Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique

Vishwa Nath Maurya; Ram Bilas Misra; Chandra K. Jaggi; Charanjeet Singh Arneja; Rama Shanker Sharma; Avadhesh Kumar Maurya

doi:doi:10.11648/j.ajtas.s.2015040201.13

Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique

Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Charanjeet Singh Arneja, Rama Shanker Sharma, Avadhesh Kumar Maurya

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1)

Received: 4 December 2014 Accepted: 5 December 2014 Published: 11 March 2015

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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.

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), 2024. Published by Science Publishing Group

Keywords

Sampling amplitude, hypothesis testing, statistical control of process (SCP), adaptive charts, Markov chains technique, standard normal cumulative function, statistical software, decision variable, transition matrix

References

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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

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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

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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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@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}
}

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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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Author Information

Vishwa Nath Maurya

Department of Pure & Applied Mathematics and Statistics, School of Science & Technology, The University of Fiji, Lautoka, Fiji Islands
Ram Bilas Misra

Division of Applied Mathematics, State University of New York, Incheon, Republic of Korea & Ex-Vice Chancellor, Dr. R. M. L. Avadh University, Faizabad, UP, India
Chandra K. Jaggi

Department of Operations Research, University of Delhi, New Delhi, India
Charanjeet Singh Arneja

Department of Agricultural Extension, Punjab Agricultural University, Ludhiana, India
Rama Shanker Sharma

Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea
Avadhesh Kumar Maurya

Department of Electronics & Communication Engineering, Lucknow Institute of Technology, U.P. Technical University, Lucknow, India

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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

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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

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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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@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}
}

Copy | Download

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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