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Statistical Design of VSS $\overline{A}$ Charts for Monitoring an AR(1) Process  

이재헌 (광주대학교 산업정보공학과)
Publication Information
Journal of Korean Society for Quality Management / v.31, no.3, 2003 , pp. 126-135 More about this Journal
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
AR(1) Model; Autocorrelation; Control Chart; Markov Chain; VSS;
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1 Prabhu, S. S., Runger, G. C., andKeats, J. B.(1993), 'An AdaptiveSample Size X Chart', InternationaIJournaI of Production Research, Vol.31, pp. 2895-2909   DOI   ScienceOn
2 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   DOI   ScienceOn
3 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
4 Zhang, N. F.(1998), 'A StatisticalControl Chart for Stationary ProcessData', Technometrics, Vol. 40, pp. 24-38   DOI   ScienceOn
5 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   DOI   ScienceOn
6 Jiang, W., Tsui, K. L., and Woodall,W. H.(2000), 'A New SPC MonitoringMethod: The ARMA Chart',Technometrics, Vol. 42, pp. 399-410   DOI   ScienceOn
7 Costa, A. F. B.(1994), ' X Chartswith Variable Sample Size', Journalof QuaIity Technology, Vol. 26, pp.155-163
8 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   DOI   ScienceOn
9 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   DOI   ScienceOn
10 Alwan, L. C. and Roberts, H.V.(1988), 'Time-Series Modeling forStatistical Process Control', Journalof Business and Economic Statistics,Vol. 6, pp. 87-95   DOI   ScienceOn
11 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
12 Vasilopoulos, A. V. and Stamboulis,A. P.(1978), 'Modification of ControlLimits in the Presence of DataCorrelation', JournaI of QuatityTechnology, Vol. 10, pp. 20-30