Neural Computing and Applications

, Volume 31, Supplement 2, pp 1173–1194 | Cite as

An integration of NSGA-II and DEA for economic–statistical design of T2-Hotelling control chart with double warning lines

  • Ali SalmasniaEmail author
  • Aram Rahimi
  • Behnam Abdzadeh
Original Article


Control charts are the most applicable tools for monitoring the quality of processes. The day-to-day changes in industrial processes and customers’ expectations motivate the process engineers to monitor multiple correlated quality characteristics, simultaneously. Hence, in this paper, the design of a “double warning lines T2-Hotelling” control chart is studied because of the advantages of this multivariate control chart in detecting moderate and small shifts in a process. In this regard, this research aims to optimize a multi-objective economic–statistical design model that considers monitoring costs and statistical features of control chart, concurrently. The non-dominated sorting genetic algorithm II is utilized to obtain a suitable Pareto set for the model. Since it is difficult for the decision makers to select the most efficient solution among the Pareto set, three different methods of data envelopment analysis consisting of Charnes–Cooper–Rhodes model, cross-efficiency technique and aggressive formulation are used to rank the members of Pareto set and to select the most efficient one. Also, in this research the performance of these three methods in discriminating between the efficient solutions is compared to each other. Eventually, a comparative study is conducted to show the better performance of the suggested model in comparison with the corresponding economic design model.


Economic–statistical design Double warning lines T2-Hotelling control chart NSGA-II Data envelopment analysis 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Al-Refaie A (2012) Optimizing performance with multiple responses using cross-evaluation and aggressive formulation in data envelopment analysis. IIE Trans 44(4):262–276CrossRefGoogle Scholar
  2. 2.
    Amiri A, Mogouie H, Doroudyan MH (2013) Multi-objective economic-statistical design of MEWMA control chart. Int J Prod Qual Manag 11(2):131–149Google Scholar
  3. 3.
    Amiri A, Moslemi A, Doroudyan MH (2015) Robust economic and economic-statistical design of EWMA control chart. Int J Adv Manuf Technol 78(1–4):511–523CrossRefGoogle Scholar
  4. 4.
    Aparisi F (1996) Hotelling’s T2 control chart with adaptive sample sizes. Int J Prod Res 34(10):2853–2862zbMATHCrossRefGoogle Scholar
  5. 5.
    Asadzadeh S, Khoshalhan F (2009) Multiple-objective design of an overline X-bar control chart with multiple assignable causes. Int J Adv Manuf Technol 43(3–4):312–322CrossRefGoogle Scholar
  6. 6.
    Bashiri M, Amiri A, Doroudyan MH, Asgari A (2013) Multi-objective genetic algorithm for economic statistical design of control chart. Sci Iran 20(3):909–918Google Scholar
  7. 7.
    Bodnar O, Schmid W (2011) CUSUM charts for monitoring the mean of a multivariate Gaussian process. J Stat Plann Inference 141(6):2055–2070MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Celano G, Fichera S (1999) Multiobjective economic design of an X control chart. Comput Ind Eng 37(1):129–132CrossRefGoogle Scholar
  10. 10.
    Deb K, Agrawal S, Pratap A, Meyarivan T, (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 849–858Google Scholar
  11. 11.
    Doyle J, Green R (1994) Efficiency and cross-efficiency in DEA: derivations, meanings and uses. J Oper Res Soc 45(5):567–578zbMATHCrossRefGoogle Scholar
  12. 12.
    Duncan AJ (1956) The economic design of X charts used to maintain current control of a process. J Am Stat Assoc 51(274):228–242zbMATHGoogle Scholar
  13. 13.
    Faraz A, Heuchenne C, Saniga E, Costa AF (2014) Double-objective economic statistical design of the VP T 2 control chart: Wald’s identity approach. J Stat Comput Simul 84(10):2123–2137MathSciNetCrossRefGoogle Scholar
  14. 14.
    Faraz A, Parsian A (2006) Hotelling’s T2 control chart with double warning lines. Stat Pap 47(4):569–593zbMATHCrossRefGoogle Scholar
  15. 15.
    Faraz A, Saniga E (2011) Economic statistical design of a T2 control chart with double warning lines. Qual Reliab Eng Int 27(2):125–139CrossRefGoogle Scholar
  16. 16.
    Hotelling H (1947) Multivariate quality control—illustrated by the air testing of sample bombsights. In: Eisenhart C, Hastay MW, Wallis WA (eds) Techniques of statistical analysis. McGraw Hill, New YorkGoogle Scholar
  17. 17.
    Lorenzen TJ, Vance LC (1986) The economic design of control charts: a unified approach. Technometrics 28(1):3–10MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Lowry CA, Montgomery DC (1995) A review of multivariate control charts. IIE Trans 27(6):800–810CrossRefGoogle Scholar
  19. 19.
    Lowry CA, Woodall WH, Champ CW, Rigdon SE (1992) A multivariate exponentially weighted moving average control chart. Technometrics 34(1):46–53zbMATHCrossRefGoogle Scholar
  20. 20.
    Memari A, Rahim ARA, Hassan A, Ahmad R (2016) A tuned NSGA-II to optimize the total cost and service level for a just-in-time distribution network. Neural Comput Appl. doi: 10.1007/s00521-016-2249-0 CrossRefGoogle Scholar
  21. 21.
    Moghaddam AS, Amiri A, Bashiri M (2014) Multi-objective economic-statistical design of cumulative count of conforming control chart. Int J Eng Trans A Basics 27(10):1591Google Scholar
  22. 22.
    Montgomery DC (1980) The economic design of control charts: a review and literature survey. J Qual Technol 12(2):75–87CrossRefGoogle Scholar
  23. 23.
    Niaki STA, Ershadi MJ, Malaki M (2010) Economic and economic-statistical designs of MEWMA control charts—a hybrid Taguchi loss, Markov chain, and genetic algorithm approach. Int J Adv Manuf Technol 48(1–4):283–296CrossRefGoogle Scholar
  24. 24.
    Niaki STA, Malaki M, Ershadi MJ (2011) A particle swarm optimization approach on economic and economic-statistical designs of MEWMA control charts. Sci Iran 18(6):1529–1536CrossRefGoogle Scholar
  25. 25.
    Prabhu SS, Montgomery DC, Runger GC (1997) Economic-statistical design of an adaptive X chart. Int J Prod Econ 49(1):1–15CrossRefGoogle Scholar
  26. 26.
    Safaei AS, Kazemzadeh RB, Gan HS (2015) Robust economic-statistical design of X-bar control chart. Int J Prod Res 53(14):4446–4458CrossRefGoogle Scholar
  27. 27.
    Safaei AS, Kazemzadeh RB, Niaki STA (2012) Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function. Int J Adv Manuf Technol 59(9–12):1091–1101CrossRefGoogle Scholar
  28. 28.
    Salmasnia A, Abdzadeh B, Namdar M (2017) A joint design of production run length, maintenance policy and control chart with multiple assignable causes. J Manuf Syst 42(1):44–56CrossRefGoogle Scholar
  29. 29.
    Saniga EM (1989) Economic statistical control-chart designs with an application to and R charts. Technometrics 31(3):313–320Google Scholar
  30. 30.
    Seif A, Faraz A, Sadeghifar M (2015) Evaluation of the economic statistical design of the multivariate T 2 control chart with multiple variable sampling intervals scheme: NSGA-II approach. J Stat Comput Simul 85(12):2442–2455MathSciNetCrossRefGoogle Scholar
  31. 31.
    Seif A, Moghadam MB, Faraz A, Heuchenne C (2011) Statistical merits and economic evaluation of t2 control charts with the vssc scheme. Arab J Sci Eng 36(7):1461–1470CrossRefGoogle Scholar
  32. 32.
    Tavana M, Khalili-Damghani K, Di Caprio D, Oveisi Z (2016) An evolutionary computation approach to solving repairable multi-state multi-objective redundancy allocation problems. Neural Comput Appl. doi: 10.1007/s00521-016-2676-y CrossRefGoogle Scholar
  33. 33.
    Zhang G, Berardi V (1997) Economic statistical design of X control charts for systems with Weibull in-control times. Comput Ind Eng 32(3):575–586CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Industrial Engineering, Faculty of EngineeringUniversity of QomQomIran

Personalised recommendations