Skip to main content
SpringerLink
Log in

Multiple-objective design of an \(\overline{{\user2{X}}} \) control chart with multiple assignable causes

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Control charts are widely implemented in firms to establish and maintain statistical control of a process which leads to the improved quality and productivity. Therefore, designs of control charts have gained particular attention from the outset. Design of control charts requires that the engineer selects a sample size, a sampling frequency, and the control limits for the chart. In this paper, a possible combination of design parameters is considered as a decision-making unit which is identified by three attributes: hourly expected cost, detection power of the chart, and in-control average run length. Subsequently, optimal design of control charts is formulated as a multiple-objective decision-making problem. Moreover, the cost function is extended from single to multiple assignable causes because there exist multiple assignable causes in real practice. An algorithm using data envelopment analysis is applied to solve the multiple-objective decision-making (MODM) model. Some numerical and experimental analyses are provided to illustrate the algorithm procedure. Sensitivity analysis is carried out to investigate the robustness of the model, and comparisons with other related published papers are made. It is shown that the proposed MODM model can overcome some drawbacks attached to the previous models and approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Montgomery DC (2001) Introduction to statistical process control, 4th edn. Wiley, New York

    Google Scholar 

  2. Duncan AJ (1956) The economic design of \(\bar X\) charts used to maintain current control of a process. J Am Stat Assoc 51(274):228–242 doi:10.2307/2281343

    Article  MATH  Google Scholar 

  3. Chung KJ (1992) Determination of optimal design parameters of an \(\bar X\) control chart. J Oper Res Soc 43(12):1151–1157

    Article  MATH  Google Scholar 

  4. Chou C-Y, Liu H-R, Chen C-H (2001) Economic design of averages control charts for monitoring a process with correlated samples. Int J Adv Manuf Technol 18(1):49–53 doi:10.1007/s001700170093

    Article  Google Scholar 

  5. Chou C-Y, Li M-HC, Wang P-H (2001) Economic statistical design of averages control charts for monitoring a process under non-normality. Int J Adv Manuf Technol 17(8):603–609 doi:10.1007/s001700170144

    Article  Google Scholar 

  6. Yu F-J, Chen Y-S (2005) An economic design for a variable-sampling-interval \(\bar X\) control chart for a continuous-flow process. Int J Adv Manuf Technol 25(3–4):370–376 doi:10.1007/s00170-003-1852-2

    Article  MathSciNet  Google Scholar 

  7. Yu F-J, Low C (2005) An algorithm for the determination of optimal design parameters of \(\bar X\) control charts. Int J Adv Manuf Technol 26(1–2):86–89 doi:10.1007/s00170-003-1969-3

    Article  Google Scholar 

  8. Montgomery DC (1980) The economic design of control charts: a review and literature survey. J Qual Technol 12(2):75–87

    Google Scholar 

  9. Vance LC (1983) A bibliography of statistical quality control chart techniques, 1970–1980. J Qual Technol 15(2):59–62

    Google Scholar 

  10. Ho C, Case KE (1994) Economic design of control charts: a literature review for 1981–1991. J Qual Technol 26(1):39–53

    Google Scholar 

  11. Woodall WH (1986) Weakness of the economic design of control charts. Technometrics 28(4):408–410 doi:10.2307/1269000

    Article  Google Scholar 

  12. Saniga EM (1989) Economic statistical control chart designs with an application to \(\bar X\) and R charts. Technometrics 31(3):313–320 doi:10.2307/3556141

    Article  Google Scholar 

  13. Del Castillo E, Mackin P, Montgomery DC (1996) Multiple-criteria optimal design of \(\bar X\) control charts. IIE Trans 28(6):467–474 doi:10.1080/07408179608966293

    Article  Google Scholar 

  14. Chen YK, Liao HC (2004) Multi-criteria design of an \(\bar X\) control chart. Comput Ind Eng 46(4):877–891 doi:10.1016/j.cie.2004.05.020

    Article  MathSciNet  Google Scholar 

  15. Duncan AJ (1971) The economic design of \(\bar X\) charts when there is a multiplicity of assignable causes. J Am Stat Assoc 66(333):107–121 doi:10.2307/2284859

    Article  MATH  Google Scholar 

  16. Tagaras G, Lee HL (1988) Economic design of control charts with different control limits for different assignable causes. Manage Sci 34(11):1347–1366

    Article  MATH  Google Scholar 

  17. Chung KJ (1994) An algorithm for computing the economically optimal \(\bar X\) control charts for a process with multiple assignable causes. Eur J Oper Res 72(2):350–363 doi:10.1016/0377-2217(94)90315-8

    Article  MATH  Google Scholar 

  18. Chen Y-S, Yu F-J (2003) Determination of optimal design parameters of moving average control charts. Int J Adv Manuf Technol 21(6):397–402 doi:10.1007/s001700300046

    Article  MathSciNet  Google Scholar 

  19. Chiu WK (1976) Economic design of np charts for processes subject to a multiplicity of assignable causes. Manage Sci 23(4):404–411

    Article  Google Scholar 

  20. Chung KJ (1995) An algorithm for the economic design of np charts for a multiplicity of assignable causes. J Oper Res Soc 46(11):1374–1385

    Article  MATH  Google Scholar 

  21. Chen YS, Yang YM (2002) Economic design of \(\bar X\) control charts with Weibull in-control times when there are multiple assignable causes. Int J Prod Econ 77(1):17–23 doi:10.1016/S0925-5273(01)00196-7

    Article  Google Scholar 

  22. Yu FJ, Hou JL (2006) Optimization of design parameters for control charts with multiple assignable cause. J Appl Stat 33(3):279–290 doi:10.1080/02664760500445541

    Article  MATH  MathSciNet  Google Scholar 

  23. Yu FJ, Tsou CS, Huang KI (2007) An economic-statistical design of \(\bar X\) control charts with multiple assignable causes. The 22nd European Conference on Operational Research

  24. Tbanassoulis E (2001) Introduction to the theory and application of data envelopment analysis. Kluwer, Norwell

    Google Scholar 

  25. Cook WD, Zhu J (2005) Modeling performance measurement. Springer, New York

    Google Scholar 

  26. Cooper WW, Seiford LM, Zhu J (2004) Handbook on data envelopment analysis. Kluwer Academic, Boston

    MATH  Google Scholar 

  27. Cook WD, Roll Y, Kazakov A (1990) A DEA model for measuring the relative efficiency of highway maintenance patrols. INFOR 28(2):113–124

    Google Scholar 

  28. Sherman HD, Ladino G (1995) Managing bank productivity using data envelopment analysis (DEA). Interfaces 25(2):60–73

    Article  Google Scholar 

  29. Wu D, Yang Z, Liang L (2006) Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis. Appl Math Comput 181(1):271–281 doi:10.1016/j.amc.2006.01.037

    Article  MATH  MathSciNet  Google Scholar 

  30. Karsak EE (2008) Using data envelopment analysis for evaluating flexible manufacturing systems in the presence of imprecise data. Int J Adv Manuf Technol 35(9–10):867–874 doi:10.1007/s00170-006-0765-2

    Article  Google Scholar 

  31. Saen RF (2008) Supplier selection by the new AR-IDEA model. Int J Adv Manuf Technol. doi:10.1007/s00170-007-1287-2

  32. Hwang CL, Masud ASM (1979) Multiple objective decision making—methods and applications. Springer, New York

    MATH  Google Scholar 

  33. Zionts S, Wallenius J (1976) An interactive programming method for solving the multiple criteria problem. Manage Sci 22(6):652–663

    Article  MATH  Google Scholar 

  34. Ignizio JP (1982) Linear programming in single and multiple objective systems. Prentice Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  35. Cooper WW, Seiford LM, Tone K (2000) Data envelopment analysis. Kluwer, Boston

    Google Scholar 

  36. Chanes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444 doi:10.1016/0377-2217(78)90138-8

    Article  Google Scholar 

  37. Banker RD, Charnes A, Cooper WW (1984) Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Manage Sci 30(9):1078–1092

    Article  MATH  Google Scholar 

  38. Chen LH (2005) A demerit control chart with linguistic weights. J Intell Manuf 16(3):349–359 doi:10.1007/s10845-005-7028-1

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Industrial Engineering, K. N. Toosi University of Technology, No. 17, Pardis St., Molla-Sadra St., Vanak Sq., Tehran, Iran, P.O. Box 19395-1999

    Shervin Asadzadeh & Farid Khoshalhan

Authors
  1. Shervin Asadzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farid Khoshalhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shervin Asadzadeh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Asadzadeh, S., Khoshalhan, F. Multiple-objective design of an \(\overline{{\user2{X}}} \) control chart with multiple assignable causes . Int J Adv Manuf Technol 43, 312–322 (2009). https://doi.org/10.1007/s00170-008-1709-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-008-1709-9

Keywords

Search

Navigation