Effect of Markoff’s model on Economic design of X- bar control chart for independent observations

Manzoor A. Khanday¹ , J. R. Singh²

Section:Research Paper, Product Type: Isroset-Journal
Vol.2 , Issue.2 , pp.1-6, Dec-2015

Online published on Jan 29, 2015

Copyright © Manzoor A. Khanday , J. R. Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, an attempt is made to determine the effect of Markoff’s model on the economic design of - control chart for independent observation. We have calculated the optimum value of sample size n and sampling interval h. Tables for n and h are available for different values of k. The presence of positive and negative autocorrelation parameters seriously affects the optimum sample size and sampling intervals. Thus, there is a need for a procedure which enables us to deal with the observations which are independent, to design control charts accordingly continue our search for the assignable causes of variation and for the optimum parameters. It may be inferred that autocorrelation seriously affects the optimum value of the sample size and optimum sampling interval. It is necessary to point out that the observations from the population should be taken in to account while designing a control chart as the optimum values of the control chart parameters are affected by the measurement of the population.

Key-Words / Index Term :
Economic Design Control Chart; Autocorrelation; Markoff’s model; Edgeworth series

References :
[1] Banerjee, P.K. and Rahim, M.A., “The economic design of control charts, A renewal theory approach” Engineering Optimization, 12, 63-73. (1987).
[2] Colledani, M., “Integrated analysis of quality and production logistics performance in manufacturing lines, In: Proceedings of IFAC world congress, 6–11 July Seoul, Korea, 8368, 1–7. (2008).
[3] Duncan, A. J. “The economic design of X-bar chart used to maintain current control of a process”, Journal of the American Statistical Association, 51, 228-242. (1956)
[4] Duncan, A. J., “The economic design of X charts when there is a multiplicity of assignable causes. Journal of the American Statistical Association, 66, 107- 121. (1971).
[5] Gershwin, S. and Kim, J., “Integrated quality and quantity modelling of a production line. OR Spectrum, 27 (2-3), 287–314. (2005).
[6] Gibra, I. N., “Economically optimal determination of the parameters of an control chart”, Management Science, 17, 635- 646. (1971).
[7] Goel, A. L., Jain, S. D. and Wu, S. M., “An algorithm for the determination of the economic design of X charts based on Duncan’s model”, Journal of the American Statistical Association, 63, 304-320. (1968).
[8] Ho, C. and Case, K. E., “Economic design of control charts: A literature review for 1981-1991” Journal of Quality Technology,26, 1- 78. (1994).
[9] Knappenberger, H. A. and Grandage, A. H. E., “Minimum cost quality control tests”, AIIE Transactions, 1, 24-32. (1969).
[10] Lorenzen, T. J. Vance, L. C., “The economic design of control charts: a unified approach”, Technometrics, 28(1), 3–10. (1986).
[11] Montgomery, D. C., “Introduction to statistical quality control”, New York: John Wiley & Sons, (2004).
[12] Montgomery, D.C. “The economic design of control charts”, A review and literature survey. Journal of Quality Technology. 12, 75–87. (1980).
[13] Montgomery, D.C. “Introduction to Statistical Process Control, 2nd edn.” John Wiley & Sons, New York, (1991).
[14] Svoboda, L. “Economic design of control charts: a review and literature survey (1979-1989), in Statistical Process Control in Manufacturing, Keats, J.B. and Montgomery, D.C. (eds)”, Marcel Dekker, New York. (l991).
[15] Vance, L. C. “A bibliography of statistical quality control chart techniques, 1970-1980”, Journal of Quality Technology, 15, 59- 62. (1983).
[16] Vispute S. and Singh J. R. “Optimum Process Mean Setting for Product with Rework Process Under Second order autocorrelation” International Journal of Scientific Research in Mathematical and Statistical Sciences, 1 (3), 1-12, (2014).