On the Monitoring of Autocorrelated Linear Profiles

Abstract

Control charts are commonly used to monitor quality of a process or product characterized by a quality characteristic or a vector of quality characteristics. However, in many practical situations the quality of a process or product can be characterized by a function or profile. Here we consider a linear function and investigate the violation of common independence assumption implicitly considered in most control charting applications. We specifically consider the case when profiles are not independent from each other over time. In this article, the effect of autocorrelation between profiles is investigated using average run length (ARL) criterion. Simulation results indicate significant impact on the ARL values when autocorrelation is overlooked. In addition, three methods based on time series approach are used to eliminate the effect of autocorrelation. Their performances are compared using ARL criterion.

Keywords:

• Autocorrelation
• Average run length
• Phase I and II
• Statistical process control

Mathematics Subject Classification:

• 62F99

Acknowledgment

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