Robust Economic-Statistical Design of Control Charts - A Case Study in Automotive Industry

Document Type : Research Paper


1 Dept. of Industrial Engineering, Babol University of Technology, Babol, I.R.

2 Dept. of Industrial Engineering, Tarbiat Modares University, I.R. Iran


     One of the most important problems of the designs proposed by traditional economic-statistical approaches of control charts is inefficiency in the face of uncertainty. Uncertainty in the parameters of economic-statistical models may lead to failure in rapidly detecting changes in processes and impose greater costs to the organization. Monitoring the machining process in an automotive industry explains the necessity of considering the robust approach to the control charts. This research intends the control charts design for monitoring process quality characteristics in conditions of uncertainty in cost and process parameters. The robust design ensures that the proposed control chart alarms the process changes earlier than the time set by the user, despite the uncertainty in model parameters. The resulted robust optimal solutions not only ensure the efficiency of solutions in any realization of parameters, but also facilitate the practical implementation of control charts and reduce organization costs through improving the quality of process outgoings.


1. Montgomery, D. C. (2005). “Introduction to Statistical Quality Control.” 5 ed., John Wiley & Son., New York.
2. Azarshab, A., Javanshir, H., and Ebrahimnejad, S. (2011). “Designing Combined EWMA-EWMA Quality Control Scheme.” Journal of Industrial Engineering. 45(1), 1-11.
3. Amiri, F., Noghondarian, K., and Safaei, A. S. (2014). “Evaluating the performance of variable scheme X-bar control chart: a Taguchi loss approach.” International Journal of Production Research, DOI:10.1080/00207543.2014.906762.
4. Faraz, A., Heuchenne, C., Saniga, E., and Foster, E. (2013). “Monitoring delivery chains using multivariate control charts.” European Journal of Operational Research, 228, 282-289.
5. Franco, B. C., Celano, G., Castagliola, P., and Costa, A. F. B. (2014). “Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies.” International Journal of Production Economics, 151, 121-130.
6. Niaki, S. T. A., Gazaneh, F. M., and Toosheghanian, M. (2013). “A Parameter-Tuned Genetic Algorithm for Economic-Statistical Design of Variable Sampling Interval X-Bar Control Charts for Non-Normal Correlated Samples.” Communications in Statistics - Simulation and Computation, 43(5), 1212-1240.
7. Yeong, W. C., Khoo, M. B. C., Lee, M. H., and Rahim, M. A. (2013). “Economic and economic statistical designs of the synthetic Xbar chart using loss functions.” European Journal of Operational Research, 48, 571-581.
8. Mortarino, C. (2010) “Duncan's model for Xbar-control charts: sensitivity analysis to input parameters”, Quality and Reliability Engineering International. 26(1), 7-26.
9. Pignatiello, J. J. and Tsai, A. (1988). “Optimal Economic Design ofX̄ Control Charts When Cost Model Parameters are Not Precisely Known.” IIE Transactions. 20(1), 103-110.
10. Linderman, K. and Choo, A. S. (2002). “Robust economic control chart design.” IIE transactions, 34(12), 1069-1078.
11. Vommi, V. B. andSeetala, M. S. N. (2007). “A simple approach for robust economic design of control charts.” Computers & Operations Research,. 34(7), 2001-2009.
12. Vommi, V. B. andSeetala, M. S .N. (2007). “A new approach to robust economic design of control charts.” Applied Soft Computing,. 7(1), 211-228.
13. Bertsimas, D. and Sim, M. (2004). “The Price of Robustness.” Operations Research, 52, 35-53.
14. Ben-Tal, A., Boyd, S., and Nemirovski, A. (2006). “Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems”. Math. Program., Ser. B,. 107, 63-89.
15. Lorenzen, T. J. and Vance, L. C. (1986). “The Economic Design of Control Charts: A Unified Approach”. Technometrics, 28(1), 3-10.
16. Bertsimas, D., Brown, D. B., and Caramanis, C. (2011). “Theory and Applicationsof Robust Optimization.” SIAM Review, 53(3), 464-501.
17. Tarokh, M. J. and Naseri, A. (2012). “Genetic Algorithm and Hybrid Method to Minimize Total Distribution Cost in Multi-level Supply Chain.” Journal of Industrial Engineering, 46(1), 15-26.
18. Bagherinejad, J., Jolai, F., and Rafiee Majd, Z. (2013). “Solving the MRCPSP/Max with the Objective of Minimizing Tardiness Costs and Maximizing Earliness Rewards of Activities with a Two-stage Genetic Algorithm.” Journal of Industrial Engineering., 47(1), 1-13.
19. Teimoury, E. and Mousavi, F. S. (2011). Proposed a Genetic Algorithm for Inventory Planning Model in Project Supply Chain. Journal of Industrial Engineering, 45(1), 45-58.
20. Niaki, S. T. A., Malaki, M., and Ershadi, M. J. (2011). “A comparative study of four evolutionary algorithms for economic and economic-statistical designs of MEWMA control charts.” Journal of Optimization in Industrial Engineering, 9(4), 1-13.
21. Barzinpour, F., Noorossana, R., Niaki, S., and Ershadi, M. (2013). “A hybrid Nelder–Mead simplex and PSO approach on economic and economic-statistical designs of MEWMA controlcharts.” The International Journal of Advanced Manufacturing Technology, 65, 1339-1348.
22. Chou, C. Y., Chen, C. -H., and Chen, C. -H. (2006). “Economic design of variable sampling intervals T2 controlcharts using genetic algorithms.” Expert Systems with Applications, 30(2), 233-242.
23. Chen, Y. K. and Chang, H. -H. (2008). “Economic design of variable parameters X̄ control charts for processes with fuzzy mean shifts. The journal of the Operational Research Society, 59(8), 1128-1135.
24. Yang, S. -F. and Chen, W. -Y. (2009). “Controlling over-adjusted process means and variances using VSI cause selecting control charts. Expert Systems with Applications, 36(3), 7170-7182.
25. Chen, F. L. andYeh, C. H. (2009). “Economic statistical design of non-uniform sampling scheme X bar control charts under non-normality and Gamma shock using genetic algorithm.” Expert Systems with Applications, 36(5), 9488-9497.
26. Taguchi, G., Chowdhury, S., and Wu,Y. (2005). “Taguchi's quality engineering handbook.”, John Wiley & Sons, Hoboken, New Jersey.
27. Bertsimas, D. and Thiele, A. (2006). “Robust and data-driven optimization: modern decision making under uncertainty, in Tutorials on Operations Research.”, INFORMS,Chapter 4, 195-222.