Evaluation of the economic statistical design of the multivariate T² control chart with multiple variable sampling intervals scheme: NSGA-II approach

References

• Hotelling H. Multivariate quality control – illustrated by the air testing of sample bombsights. In: Eisenhart C, Hastay MW, Wallis WA, editors. Techniques of statistical analysis. New York: MacGraw-Hill; 1947. p. 111–184.
   Google Scholar
• Jackson JE. Multivariate quality control. Comm Statist Theory Methods. 1985;14:2657–2688.
   Web of Science ®Google Scholar
• Alt FB. Multivariate quality control. The encyclopedia of statistical sciences. New York: John Wiley; 1985.
   Google Scholar
• Mason RL, Young JC. Multivariate statistical process control with industrial applications. Philadelphia, PA: ASASIAM; 2002.
   Google Scholar
• Fuchs C, Kenett RS. Multivariate quality control, theory and applications. NewYork: Marcel Dekker; 1998.
   Google Scholar
• Mason RL, Tracy ND, Young JC. A practical approach for interpreting multivariate T2 control chart signals. J Qual Technol. 1997;29:396–406.
   Web of Science ®Google Scholar
• Lowry CA, Montgomery DC. A review of multivariate control charts. IIE Trans. 1995;27:800–810.
   Web of Science ®Google Scholar
• Duncan AJ. The economic design of X charts used to maintain current control of a process. J Amer Statist Assoc. 1956;51:228–242.
   Web of Science ®Google Scholar
• Woodall WH. Weaknesses of the economical design of control charts. Technometrics. 1986;28:408–409.
   Web of Science ®Google Scholar
• Saniga EM. Economic statistical control chart designs with an application to X and R charts. Technometrics. 1989;31:313–320.
   Web of Science ®Google Scholar
• Montgomery DC, Woodall WH. A discussion on statistically based process monitoring and control. J Qual Technol. 1997;29:121–162.
   Web of Science ®Google Scholar
• Taylor HM. Markovian sequential replacement processes. Ann Math Stat. 1965;36:13–21.
   Google Scholar
• Chen YK. Economic design of variable sampling interval T2 control charts – a hybrid Markov chain approach with genetic algorithms. Expert Syst Appl. 2007;33:683–689.
   Web of Science ®Google Scholar
• Chao YC, Chun HC, Chung, HC. Economic design of variable sampling intervals T2 control charts using genetic algorithms. Expert Syst Appl. 2006;30:233–242.
   Web of Science ®Google Scholar
• Faraz A, Saniga E, Kazemzade RB. Economic and economical statistical design of Hotelling's T2 control chart with two-state adaptive sample size. J Stat Comput Simul. 2009. doi:10.1080/00949650903062574.
   Web of Science ®Google Scholar
• Chen YK. Economic design of variable T2 control chart with the VSSI sampling scheme. Qual Quant. 2009. doi:10.1007/s11135-007-9101-7.
   PubMed Web of Science ®Google Scholar
• Faraz A, Kazemzadeh R, Parsian A, Moghadam MB. On the advantages of economically designed Hotelling's T2 control chart with variable sample sizes and sampling intervals. Qual Quant. 2012;46:39–53.
   Web of Science ®Google Scholar
• Faraz A, Saniga E. Economic and economic statistical design of Hotelling's T2 control chart with double warning lines. Qual Reliab Eng Int. 2011;27:125–139. doi:10.1002/qre.1095.
   Web of Science ®Google Scholar
• Torabian M, Moghadam MB, Faraz A. economically designed Hotelling's T2 control chart using VSICL scheme. Arab J Sci Eng. 2010;35:251–263.
   Web of Science ®Google Scholar
• Seif A, Moghadam MB, Faraz A, Heuchenne C. Statistical merits and economic evaluation of T2 control charts with the VSSC scheme. Arab J Sci Eng. 2011;36:1461–1470.
   Web of Science ®Google Scholar
• Seif A, Faraz A, Heuchenne C, Saniga E, Moghadam MB. A modified economicstatistical design of T2 control chart with variable sample sizes and control limits. J Appl Stat. 2011;38:2459–2469.
   Web of Science ®Google Scholar
• Costa AFB, Rahim MA. Economic design of X¯ charts with variable parameters: the Markov chain approach. J Appl Stat. 2001;28:875–885.
   Web of Science ®Google Scholar
• Faraz A, Heuchenne C, Saniga E. Optimal T2 control chart with double sampling scheme – an alternative to the MEWMA chart. Qual Reliab Eng Int. 2012;28:751–760.
   Web of Science ®Google Scholar
• Faraz A, Saniga E. Multiobjective genetic algorithm approach to the economic statistical design of control charts with an application to Xbar and S2 charts. Qual Reliab Eng Int. 2013;29:407–415. doi:10.1002/qre.1390.
   Web of Science ®Google Scholar
• Faraz A, Heuchenne C, Saniga E, Costa AFB. Double-objective economic statistical design of the VP T2 control chart: Wald's identity approach. J Stat Comput Simul. 2014;84:2123–2137. doi:10.1080/00949655.2013.784315.
   Web of Science ®Google Scholar
• Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol Comput. 2002;6:184–197.
   Web of Science ®Google Scholar
• Bai DS, Lee KT. An economic design of variable sampling interval X¯ control charts. Int J Prod Econ. 1998;54:57–64.
   Web of Science ®Google Scholar
• Reynolds MRJr., Arnold JC. Optimal one-side Shewhart control chart with variable sampling intervals. Sequential Anal. 1989;8:51–77.
   Google Scholar
• Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the International Conference on Genetic Algorithm and their Applications; 1985.
   Google Scholar
• Horn J, Nafpliotis N. Multiobjective optimization using the niched genetic algorithm. Technical Report IIIiGAI Report 93005, University of Illinoisat Urbana-Champaign, Urbana, IL; 1993.
   Google Scholar
• Zitzler E, Thiele L. Multiobjective optimization using evolutionary algorithms – a comparative case study. In: Eiben AE, et al., editors. Parallel problem solving from nature-PPSN V. Berlin: Sprinter; 1998.
   Google Scholar