Abstract
In this article a method, using finite Markov chains, to obtain the run-length properties of a two-stage control process is presented. The method furnishes the obtaining of the distribution of waiting time to signal that gives additional insight into the design and performance of a control chart when a warning zone is considered to feature a two-stage control process and when a departure from the null assumption can be clearly defined. An example is given for illustration when samples come from a normal population, though not necessary, with an outlined process inspection scheme. A second example is given to demonstrate the extension of our approach to modelling Markov dependent data observations.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their comments that helped to strengthen areas of this paper and improve its readability. Hsing-Ming Chang acknowledges the financial support by the Ministry of Science and Technology, R.O.C., through the Grant 108-2118-M-006-003-, which enabled his visit to Dr. James C. Fu. The authors were glad to have a light discussion with Dr. Yung-Ming Chang at the National Taitung University on a number of points made in help to further clarify the difference of this work from that in Fu et al. (2003).
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Chang, HM., Fu, J.C. On Distribution and Average Run Length of a Two-Stage Control Process. Methodol Comput Appl Probab 24, 2723–2742 (2022). https://doi.org/10.1007/s11009-022-09935-4
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DOI: https://doi.org/10.1007/s11009-022-09935-4