Monitoring profile based on a linear regression model with correlated errors

Abstract

Profile monitoring is becoming popular in the area of quality control. It is used when the process is characterized by the relationship between a response variable and some explanatory variables at each time period. This paper considers the situation where profiles are modeled parametrically using a multiple linear regression with random errors following an autoregressive moving-average process. Diagnostic schemes to find out-of-control samples are developed for this purpose. A simulation study examines the performance of the proposed approach based on the average run length criterion. Lastly, a real example illustrates the results, after considering both Phase I and Phase II schemes.

Keywords:

• Correlated errors
• Hotelling’s T² statistic
• statistical process control

Funding

This research of the first author was partially supported by [grant number NSC100-2118-M-004-002] of the National Science Council in Taiwan. This research of the second author was partially supported by the College of Commerce, National Chengchi University, Taiwan.