procedures. Then, five control schemes are proposed to monitor the parameters of the profile with uncorrelated error terms. The performances of the proposed control charts are evaluated and are compared through simulation experiments based on different values of autocorrelation coefficient as well as different shift scenarios in the parameters of the profile in terms of probability of receiving an out-of-control signal.

Keywords:

• Autocorrelation
• Phase I
• Principal component analysis
• Simple linear profile
• Statistical process control.

Mathematics Subject Classification:

• Primary: 62F99; Secondary: 62J05

Acknowledgments

The authors are thankful to anonymous reviewers for their valuable comments, time, and considerations spent on this manuscript. Taking care of the comments significantly improved the presentation of the manuscript.