Present paper aims to plan and estimate the optimal parameters of an adaptive control chart model for monitoring the mean of a process using sample size and variable interval. Here, the X_BARRA-VSSI chart has been chosen because of its two special features- firstly being an adaptive scheme with great potential for practical application, and secondly the chart only requires knowledge of the sample size and the time between sample selections after established the optimal parameters for the chart. To estimate the optimal parameters of chosen control chart model, the Markov chains technique has been applied. Two functions written in R language are presented in order to assist the user in planning a statistical project based on the X_BARRA-VSSI adaptive scheme. Evaluating the effectiveness of the control chart of by means of Markov chains has been examined and the optimal parameters of the adaptive control chart model have been explored. In addition to this, a numerical example for application of the control chart model has also been illustrated and finally some conclusive observations with significant suggestions for its future scope are carried out.
| Published in |
American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1)
This article belongs to the Special Issue Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process |
| DOI | 10.11648/j.ajtas.s.2015040201.13 |
| Page(s) | 19-26 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Sampling amplitude, hypothesis testing, statistical control of process (SCP), adaptive charts, Markov chains technique, standard normal cumulative function, statistical software, decision variable, transition matrix
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APA Style
Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Charanjeet Singh Arneja, Rama Shanker Sharma, et al. (2015). Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique. American Journal of Theoretical and Applied Statistics, 4(2-1), 19-26. https://doi.org/10.11648/j.ajtas.s.2015040201.13
ACS Style
Vishwa Nath Maurya; Ram Bilas Misra; Chandra K. Jaggi; Charanjeet Singh Arneja; Rama Shanker Sharma, et al. Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique. Am. J. Theor. Appl. Stat. 2015, 4(2-1), 19-26. doi: 10.11648/j.ajtas.s.2015040201.13
AMA Style
Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Charanjeet Singh Arneja, Rama Shanker Sharma, et al. Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique. Am J Theor Appl Stat. 2015;4(2-1):19-26. doi: 10.11648/j.ajtas.s.2015040201.13
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Download@article{10.11648/j.ajtas.s.2015040201.13,
author = {Vishwa Nath Maurya and Ram Bilas Misra and Chandra K. Jaggi and Charanjeet Singh Arneja and Rama Shanker Sharma and Avadhesh Kumar Maurya},
title = {Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {4},
number = {2-1},
pages = {19-26},
doi = {10.11648/j.ajtas.s.2015040201.13},
url = {https://doi.org/10.11648/j.ajtas.s.2015040201.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2015040201.13},
abstract = {Present paper aims to plan and estimate the optimal parameters of an adaptive control chart model for monitoring the mean of a process using sample size and variable interval. Here, the X_BARRA-VSSI chart has been chosen because of its two special features- firstly being an adaptive scheme with great potential for practical application, and secondly the chart only requires knowledge of the sample size and the time between sample selections after established the optimal parameters for the chart. To estimate the optimal parameters of chosen control chart model, the Markov chains technique has been applied. Two functions written in R language are presented in order to assist the user in planning a statistical project based on the X_BARRA-VSSI adaptive scheme. Evaluating the effectiveness of the control chart of by means of Markov chains has been examined and the optimal parameters of the adaptive control chart model have been explored. In addition to this, a numerical example for application of the control chart model has also been illustrated and finally some conclusive observations with significant suggestions for its future scope are carried out.},
year = {2015}
}
TY - JOUR T1 - Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique AU - Vishwa Nath Maurya AU - Ram Bilas Misra AU - Chandra K. Jaggi AU - Charanjeet Singh Arneja AU - Rama Shanker Sharma AU - Avadhesh Kumar Maurya Y1 - 2015/03/11 PY - 2015 N1 - https://doi.org/10.11648/j.ajtas.s.2015040201.13 DO - 10.11648/j.ajtas.s.2015040201.13 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 19 EP - 26 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.s.2015040201.13 AB - Present paper aims to plan and estimate the optimal parameters of an adaptive control chart model for monitoring the mean of a process using sample size and variable interval. Here, the X_BARRA-VSSI chart has been chosen because of its two special features- firstly being an adaptive scheme with great potential for practical application, and secondly the chart only requires knowledge of the sample size and the time between sample selections after established the optimal parameters for the chart. To estimate the optimal parameters of chosen control chart model, the Markov chains technique has been applied. Two functions written in R language are presented in order to assist the user in planning a statistical project based on the X_BARRA-VSSI adaptive scheme. Evaluating the effectiveness of the control chart of by means of Markov chains has been examined and the optimal parameters of the adaptive control chart model have been explored. In addition to this, a numerical example for application of the control chart model has also been illustrated and finally some conclusive observations with significant suggestions for its future scope are carried out. VL - 4 IS - 2-1 ER -
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