Advanced SearchSearch Tips
Economic-Statistical Design of Double Sampling T2 Control Chart under Weibull Failure Model
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Economic-Statistical Design of Double Sampling T2 Control Chart under Weibull Failure Model
Hong, Seong-Ok; Lee, Min-Koo; Lee, Jooho;
  PDF(new window)
Purpose: Double sampling 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 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 chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling 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.
Control Chart;Double Sampling;Weibull Failure Model;Economic-Statistical Design;
 Cited by
Banerjee, P. K., and Rahim, M. A. 1988. "Economic design of $\overline{X}$ control charts under Weibull shock models." Technometrics 30(4):407-414.

Champ, C. W., and Aparisi, F. 2008. "Double sampling Hotelling's $T^2$ charts." Quality and Reliability Engineering International 24:153-166. crossref(new window)

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. crossref(new window)

Daudin, J. J. 1992. "Double sampling $\overline{X}$ charts." Journal of Quality Technology 24(2):78-87.

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.

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.

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.

Montgomery, D. C. 1980. "The economic design of control charts: A review and literature survey." Journal of Quality Technology 12(2):75-87.

Montgomery, D. C. 2004. Introduction to Statistical Quality Control. 5th Edition. New York: Wiley.

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. crossref(new window)

Ross, S. M. 1983. Stochastic Processes. New York: Wiley.

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.

Seo, O.-E. 2013. "Economic-statistical design of double sampling $\overline{X}$ control chart under Weibull shock model." Ph.D. thesis, Chungnam National University.

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. crossref(new window)

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. crossref(new window)