TY - JOUR
T1 - On Distribution and Average Run Length of a Two-Stage Control Process
AU - Chang, Hsing Ming
AU - Fu, James C.
N1 - Funding Information:
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 ).
Funding Information:
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. ().
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85128009294&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85128009294&partnerID=8YFLogxK
U2 - 10.1007/s11009-022-09935-4
DO - 10.1007/s11009-022-09935-4
M3 - Article
AN - SCOPUS:85128009294
SN - 1387-5841
VL - 24
SP - 2723
EP - 2742
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 4
ER -