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Economic Design of $\bar{X}$ Control Chart Using a Surrogate Variable  

Lee, Tae-Hoon (Nuclear Hydrogen Reactor Technology Development Division, Korea Atomic Energy Research Institute)
Lee, Jae-Hoon (Department of Information & Statistics, Chungnam National University)
Lee, Min-Koo (Department of Information & Statistics, Chungnam National University)
Lee, Joo-Ho (Department of Information & Statistics, Chungnam National University)
Publication Information
Journal of Korean Society for Quality Management / v.37, no.2, 2009 , pp. 46-57 More about this Journal
Abstract
The traditional approach to economic design of control charts is based on the assumption that a process is monitored using a performance variable. However, various types of automatic test equipments recently introduced as a part of factory automation usually measure surrogate variables instead of performance variables that are costly to measure. In this article we propose a model for economic design of a control chart which uses a surrogate variable that is highly correlated with the performance variable. The optimum values of the design parameters are determined by maximizing the total average income per cycle time. Numerical studies are performed to compare the proposed $\bar{X}$ control charts with the traditional model using the examples in Panagos et al. (1985).
Keywords
X bar Control Chart; Performance Variable; Surrogate Variable; Economic Design;
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  • Reference
1 Boys. R. J. and Dunsmore, I. R. (1987), "Diagonostic and Sampling Models in Screening", Biometrika, Vol. 74, pp. 356-374
2 Lee, M. K., Hong, S. H., and Elsayed E. A. (2001), "The Optimum Target Value Under Single and Two-Stage Screenings", Journal of Quality Technology. Vol. 33, pp. 506-514
3 Lorenzen, T. J. and Vance, L. C. (1986), "The Economic Design of Control Charts: A Unified Approach" , Technometrics, Vol. 28, pp. 3-10   DOI   ScienceOn
4 Owen, D. B., McIntire, D., and Seymour, E. (1975), "Tables Using One or Two Screening Variables to Increase Acceptable Product Under One-Sided Specifications" , Journal of Quality Technology, Vol. 7, pp. 127-138
5 Costa, A. F. B. and De Magalh$\tilde{a}$es, M. S. (2002) "Economic design of two-stage $\bar{X}$ charts : The Markov chain approach", International Journal of Production Economics, Vol. 95, pp. 9-20   DOI   ScienceOn
6 Woodall, W. H. (1986), "Weaknesses of the Economic Design of Control Charts", Technometrics, Vol. 28, pp. 408-409   DOI   ScienceOn
7 Panagos, M. R., Heikes, R. G., and Montgomery, D. C. (1985), "Economic Design of $\bar{X}$ Control Charts for Two Manufacturing Process Models", NavaI Research Logistics, Vol. 32, pp. 631-646   DOI
8 Lee, M. K. (2000), "Determination of the Optimum Process Mean and Screening Limit for a Production Process Based on Two Correlated Variable", Journal of the Korean Society for Quality Management, Vol. 28, pp. 155-164
9 Li, L. and Owen, D. B. (1979), "Two-Sided Screening Procedures in the Bivariate Case", Technometrics, Vol. 21, pp. 79-85   DOI   ScienceOn
10 Wong, A., Meeker, J. B., and Selwyn, M.R. (1985), "Screening on Correlated Variables: A Bayesian Approach", Technometrics, Vol. 27, pp. 423-431   DOI   ScienceOn
11 Montgomery, D. C. (2004), Introduction to Statistical Quality Control, 5th Edition, John Wiley & Sons, New York
12 Duncan, A. J. (1956), "The Economic Design of $\bar{X}$-Charts Used to Maintain Current Control of a Process", Journal of the American Statistical Association, Vol. 51, pp. 228-242   DOI   ScienceOn
13 Kwon, H. M., Lee, M. K., Kim, S. B., and Hong, S. H (1999), "A Process Monitoring Procedure Using a Correlated Variable", Journal of the Korean Society for Quality Management, Vol. 27, pp. 35-45
14 Lee, J. and Kwon, W. J. (1999), "Economic Design of a Two-Stage Control Chart Based on Both Performance and Surrogate Variables", Naval Research Logistics, Vol. 46, pp. 958-977   DOI   ScienceOn