Economic design of a nonparametric EWMA control chart for location
Hariba, Patil Subhash; Tukaram, Shirke Digambar
http://dx.doi.org/10.1590/0103-6513.209916
Production, vol.26, n4, p.698-706, 2016
Abstract
In this article, we have proposed an economic design of Exponentially Weighted Moving Average control chart based on sign statistic to control location parameter of the process. The economic performance of the chart is evaluated for different shifts in the location. It is observed that, as shift in the process location increases, sample size to detect the shift and the loss cost from the process decrease. The power of the chart increases with increasing shift. The design gives better economic/statistical performance for large shifts in the process. This economic procedure can be applied to any process having known or unknown process outcome distribution. The sensitivity of the design is also carried out to check the effect on statistical as well as economic performance of the design due to change in different time and cost parameters.
Keywords
Economic design, Production cycle, EWMA control chart, Markov chain, Expected loss.
References
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Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of Cusum run length. Biometrika, 59(3), 539-549. http://dx.doi.org/10.1093/biomet/59.3.539.
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Chen, F. L., & Yeh, C. H. (2006). Economic design of control charts with Burr distribution for non-normal data, under Weibull failure mechanism. Journal of the Chinese Institute of Industrial Engineering, 23(3), 200-206. http://dx.doi.org/10.1080/10170660609509009.
Chen, Y. K. (2004). Economic design of X̄ control charts for non-normal data using variable sampling policy. International Journal of Production Economics, 92(1), 61-74. http://dx.doi.org/10.1016/j.ijpe.2003.09.011.
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Chou, C. Y., Li, M.-H. C., & Wang, P.-H. (2001). Economic statistical design of averages control charts for monitoring a process under non-normality. International Journal of Advanced Manufacturing Technology, 17(8), 603-609. http://dx.doi.org/10.1007/s001700170144.
Duncan, A. J. (1956). The economic design of X̄ charts to maintain current control of a process. Journal of the American Statistical Association, (June), 228-242.
He, Y., Kai, M., & Wenbing, C. (2009). Economic design of EWMA control chart using quality cost model based on ARL. In IEEE International Conference on Industrial Engineering and Engineering Management (pp. 945-949), Hong Kong, China.
Khilare, S. K., & Shirke, D. T. (2010). A nonparametric synthetic control chart using sign statistic. Communications in Statistics. Theory and Methods, 39(18), 3282-3293. http://dx.doi.org/10.1080/03610920903249576.
Koo, T. Y., & Case, K. E. (1990). Economic design of x-bar control charts for use in monitoring continuous flow process. International Journal of Production Research, 28(11), 2001-2011. http://dx.doi.org/10.1080/00207549008942848.
Kooli, I., & Limam, M. (2015). Economic design of attribute np control charts using a variable sampling policy. Applied Stochastic Models in Business and Industry, 31(4), 483-494. http://dx.doi.org/10.1002/asmb.2042.
Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: a unified approach. Technometrics, 28(1), 3-10. http://dx.doi.org/10.1080/00401706.1986.10488092.
Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32(1), 1-12. http://dx.doi.org/10.1080/00401706.1990.10484583.
Mahadik, S. B., & Shirke, D. T. (2007). Economic design of a modified variable sample size and sampling interval X̄ chart. Economic Quality Control, 22(2), 273-293. http://dx.doi.org/10.1515/EQC.2007.273.
McWillims, T. P. (1989). Economic control chart designs and the in control time distribution: a sensitivity study. Journal of Quality Technology, 21(2), 103-110.
Montgomery, D. C. (1980). The economic design of control charts: a review and literature survey. Journal of Quality Technology, 12(2), 75-87.
Montgomery, D. C. (2008). Introduction to statistical quality control (6th ed.). New York: John Wiley and Sons.
Pan, J. N., & Chen, S. T. (2005). The economic design of CUSUM chart for monitoring environmental performance. Asia Pacific Management Review, 10(2), 155-161.
Patil, S. H., & Rattihalli, R. N. (2009). Economic design of moving average control chart for continued and ceased production process. Economic Quality Control, 24(1), 129-142. http://dx.doi.org/10.1515/EQC.2009.129.
Patil, S. H., & Shirke, D. T. (2015). Economic design of moving average control chart for non-normal data using variable sampling intervals. Journal of Industrial and Production Engineering, 32(2), 133-147. http://dx.doi.org/10.1080/21681015.2015.1023854.
Rahim, M. A. (1985). Economic model of X̄ chart under non-normality and measurement errors. Computers & Operations Research, 12(3), 291-299. http://dx.doi.org/10.1016/0305-0548(85)90028-0.
Rahim, M. A. (1989). Determination of optimal design parameters of joint X̄ and R charts. Journal of Quality Technology, 21(1), 65-70.
Reynolds Junior, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). X̄ charts with variable sampling intervals. Technometrics, 30(2), 181-192. http://dx.doi.org/10.1080/00401706.1988.10488366.
Saghaei, A., Ghomi, S. M. T. F., & Jaberi, S. (2014). Economic design of exponentially weighted moving average control chart based on measurement error using genetic algorithm. Quality and Reliability Engineering International, 30(8), 1153-1163. http://dx.doi.org/10.1002/qre.1538.
Saniga, E. M. (1989). Economic statistical control-chart designs with an application to X̄ and R charts. Technometrics, 31(3), 313-320. http://dx.doi.org/10.1080/00401706.1989.10488554.
Serel, D. A. (2009). Economic design of EWMA control charts based on loss function. Mathematical and Computer Modelling, 49(3-4), 745-759. http://dx.doi.org/10.1016/j.mcm.2008.06.012.
Serel, D. A., & Moskowitz, H. (2008). Joint economic design of EWMA control charts for mean and variance. European Journal of Operational Research, 184(1), 157-168. http://dx.doi.org/10.1016/j.ejor.2006.09.084.
Shewhart, W. A. (1931). Economic control of quality of manufactured product. New York: D. Van Nostrand Company.
Yang, S. F., Lin, J. S., & Cheng, S. W. (2011b). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38, 6239-6243. http://dx.doi.org/10.1016/j.eswa.2010.11.044.
Yang, S. F., Tsai, W. C., Huang, T. M., Yang, C. C., & Cheng, S. (2011a). Monitoring process mean with a EWMA control chart. Production, 21(2), 217-222. http://dx.doi.org/10.1590/S0103-65132011005000026.
Yeh, L. L., & Chen, F. L. (2010). An extension of Banerjee and Rahim’s model for an economic design of X̄ control chart for non-normally distributed data, under gamma failure model. Communications in Statistics. Simulation and Computation, 39(5), 994-1015. http://dx.doi.org/10.1080/03610911003734815.
Bai, D. S., & Lee, K. T. (1998). An economic design of variable sampling interval X̄ control charts. International Journal of Production Economics, 54(1), 57-64. http://dx.doi.org/10.1016/S0925-5273(97)00125-4.
Banerjee, P. K., & Rahim, M. A. (1987). The economic design of control charts: a renual theory approach. Engineering Optimization, 12(1), 63-73. http://dx.doi.org/10.1080/03052158708941084.
Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of Cusum run length. Biometrika, 59(3), 539-549. http://dx.doi.org/10.1093/biomet/59.3.539.
Celano, G. (2011). On the constrained economic design of control charts: a literature review. Production, 21(2), 223-234. http://dx.doi.org/10.1590/S0103-65132011005000014.
Chen, F. L., & Yeh, C. H. (2006). Economic design of control charts with Burr distribution for non-normal data, under Weibull failure mechanism. Journal of the Chinese Institute of Industrial Engineering, 23(3), 200-206. http://dx.doi.org/10.1080/10170660609509009.
Chen, Y. K. (2004). Economic design of X̄ control charts for non-normal data using variable sampling policy. International Journal of Production Economics, 92(1), 61-74. http://dx.doi.org/10.1016/j.ijpe.2003.09.011.
Chiu, W. C. (2015). Economic-Statistical design of EWMA control charts based on Taguchi’s loss function. Communications in Statistics. Simulation and Computation, 44(1), 137-153. http://dx.doi.org/10.1080/03610918.2013.773346.
Chou, C. Y., Li, M.-H. C., & Wang, P.-H. (2001). Economic statistical design of averages control charts for monitoring a process under non-normality. International Journal of Advanced Manufacturing Technology, 17(8), 603-609. http://dx.doi.org/10.1007/s001700170144.
Duncan, A. J. (1956). The economic design of X̄ charts to maintain current control of a process. Journal of the American Statistical Association, (June), 228-242.
He, Y., Kai, M., & Wenbing, C. (2009). Economic design of EWMA control chart using quality cost model based on ARL. In IEEE International Conference on Industrial Engineering and Engineering Management (pp. 945-949), Hong Kong, China.
Khilare, S. K., & Shirke, D. T. (2010). A nonparametric synthetic control chart using sign statistic. Communications in Statistics. Theory and Methods, 39(18), 3282-3293. http://dx.doi.org/10.1080/03610920903249576.
Koo, T. Y., & Case, K. E. (1990). Economic design of x-bar control charts for use in monitoring continuous flow process. International Journal of Production Research, 28(11), 2001-2011. http://dx.doi.org/10.1080/00207549008942848.
Kooli, I., & Limam, M. (2015). Economic design of attribute np control charts using a variable sampling policy. Applied Stochastic Models in Business and Industry, 31(4), 483-494. http://dx.doi.org/10.1002/asmb.2042.
Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: a unified approach. Technometrics, 28(1), 3-10. http://dx.doi.org/10.1080/00401706.1986.10488092.
Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32(1), 1-12. http://dx.doi.org/10.1080/00401706.1990.10484583.
Mahadik, S. B., & Shirke, D. T. (2007). Economic design of a modified variable sample size and sampling interval X̄ chart. Economic Quality Control, 22(2), 273-293. http://dx.doi.org/10.1515/EQC.2007.273.
McWillims, T. P. (1989). Economic control chart designs and the in control time distribution: a sensitivity study. Journal of Quality Technology, 21(2), 103-110.
Montgomery, D. C. (1980). The economic design of control charts: a review and literature survey. Journal of Quality Technology, 12(2), 75-87.
Montgomery, D. C. (2008). Introduction to statistical quality control (6th ed.). New York: John Wiley and Sons.
Pan, J. N., & Chen, S. T. (2005). The economic design of CUSUM chart for monitoring environmental performance. Asia Pacific Management Review, 10(2), 155-161.
Patil, S. H., & Rattihalli, R. N. (2009). Economic design of moving average control chart for continued and ceased production process. Economic Quality Control, 24(1), 129-142. http://dx.doi.org/10.1515/EQC.2009.129.
Patil, S. H., & Shirke, D. T. (2015). Economic design of moving average control chart for non-normal data using variable sampling intervals. Journal of Industrial and Production Engineering, 32(2), 133-147. http://dx.doi.org/10.1080/21681015.2015.1023854.
Rahim, M. A. (1985). Economic model of X̄ chart under non-normality and measurement errors. Computers & Operations Research, 12(3), 291-299. http://dx.doi.org/10.1016/0305-0548(85)90028-0.
Rahim, M. A. (1989). Determination of optimal design parameters of joint X̄ and R charts. Journal of Quality Technology, 21(1), 65-70.
Reynolds Junior, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). X̄ charts with variable sampling intervals. Technometrics, 30(2), 181-192. http://dx.doi.org/10.1080/00401706.1988.10488366.
Saghaei, A., Ghomi, S. M. T. F., & Jaberi, S. (2014). Economic design of exponentially weighted moving average control chart based on measurement error using genetic algorithm. Quality and Reliability Engineering International, 30(8), 1153-1163. http://dx.doi.org/10.1002/qre.1538.
Saniga, E. M. (1989). Economic statistical control-chart designs with an application to X̄ and R charts. Technometrics, 31(3), 313-320. http://dx.doi.org/10.1080/00401706.1989.10488554.
Serel, D. A. (2009). Economic design of EWMA control charts based on loss function. Mathematical and Computer Modelling, 49(3-4), 745-759. http://dx.doi.org/10.1016/j.mcm.2008.06.012.
Serel, D. A., & Moskowitz, H. (2008). Joint economic design of EWMA control charts for mean and variance. European Journal of Operational Research, 184(1), 157-168. http://dx.doi.org/10.1016/j.ejor.2006.09.084.
Shewhart, W. A. (1931). Economic control of quality of manufactured product. New York: D. Van Nostrand Company.
Yang, S. F., Lin, J. S., & Cheng, S. W. (2011b). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38, 6239-6243. http://dx.doi.org/10.1016/j.eswa.2010.11.044.
Yang, S. F., Tsai, W. C., Huang, T. M., Yang, C. C., & Cheng, S. (2011a). Monitoring process mean with a EWMA control chart. Production, 21(2), 217-222. http://dx.doi.org/10.1590/S0103-65132011005000026.
Yeh, L. L., & Chen, F. L. (2010). An extension of Banerjee and Rahim’s model for an economic design of X̄ control chart for non-normally distributed data, under gamma failure model. Communications in Statistics. Simulation and Computation, 39(5), 994-1015. http://dx.doi.org/10.1080/03610911003734815.
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