Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 2-1, March 2015, Pages: 19-26
Received: Dec. 4, 2014;
Accepted: Dec. 5, 2014;
Published: Mar. 11, 2015
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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
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.
Vishwa Nath Maurya,
Ram Bilas Misra,
Chandra K. Jaggi,
Charanjeet Singh Arneja,
Rama Shanker Sharma,
Avadhesh Kumar Maurya,
Design and Estimate of the Optimal Parameters of Adaptive Control Chart Model Using Markov Chains Technique, American Journal of Theoretical and Applied Statistics. Special Issue: Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process.
Vol. 4, No. 2-1,
2015, pp. 19-26.
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