Estimation of the Change Point in Monitoring the Mean of Autocorrelated Processes

Title & Authors
Estimation of the Change Point in Monitoring the Mean of Autocorrelated Processes
Lee, Jae-Heon; Han, Jung-Hee; Jung, Sang-Hyun;

Abstract
Knowing the time of the process change could lead to quicker identification of the responsible special cause and less process down time, and it could help to reduce the probability of incorrectly identifying the special cause. In this paper, we propose the maximum likelihood estimator (MLE) for the process change point when a control chart is used in monitoring the mean of a process in which the observations can be modeled as an AR(1) process plus an additional random error. The performance of the proposed MLE is compared to the performance of the built-in estimator when they are used in EWMA charts based on the residuals. The results show that the proposed MLE provides good performance in terms of both accuracy and precision of the estimator.
Keywords
Process change point;autocorrelated process;exponentially weighted moving average chart;residual;maximum likelihood estimator;
Language
English
Cited by
1.
누적이동평균(1,1) 모형에서 공정 변화시점의 추정,이호윤;이재헌;

Journal of the Korean Data and Information Science Society, 2009. vol.20. 2, pp.435-443
References
1.
Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control. 3rd ed., Prentice Hall, Englewood Cliffs, New Jersey

2.
Hawkins, D. M., Qiu, P. and Kang, C. W. (2003). The changepoint model for statistical process control. Journal of Quality Technology, 35, 355-366

3.
Lee, J. and Park, C. (2006). Estimation of the change point in monitoring the process mean and variance. Communications in Statistics: Simulation and Computation, submitted for publication

4.
Lu, C. W. and Reynolds, M. R., Jr. (1999). EWMA control charts for monitoring the mean of autocorrelated processes. Journal of Quality Technology, 31, 166-188

5.
Lucas, J. M. and Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32, 1-12

6.
MacGregor, J. F. and Harris, T. J. (1993). The exponentially weighted moving variance. Journal of Quality Technology, 25, 106-118

7.
Nishina, K. (1992). A comparison of control charts from the viewpoint of change-point estimation. Quality and Reliability Engineering International, 8, 537-541

8.
Padgett, C. S., Thombs, L. A., and Padgett, W. J. (1992). On the $\alpha$-risks for Shewhart control charts. Communications in Statistics: Simulation and Computation, 21, 1125-1147

9.
Pignatiello, J. J., Jr. and Samuel, T. R. (2001). Estimation of the change point of a normal process mean in SPC applications. Journal of Quality Technology, 33, 82-95

10.
Reynolds, M. R., Jr., Arnold, J. C., and Baik, J. W. (1996). Variable sampling interval $\bar{X}$ charts in the presence of correlation. Journal of Quality Technology, 28, 12-30

11.
Samuel, T. R., Pignatiello, J. J., Jr. and Calvin, J. A. (1998). Identifying the time of a step change with $\bar{X}$ control charts. Quality Engineering, 10, 521-527