Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지
DOI QR코드

DOI QR Code

Economic-Statistical Design of Double Sampling T2 Control Chart under Weibull Failure Model

와이블 고장모형 하에서의 이중샘플링 T2 관리도의 경제적-통계적 설계 (이중샘플링 T2 관리도의 경제적-통계적 설계)

  • Hong, Seong-Ok (General Services Division, Statistics Korea) ;
  • Lee, Min-Koo (Department of Information & Statistics, Chungnam National University) ;
  • Lee, Jooho (Department of Information & Statistics, Chungnam National University)
  • 홍성옥 (통계청 운영지원과) ;
  • 이민구 (충남대학교 정보통계학과) ;
  • 이주호 (충남대학교 정보통계학과)
  • Received : 2015.05.15
  • Accepted : 2015.10.23
  • Published : 2015.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Purpose: Double sampling $T^2$ chart is a useful tool for detecting a relatively small shift in process mean when the process is controlled by multiple variables. This paper finds the optimal design of the double sampling $T^2$ chart in both economical and statistical sense under Weibull failure model. Methods: The expected cost function is mathematically derived using recursive equation approach. The optimal designs are found using a genetic algorithm for numerical examples and compared to those of single sampling $T^2$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling $T^2$ chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling $T^2$ chart can be designed to satisfy both economic and statistical requirements under Weibull failure model and the resulting design is better than the single sampling counterpart.

Keywords

Acknowledgement

Supported by : 충남대학교

References

  1. Banerjee, P. K., and Rahim, M. A. 1988. "Economic design of $\overline{X}$ control charts under Weibull shock models." Technometrics 30(4):407-414.
  2. Champ, C. W., and Aparisi, F. 2008. "Double sampling Hotelling's $T^2$ charts." Quality and Reliability Engineering International 24:153-166. https://doi.org/10.1002/qre.872
  3. Croasdale, R. 1974. "Control charts for a double-sampling scheme based on average production run lengths." International Journal of Production Research 12(5):585-592. https://doi.org/10.1080/00207547408919577
  4. Daudin, J. J. 1992. "Double sampling $\overline{X}$ charts." Journal of Quality Technology 24(2):78-87. https://doi.org/10.1080/00224065.1992.12015231
  5. Duncan, A. J. 1956. "The Economic Design of $\overline{X}$ Charts used to Maintain Current Control of a Process." Journal of the American Statistical Association 51:228-242.
  6. Ho, C., and Case, K. E. 1994. "Economic Design of Control Charts: A Literature Review for 1981-1991." Journal of Quality Technology 26(1):39-53. https://doi.org/10.1080/00224065.1994.11979497
  7. Hu, P. W. 1984. "Economic Design of $\overline{X}$-Control Chart Under Non-Poisson Process Shift." Abstract, TIMS/ORSA Joint National Meeting, San Francisco:87.
  8. Montgomery, D. C. 1980. "The economic design of control charts: A review and literature survey." Journal of Quality Technology 12(2):75-87. https://doi.org/10.1080/00224065.1980.11980940
  9. Montgomery, D. C. 2004. Introduction to Statistical Quality Control. 5th Edition. New York: Wiley.
  10. Rahim, M. A. 1993. "A Generalized Model for the Economic Design of $\overline{X}$ Control Charts for Production Systems with Increasing Failure Rate and Early Replacement." Naval Research Logistics 40(6):787-809. https://doi.org/10.1002/1520-6750(199310)40:6<787::AID-NAV3220400605>3.0.CO;2-4
  11. Ross, S. M. 1983. Stochastic Processes. New York: Wiley.
  12. Saniga, E. M. 1989. "Economic Statistical Control-Chart Designs with an Application to $\overline{X}$ and R Charts." American Society for Quality 31(3):313-320.
  13. Seo, O.-E. 2013. "Economic-statistical design of double sampling $\overline{X}$ control chart under Weibull shock model." Ph.D. thesis, Chungnam National University.
  14. Torng, C.-C., Lee, P.-H., and Liao, N.-Y. 2009. "An economic-statistical design of double sampling $\overline{X}$ control chart." International Journal of Production Economics 120(2):495-500. https://doi.org/10.1016/j.ijpe.2009.03.013
  15. Yang, S. F., and Rahim, M. A. 2006. "Multivariate extension to the economic design of $\overline{X}$ control chart under Weibull shock model." Journal of Statistical Computation and Simulation 76(12):1035-1047. https://doi.org/10.1080/10629360600569188

Cited by

  1. Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling pp.15241904, 2018, https://doi.org/10.1002/asmb.2419