Design of a Curtailed-SPRT Control Chart

단축-축차관리도의 설계

  • Published : 2009.03.31

Abstract

This paper proposes a curtailed-sequential probability ratio test (SPRT) control chart. For using the conventional SPRT control chart, the number of items inspected in a sampling point should have no restriction since items in a sampling point are inspected one by one until an SPRT Is terminated. The number of observations taken in a sampling point, however, has an upper bound since sampling and testing of an item is time-consuming or expensive. When the sample size reaches the upper bound without evidence of an in-control or out-of-control state of a process, the proposed chart makes a decision using the sample mean of all observations taken in a sampling point. The properties of the Proposed chart are obtained by a Markov chain approach and the performance of the chart is compared with fixed sample size (FSS) and variable sample size (VSS) control charts. A comparative study shows that the proposed chart performs better than VSS control charts as well as conventional FSS control charts.

Keywords

References

  1. Brook, D. and D.A. Evans, 'An Approach to the Probability Distribution of CUSUM Run Length,' Biometrika, Vol.59, No.3(1972), pp.539-549 https://doi.org/10.1093/biomet/59.3.539
  2. Chang, Y.S. and D.S. Bai, 'Cumulative Se-quential Control Charts with Sample Size Bound,' Journal of the Korean Institute of Industrial Engineering, Vol.25, No.4(1999), pp.448-458
  3. Costa, AF.B., '\overline{\text{X}}Chart with Variable SampIe Size,' Journal of Quality Technology, Vol.26, No.3(1994), pp.155-163 https://doi.org/10.1080/00224065.1994.11979523
  4. IMSL Library, Reference Manual, Visual Numerics, Inc., Houston, TX, 1990
  5. Reynolds, M.R and K. Kim, 'Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential SampIing,' Sequential Analysis, Vol.26, No.3 (2007), pp.253-315
  6. Reynolds, M.R. and Z.G. Stoumbos, 'The SPRT Chart for Monitoring a Proportion,' lIE Transactions, Vol.30, No.6(1998), pp.545-561 https://doi.org/10.1023/A:1007515911714
  7. Reynolds, M.R, RW. Amin, lC. Arnold, and lA Nachlas, '\overline{\text{X}}Chart with Variable Sampling Intervals,' Technometrics, Vol.30, No.2(1988), pp.181-192 https://doi.org/10.2307/1270164
  8. Runger, G.C. and D.C. Montgomery, 'Adaptive Sampling Enhancements for Shewhart Control Charts,' lIE Transactions, Vol.25, No.3(1993), pp.41 -51
  9. Stoumbos, Z.G. and M.R. Reynolds, 'Control Charts Applying a Sequential Test at Fixed Sampling Intervals, 'Journal of Quality Technology, Vol.29, No.1 (1997), pp.21 -29 https://doi.org/10.1080/00224065.1997.11979722
  10. Stoumbos, Z.G. and M.R Reynolds, 'The SPRT Control Charts for the Process Mean with Samples Starting at Fixed Times,' Nonlinear Analysis: Real World Applications, Vol.2, No.1 (2001), pp.1-34 https://doi.org/10.1016/S0362-546X(99)00286-2
  11. Tagaras, G., 'A Survey of Recent Developments in the Design of Adaptive Control Charts,' Journal of Quality Technology, Vol.30, No.3(1998), pp.212-231 https://doi.org/10.1080/00224065.1998.11979850
  12. Wald, A., Sequential Analysis, Dover Publications, Inc., New York, 1947
  13. Zimmer, L.S., D.C. Montgomery, G.C. Runger, 'Guidelines for the Applications of Adaptive Control Charting Schemes,' International Journal of Production Research, Vol.38, No.9(2000), pp.1977-1992 https://doi.org/10.1080/002075400188447