Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Statistical Design of VSS $\overline{A}$ Charts for Monitoring an AR(1) Process

AR(l) 공정을 탐지하는 VSS $\overline{A}$ 관리도의 통계적 설계

  • 이재헌 (광주대학교 산업정보공학과)
  • Published : 2003.09.01
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Abstract

A basic assumption in standard applications of control charts is that the observations are statistically independent. However, this assumption is often violated from processes in many industries. The presence of autocorrelation has a serious impact on the performance of control charts, causing a dramatic increase in the frequency of false alarms. This paper considers a process in which the observations can be modeled as a first order autoregressive(AR(1)) process, and develops (equation omitted) charts with the variable sample size(VSS) scheme for monitoring the mean of this process.

Keywords

References

  1. Alwan, L. C. and Roberts, H.V.(1988), 'Time-Series Modeling forStatistical Process Control', Journalof Business and Economic Statistics,Vol. 6, pp. 87-95 https://doi.org/10.2307/1391421
  2. Costa, A. F. B.(1994), ' X Chartswith Variable Sample Size', Journalof QuaIity Technology, Vol. 26, pp.155-163
  3. Jiang, W., Tsui, K. L., and Woodall,W. H.(2000), 'A New SPC MonitoringMethod: The ARMA Chart',Technometrics, Vol. 42, pp. 399-410 https://doi.org/10.2307/1270950
  4. Lasdon, L. S., Waren, A. D., Jain, A.,and Ranter, M.(1978), 'Design andTesting of Generalized ReducedGradient Code for Nonlinear Programming', ACM Transactions onMathematical Software, Vol. 4, pp.34-50 https://doi.org/10.1145/355769.355773
  5. Lu, C. W. and Reynolds, M. R.,Jr.(1999), 'EWMA Control Charts forMonitoring the Mean ofAutocorrelated Processes', Journal ofQuaIity Technology, Vol. 31, pp.166-188
  6. Park, C. and Reynolds, M. R.,Jr.(1994), 'Economic Design of aVariable Sample Size X-Charts',Communications in Statistics:SimuIation and Computation, Vol. 23,pp. 467-483 https://doi.org/10.1080/03610919408813182
  7. Prabhu, S. S., Runger, G. C., andKeats, J. B.(1993), 'An AdaptiveSample Size X Chart', InternationaIJournaI of Production Research, Vol.31, pp. 2895-2909 https://doi.org/10.1080/00207549308956906
  8. Reynolds, M. R., Jr., Arnold, J. C.,and Baik, J. W.(1996), 'VariableSampling Interval X Charts in the Presence of Correlation', Journal ofQuality Technology, Vol. 28, pp.12-30
  9. VanBrackle, L. N. and Reynolds, M.R., Jr.(1997), 'EWMA and CUSUMControl Charts in the Presence ofCorrelation', Communications inStatistics : SimuIation andComputation, Vol. 26, pp. 979-1008 https://doi.org/10.1080/03610919708813421
  10. Vasilopoulos, A. V. and Stamboulis,A. P.(1978), 'Modification of ControlLimits in the Presence of DataCorrelation', JournaI of QuatityTechnology, Vol. 10, pp. 20-30
  11. Zhang, N. F.(1998), 'A StatisticalControl Chart for Stationary ProcessData', Technometrics, Vol. 40, pp. 24-38 https://doi.org/10.2307/1271390
  12. Zimmer, L. S., Montgomery, D. C.,and Runger, G. C.(1998), 'Evaluationof a Three-State Adaptive SampleSize X Control Chart', InternationalJournaI of Production Research, Vol.36, pp. 733-743 https://doi.org/10.1080/002075498193660