Abstract
The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. The proposed approach combines the CUSUM control chart with the Bayesian estimation technique. We show that the control chart has some information about the change point and this information can be used to make an informative prior. Two Bayes estimators corresponding to the informative and a non informative prior along with MLE, frequentist approach, are considered. Their mean square error of estimators, are compared through a series of simulations. The results show that the Bayes estimator with the informative prior is more accurate and more precise for almost all values of the shift in the process mean compared to Bayes estimator with a non-informative prior and MLE.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dehghan Monfared M.E. and Lak F. (2013). Bayesian estimation of the change point using X control chart. Communications in Statistics - Theory and Methods 42, 8, 1572–1582.
Montgomery D.C. (2009). Introduction to statistical quality control, 6th ed. Wiley, New York.
Pignatiello J.J. and Samuel T.R. (2001). Estimation of the change point of a normal process mean in SPC applications. Journal of Quality Technology 33, 1, 82–95.
Samuel T.R., Pignatiello J.J. and Calvin J.A. (1998). Identifying the time of a step change with X control charts. Quality Engineering 10, 3, 521–527.
Shao Y.E. and Hou C.D. (2004). A study on identifying thr time of a step change disturbance with S control charts and MLE method. Journal of the Chinese Institute of Industrial Engineers 21, 4, 349–357.
Shao Y.E. and Hou C.D. (2006). Estimation of the starting time of a step change disturbance in a gamma process. Journal of the Chinese Institute of Industrial Engineers 23, 4, 319–327.
Shao Y.E., Hou C.D. and Wang H.J. (2006). Estimation of the change point of a gamma process by using the S control chart and MLE. Journal of the Chinese Institute of Industrial Engineers 23, 3, 207–214.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dehghan Monfared, M.E., Lak, F. Bayesian Estimation of the Change Point Using CUSUM Control Chart. Sankhya B 79, 94–111 (2017). https://doi.org/10.1007/s13571-016-0125-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13571-016-0125-7