Design of Combined Shewhart-CUSUM Control Chart using Bootstrap Method

Bootstrap 방법을 이용한 결합 Shewhart-CUSUM 관리도의 설계

  • 송서일 (동아대학교 산업시스템공학과) ;
  • 조영찬 (동아대학교 산업시스템공학과) ;
  • 박현규 (동아대학교 산업시스템공학과)
  • Published : 2002.08.01

Abstract

Statistical process control is used widely as an effective tool to solve the quality problems in practice fields. All the control charts used in statistical process control are parametric methods, suppose that the process distributes normal and observations are independent. But these assumptions, practically, are often violated if the test of normality of the observations is rejected and/or the serial correlation is existed within observed data. Thus, in this study, to screening process, the Combined Shewhart - CUSUM quality control chart is described and evaluated that used bootstrap method. In this scheme the CUSUM chart will quickly detect small shifts form the goal while the addition of Shewhart limits increases the speed of detecting large shifts. Therefor, the CSC control chart is detected both small and large shifts in process, and the simulation results for its performance are exhibited. The bootstrap CSC control chart proposed in this paper is superior to the standard method for both normal and skewed distribution, and brings in terms of ARL to the same result.

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References

  1. Bajgier, S. M.; 'The Use of Bootstrapping to Construct Limits on Control Charts,' Proceeding of the Decision Science Institute, San Diego, CA., pp. 1611-1613, 1992
  2. Efron, B.; 'Bootstrap Methods : Another Look at Jacknife,' Ann. Stat. Vol. 7, No. 1, pp. 1-26, 1979 https://doi.org/10.1214/aos/1176344552
  3. Liu, R. Y. and Tang, J.; 'Control Charts for Dependent and Indepent Measurements Based on Bootstrap,' Journal of the American Statistical Association, Vol. 91, No. 436, pp. 1694-1700, 1996 https://doi.org/10.2307/2291598
  4. Lucas, J. M.; 'A Modified V-Mask Control Schemes,' Journal of Quality Technology, Vol. 8, No. 1, pp. 1-12, 1973
  5. Lucas, J. M.; 'Combined Shewhart-CUSUM Quality Control Schemes,' Journal of Quality Technology, Vol. 14, No. 2, pp. 51-59, 1982
  6. Lucas, J. M., and Crosier, R. B.; 'Fast Initial Response for CUSUM Quality Control Schemes : Give Your CUSUM a Head Start,' Technometrics, Vol. 24, No. 3, pp. 199-205, 1982 https://doi.org/10.2307/1268679
  7. Padgett, C. S., Thomas, L.A., and Padgett, W.J.; 'On the -risks for Shewhart Control Charts,' Communications in Statistics and Simulation, Vol. 21, No. 4, pp. 1125-1147, 1992 https://doi.org/10.1080/03610919208813068
  8. Seppala, T., Moskowitz, H., Plante, R. 와Tang, J.; 'Statistical Process Control via the Subgroup,' Journal of Quality Technology, Vol. 27, No. 2, pp. 139-153, 1995