Bi-objective Economic statistical design of the joint Xbar and S charts incorporating Taguchi loss function

Document Type: Research Paper

Authors

1 Department of Industrial Engineering, University of Sistan and Baluchestan, Zahedan, Iran

2 Department of Industrial Engineering, Babol University of Technology,Babol,Iran

Abstract

In this research, we propose a bi-objective model for the economic-statistical design of the X-bar and S control charts. The model minimizes out-of-control average time to signal as well as minimizing mean hourly loss-cost where it incorporates the Taguchi loss function. Statistical constraint is considered in the model to achieve desired in-control time to signal. A non-dominated sorting genetic algorithm is developed to obtain the Pareto optimal scheme of the control chart. Sensitivity analysis and comparison study with traditional economic models proves that the proposed bi-objective design of X-bar and S control chart ensures a better approach to improve the quality system and increase the plans ease of use.

Keywords

Main Subjects


AMIRI, A., BASHIRI, M., MALEKI, M. R. & MOGHADDAM, A. S. 2014. Multi-objective Markov-based economic-statistical design of EWMA control chart using NSGA-II and MOGA algorithms. International Journal of Multicriteria Decision Making, 4, 332-347.

AMIRI, A., MOGOUIE, H. & DOROUDYAN, M. H. 2013. Multi-objective economic-statistical design of MEWMA control chart. International Journal of Productivity and Quality Management, 11, 131-149.

ASADZADEH, S. & KHOSHALHAN, F. 2008. Multiple-objective design of an X̄ control chart with multiple assignable causes. International journal of advanced manufacturing technology, 43, 312-322.

AUGUSTO, O. B., RABEAU, S., DE´PINCE´, P. & BENNIS, F. 2006. Multi-objective genetic algorithms: A way to improve the convergence rate. Engineering Applications of Artificial Intelligence 19, 501-510.

BAKIR, M. A. & ALTUNKAYNAK 2004. The optimization with the genetic algorithm approach of the multi-objective, joint economical design of the x̄ and R control charts. Journal of Applied Statistics, 31, 753-772.

BEN-DAYA, M. & DUFFUAA, S. O. 2003. Integration of Taguchi’s loss function approach in the economic design of x¯chart. International Journal of Quality & Reliability Management, 20 607-619.

CARLYLE, W. M., FOWLER, J. W. & GEL, E. S., KIM, B. 2003. Quantitative comparison of approximate solution sets for bi-criteria optimization problems. Decision Sciences, 34, 63-82.

CELANO, G. & FICHERA, S. 1999. Multiobjective economic design of an X̄ control chart. Computers & industrial engineering, 37, 129-132.

CHEN, F. L. & YEH, 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, 9488-9497.

CHEN, Y. K. & LIAO, H. C. 2004. Multi-criteria design of an X control chart. Computers & Industrial Engineering 46, 877-891.

CHOU, C.-Y., CHEN, C.-H. & LIU, H.-R. 2000. Economic-statistical design of X̄ charts for non-normal data by considering quality loss. Journal of Applied Statistics, 27, 939 - 951.

DEB, K. 2001. Multi-objective Optimization Using Evolutionary Algorithms, Chichester, UK, John Wiely.

EHRGOTT, M. & GANDIBLEUX, X. 2003. Multiple criteria optimization: state of the art annotated bibliographic surveys, Kluwer Academic Publishers.

FARAZ, A., HEUCHENNE, C. & SANIGA, E. 2011. Optimal T2 Control Chart with a Double Sampling Scheme – An Alternative to the MEWMA Chart. Quality and Reliability Engineering International.

FARAZ, A., HEUCHENNE, C., SANIGA, E. & COSTA, A. F. B. 2014. Double-objective economic statistical design of the VP T2 control chart: Wald's identity approach. Journal of Statistical Computation and Simulation, 84, 2123-2137.

FARAZ, A. & SANIGA, E. 2013. Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to X¯bar and S2 Charts. Quality and Reliability Engineering International, 29, 407-415.

KHATTREE, R. & RAO, C. R. 2003. Statistics in Industry, Elsevier Publishing Company.

LORENZEN, T. J. & VANCE, L. C. 1986. The Economic Design of Control Charts: A Unified Approach. Technometrics, 28, 3-10.

MCWILLIAMS, T. P., SANIGA, E. M. & DAVIS, D. J. 2001. Economic-statistical design of X̄ and R or X̄ and S charts. Journal of Quality Technology, 33, 234-241.

MORABI, Z. S., OWLIA, M. S., BASHIRI, M. & DOROUDYAN, M. H. 2015. Multi-objective design of control charts with fuzzy process parameters using the hybrid epsilon constraint PSO. Applied Soft Computing, 30, 390-399.

MOSKOWITZ, H., PLANTE, R. & CHUN, Y. H. 1994. Effect of quality loss functions on the economic design of x process control charts. European journal of operational research, 72, 333-349.

NIAKI, S., ERSHADI, M. & MALAKI, M. 2010a. Economic and economic-statistical designs of MEWMA control charts—a hybrid Taguchi loss, Markov chain, and genetic algorithm approach. The International Journal of Advanced Manufacturing Technology, 48, 283-296.

NIAKI, S. T., ERSHADI, M. & MALAKI, M. 2010b. Economic and economic-statistical designs of MEWMA control charts—a hybrid Taguchi loss, Markov chain, and genetic algorithm approach. The International Journal of Advanced Manufacturing Technology.

PANDEY, D., KULKARNI, M. S. & VRAT, P. 2011. A methodology for joint optimization for maintenance planning, process quality and production scheduling. Computers & Industrial Engineering, 61, 1098-1106.

PIGNATIELLO, J. J. & TSAI, A. 1988. Optimal Economic Design of X̄ Control Charts When Cost Model Parameters are Not Precisely Known. IIE Transactions, 20, 103-110.

REYNOLDS, M. R., JR. & CHO, G. Y. 2006. Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix. Journal of Quality Technology, 38, 230-253.

SAFAEI, A., KAZEMZADEH, R. & NIAKI, S. 2012a. Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function. The International Journal of Advanced Manufacturing Technology, 59, 1091-1101.

SAFAEI, A. S., KAZEMZADEH, R. B. & NIAKI, S. T. A. 2012b. Multiobjective Design of an S Control Chart for monitoring process variability. International Journal of Multicriteria Decision Making, 2, 408-424.

SANIGA, E. M. 1989. Economic Statistical Control-Chart Designs with an Application to  X̄ and R Charts. Technometrics, 31, 313-320.

SEREL, D. A. 2009. Economic design of EWMA control charts based on loss function. Mathematical and Computer Modelling, 49, 745-759.

SEREL, D. A. & MOSKOWITZ, H. 2008. Joint economic design of EWMA control charts for mean and variance. European Journal of Operational Research, 184, 157-168.

SHAIBU, A.-B. & CHO, B. 2006. Development of realistic quality loss functions for industrial applications. Journal of Systems Science and Systems Engineering, 15, 385-398.

TAGUCHI, G., ELSAYED, E. & HSIANG, T. 1989. Quality Engineering in Production Systems, New York, NY., McGraw-Hill.

WOODALL, W. H. 1986. Weaknesses of the Economic Design of Control Charts. Technometrics, 28, 408-410.

YEONG, W. C., KHOO, M. B. C., WU, Z. & CASTAGLIOLA, P. 2011. Economically Optimum Design of a Synthetic X¯ Chart. Quality and Reliability Engineering International, 28, 725-741.