Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지

Economic Design of Synthetic Control Charts

합성 관리도의 경제적 설계

  • 임태진 (숭실대학교 산업·정보시스템공학과) ;
  • 김용덕 (숭실대학교 산업·정보시스템공학과)
  • Published : 2003.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper investigates the economic design of synthetic control charts. The synthetic control chart has been proven to be statistically superior to the $\bar{X}$-control chart, but its economic characteristics have not been known. We develop an economic model of the synthetic control chart, based on Duncan's model. The synthetic chart has one more decision variable, the lower control limit for the conforming run length. In addition to this, the significance level and the power of the synthetic chart are more complicated than those of the $\bar{X}$-chart. These features make the optimization problem more difficult. We propose an optimization algorithm by adapting the congruent gradient algorithm. We compare the optimal cost of the synthetic chart with that of (equation omitted)-control chart, under the same input parameter set of Duncan’s. For all cases investigated, the synthetic chart shows superior to the $\bar{X}$-chart. The synthetic control chart is easy to implement, and it has better characteristics than the $\bar{X}$-chart in economical sense as well as in statistical sense, so it will be a good alternative to the traditional control charts.

Keywords

References

  1. 김성인(1985), '통계적 품질관리-관리도' , 박문사
  2. 박성현, 박영현(1996), '통계적 품질관리' , 민영사
  3. 박창순(1995), '통계적 품질관리-SAS 응용과 함께', 율곡 출판사
  4. 류연선, 임오강, 박경진(1994), '최적 설계 입문', 반도 출판사
  5. Bazaraa, M. S., Sherali, H. D., Shetty,C. M.(1993), Nontinear Programming- Theory and Atgorithms, Wiley
  6. Bourke, P. D.(1991), 'Detecting a Shift in Fraction Nonconforming UsingRun- Length Control Charts with100% Inspection', JourrnI of QualityTechnology, Vol. 23, No. 3, pp.225-238
  7. Calzada, M. E. and Scariano, S.M.(2001), 'The Robustness of the Synthetic Control Chart to Non-Normality', Communicationsin Statistics-Simulation and Computation, Vol. 30, No. 2, pp.311-326 https://doi.org/10.1081/SAC-100002369
  8. Duncan, A. J.(1956), 'The EconomicDesign of X Charts used to Maintain Current Control of a Process', Journal ofthe Americon Statistical Association Vol. 51, pp. 228-242 https://doi.org/10.2307/2281343
  9. Goel, A. L., Jain, S. C. and Wu, S.M.(1968), 'An Algorithm for the Determination of the Economic Design ofX charts Based on the Duncan's Model', JournaI of American Statistical Association, Vol. 63, No. 321, pp.304-320 https://doi.org/10.2307/2283850
  10. Lasdon, L. S., Mitter, S. K. andWaren, A. D.(1967), 'The ConjugateGradient Method for Optimal ControlProblems', IEEE Trans. Automat.Contr., Vol. AC- 12, No. 2,pp.132-138 https://doi.org/10.1109/TAC.1967.1098538
  11. Lorenzen, T. J. and Vance, L.C.(1986), 'The Economic Design ofControl Chart : A Unified Approach', Technometrics Vol. 28, No. 1, pp.3-10 https://doi.org/10.2307/1269598
  12. Montgomery, D. C.(2001), Introduction to Statistical Quality Control, Wiley
  13. Wu, Z. and Spedding, T. A.(2000),'A Synthetic Control Chart for Detecting Small Shifts in the Process Mean', JournaI of Quality TechnoIogy, Vol. 32, No. 1, pp.32-38
  14. Wu, Z. and Spedding, T. A.(2000),'Implementing Synthetic Control Charts', JournaI of QuaIity TechnoIogy, Vol. 32, No. 1, pp.75-78
  15. Wu, Z., Yeo, S. H. and Spedding, T.A.(2001), 'A Synthetic Control Chartfor Detecting Fraction Nonconforming Increases', journal of QualityTechnology, Vol. 33, No. 1, pp.104-111
  16. Wu, Z., Yeo, S. H.(2001),'Implementing Synthetic ControlCharts for Attributes', Journal of Quality Technology, Vol. 33, No. 1,pp.112-114