The monitoring of simple linear regression profiles with two observations per sample

Abstract

We evaluate and compare the performance of Phase II simple linear regression profile approaches when only two observations are used to establish each profile. We propose an EWMA control chart based on average squared deviations from the in-control line, to be used in conjunction with two EWMA control charts based on the slope and Y-intercept estimators, to monitor changes in the three regression model parameters, i.e., the slope, intercept and variance. Simulations establish that the performance of the proposed technique is generally better than that of other approaches in detecting parameter shifts.

Keywords:

• change point
• exponentially weighted moving average chart
• likelihood ratio
• phase II analysis
• profile monitoring
• statistical process control

Acknowledgements

The authors appreciate the helpful comments of the editor and anonymous referees. J.P. Morgan was supported by the United States National Science Foundation grant DMS06-04997. The research of Dr. Woodall was supported in part by NSF grant CMMI-0927323.