Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지

A VSR $\bar{X}$ Chart with Multi-state VSS and 2-state VSI Scheme

  • Published : 2004.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Variable sampling Interval (VSI) control charts vary the sampling interval according to value of the control statistic while the sample size is fixed. It is known that control charts with 2-state VSI scheme, which uses only two sampling intervals, give good statistical properties. Variable sample size (VSS) control charts vary the sample size according to value of the control statistic while the sampling interval is fixed. In the VSS scheme no optimal results are known for the number of sample sizes. It is also known that the variable sampling rate (VSR) $\bar{X}$ control chart with 2-state VSS and 2-state VSI scheme leads to large improvements In performance over the fixed sampling rate (FSR) $\bar{X}$ chart, but the optimal number of states for sample size Is not known. In this paper, the VSR Χ charts with multi-state VSS and 2-state VSI scheme are designed and compared to 2-state VSS and 2-state VSI scheme. The multi-state VSS scheme is considered to, achieve an additional improvement by switching from the 2-state VSS scheme. On the other hand, the multi-state VSI scheme is not considered because the 2-state scheme is known to be optimal. The 3-state VSS scheme improves substantially the sensitivity of the $\bar{X}$ chart especially for small and moderate mean shifts.

Keywords

References

  1. Costa, A. F. B. (1997), ' Charts with Variable Sample Sizes and Sampling Interval', Journal of Quality Technology, Vol. 29, pp. 197-204 https://doi.org/10.1080/00224065.1997.11979750
  2. Park, C. and Reynolds, M. R., Jr. (1999), 'Economic Design of a Variable Sampling Rate Chart', Journal of Quality Technology, Vol. 31, pp. 427-443 https://doi.org/10.1080/00224065.1999.11979949
  3. Prabhu, S. S., Montgomery, D. C., and Runger, G. C. (1994), 'A Combined Adaptive Sample Size and Sampling Interval Control Scheme', Journal of Quality Technology, Vol. 26, pp. 164-176 https://doi.org/10.1080/00224065.1994.11979524
  4. Reynolds, M. R., Jr. and Arnold, J. C. (1989), 'Optimal Shewhart Control Charts with Variable Sampling Intervals between Samples', Sequential Analysis, Vol. 8, pp. 51-77 https://doi.org/10.1080/07474948908836167
  5. Reynolds, M. R., Jr. and Arnold, J. C. (2001), 'EWMA Control Charts with Variable Sample Sizes and Variable Sampling Intervals', IIE Transactions, Vol. 33, pp. 511-530
  6. Runger, G. C. and Montgomery, D. C. (1993), 'Adaptive Sampling Enhance- ments for Shewhart Control Charts', IIE Transactions, Vol. 25, pp. 41-51 https://doi.org/10.1080/07408179308964289
  7. Zimmer, L. S., Montgomery, D. C., and Runger, G. C. (1998), 'Evaluation of a Three-state Adaptive Sample Size Control Chart', International Journal of Production Research, Vol. 36, pp. 733-743 https://doi.org/10.1080/002075498193660