Bayesian Approach in Control Charts Techniques

Amin Shaka Aunali¹ , D. Venkatesan²

Section:Survey Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.217-221, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.217221

Online published on Apr 30, 2019

Copyright © Amin Shaka Aunali, D. Venkatesan . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The major use of Bayesian methods in SPC is the area which aims to estimate the control chart parameters more efficiently, considering cost of sampling and chart performance. This issue is now being investigated for economical design of control charts and more recently for adaptive control charts. The traditional approach to a control chart design considers the classical control chart framework with the objective of determining the values of the chart parameters, namely the sample size, sampling interval, and the control limits to satisfy economic or statistical requirements. Under a Bayesian approach, the focus can be shifted to determining the optimal control policy based on the posterior probability that the process is out of control, minimizing the total expected cost over a finite horizon, or the long-run expected average cost. In this paper, the Bayesian control charts is developed.

Key-Words / Index Term :
Statistical Process Control, Bayesian approach, Prior and Posterior distribution

References :
[1] A. Gelman, J. Carlin, H. Stern, and D. Rubin, “Bayesian Data Analysis”, Chapman & Hall/CRC. 2004.
[2] D. C. Montgomery, “Introduction to Statistical Quality Control”, 7th ed., Wiley, New York, 2012.
[3] E. S. Page, “A Test for a change in parameter occurring at an unknown Time Point”, Biometrica, 44, pp. 523-527, 1955.
[4] L. D. Broemeling,, “Bayesian Analysis of Linear Models”, Marcel Deeker, New York, 1985.
[5] P. F. Craigmile, A. C. Catherine, Li Hongfei, P. Rajib and C. Noel, “Hierarchical Model Building, Fitting, and Checking: A Behind-the-Scenes Look at a Bayesian Analysis of Arsenic Exposure Pathways”, International Society for Bayesian Analysis, Vol. 4, No 1, pp. 1-36, 2009.
[6] Shaka A. Amin and D. Venkatesan, “Comparison of Bayesian Method and Classical Charts in Detection of Small Shifts in the Control Charts”, International Journal of Operations Research and Optimization, Vol. 8, No. 1, pp. 23-35, 2017.
[7] Shaka A. Amin and D. Venkatesan, “Recent Developments in Control Charts Techniques”, International Journal of Operations Research and Optimization, Vol. 8, No. 1, pp. 23-35, 2019.