Title page for 984206027


[Back to Results | New Search]

Student Number 984206027
Author Jhe-hung Yeh(¸­­õ§»)
Author's Email Address who760214@hotmail.com
Statistics This thesis had been viewed 534 times. Download 298 times.
Department Graduate Institute of Industrial Management
Year 2010
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Applying Filter design Approach to Statistical Process Control for Lewis¡¦s ARMA Model
Date of Defense 2011-06-27
Page Count 29
Keyword
  • autocorrelation
  • EWMA control chart
  • Abstract In this study, we apply filter design to statistical process control (SPC) and discuss the impact of different process distributions. Instead of using conventional autoregressive moving-average processes, we assume Lewis¡¦s autoregressive moving-average (ARMA) processes as data processes. The control chart we used in this study is the exponentially weighted moving average (EWMA) control chart. We will apply linear filter on the observations generated from our data process to obtain our control chart statistic. With the control chart statistic, we can calculate the out-of-control ARL by Markov chain method. And our research objective is to reduce the out-of-control ARL with a predetermined in-control ARL. In the final, we adjust parameter and transform distribution to propose a relatively simple algorithm. Therefore, we can avoid complex and time-consuming calculation.
    Table of Content ¤¤¤åºK­nI
    AbstractII
    Table of ContentIII
    List of TablesIV
    List of FiguresV
    1. Introduction1
    1.1 Background and motivation1
    1.2 Research objective2
    1.3 Research framework3
    2. Literature review5
    2.1 Filter design5
    2.2 EWMA control chart6
    2.3 Time series7
    3. The model9
    3.1 Model description11
    3.2 Applying the filter design14
    3.3 Proposed algorithm16
    4. Numerical Analysis18
    4.1 Distribution comparison18
    4.2 Sensitive analysis21
    4.3 Normal approximation method23
    5. Conclusion and future research25
    5.1 Conclusion25
    5.2 Future research25
    References27
    Reference 1. Alwan, L. C. and Roberts, H. V.,(1988). ¡¨Time-Series Modeling for Statistical Process Control¡¨. Journal of Business & Economic Statistics, 6(1), 87-95.
    2. Apley, D. W. and Chin, C.,(2006). ¡§Optimal Design of Second-Order Linear Filters for Control charting¡¨. Technometrics 45(3), 337-348.
    3. Apley, D. W. and Chin, C.,(2007). ¡§An Optimal Filter Design Approach to Statistical Process Control¡¨. Journal of Quality Technology, 39(2), 93-117.
    4. Apley, D. W. and Shi, J.,(1999). ¡§GLRT for Statistical Process Control of
    Autocorrelated Processes¡¨. IIE Transactions, 31(12), 1123-1134.
    5. Borror, C. M., Montgomery, D. C., Runger, G. C.,(1999). ¡§Robustness of the EWMA control chart to non normality¡¨. J. Qual. Technol. 31:309-316.
    6. Box, G. E. P., M. E. Muller and G. M. Jenkins., (1976). ¡§Time series analysis
    forecasting and control¡¨, 2th ed. Holden Day: San Francisco.
    7. Box, G. E. P. and Ramírez, J., (1992). ¡§Cumulative Score Charts¡¨.Quality and
    Reliability Engineering International, 8(1), 1727.
    8. Box, G., Jenkins, G., and Reinsel, G.,(1994). ¡§Time Series Analysis, Forecasting,
    and Control¡¨, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall.
    9. Crowder, S. V.,(1987). ¡§A Simple Method for Studying Run Length Distributions of Exponentially Weighted Moving Average Control Charts¡¨, Technometrics,29 ,
    401-407.
    10. Crowder, S. V. and Hamilton, M.,(1992). ¡§An EWMA for Monitoring a Standard
    Deviation¡¨. Journal of Quality Technology, 24(1), 12-21.
    11. Granger, C. M. and A. P. Anderson.,(1978). ¡§An introduction to bilinear time series models¡¨. Vandenhoeck and Ruprecht: Gottingen.
    12. Hawkins, D. M. and Wixley, R. A. J., (1986), ¡§A Note on the Transformation
    of Chi-Squared Variables to Normality¡¨. The American Statistician, 40, 296-298.
    13. Jiang, W., Tsui, K., and Woodall, W. H.,(2000). ¡§A New SPC Monitoring Method:
    The ARMA Chart¡¨ .Technometrics, 42, 399-410.
    14. Johnson, R. A. and Bagshaw, M.,(1974). ¡§The Effect of Serial Correlation on the
    Performance of CUSUM Tests¡¨.Technometrics, 16(1), 103-112.
    15. J. Abate and W. Whitt.,( 1995). ¡§Numerical inversion of Laplace transforms of
    probability distributions¡¨, ORSA J. on Computing 7, 36¡V43.
    16. L. Shu and W. Jiang.,(2008). ¡§A new EWMA chart for monitoring process
    dispersion¡¨.Journal of Quality Technology 40 , 319-331.
    17. Lewis. P.A.W.,(1982). ¡§Simple multivariate time series for simulations of complex
    systems¡¨. Winter Simulation Conf., 389-390.
    18. Lu, C. W., and Reynolds, M. R.,(1999). ¡§EWMA Control Charts for Monitoring
     the Mean of Autocorrelated Processes¡¨ Journal of Quality Technology, 31,
    166-188.
    19. Machado, M.A.G., Costa, A.F.B.,(2008). ¡§The double sampling and the EWMA
    charts based on the sample variances¡¨. International Journal of Production
    Economics 114, 134-148.
    20. Maravelakis, P.E., Castagliola, P.,(2009). ¡§An EWMA chart for monitoring the
    processstandard deviation when parameters are estimated¡¨. Computational
    Statistics and Data Analysis 53, 2653-2664.
    21. Miller, R. B.,(1979). Book review on ¡§An introduction to bilinear time
    seriesmodels¡¨, by C. W. Granger and A. P. Anderson. J. Amer. Statist. Ass. 74, 927.
    22. Montgomery, D. C., and Mastrangelo, C. M.,(1991). ¡§Some Statistical Process
    Control Methods for Autocorrelated Data¡¨ Journal of Quality Technology, 23,
    179-193.
    23. Roberts, S. W.,(1959). ¡§Control Chart Tests Based on Geometric Moving Averages¡¨ Technometrics1, 239-250.
    24. Robinson, P. B., and Ho, T. Y.,(1978). ¡§Average Run Lengths of Geometric Moving Average Charts by Numerical Methods¡¨ Technometrics, 20, 85-93.
    25. Stoumbos, Z. G., Reynolds, M. R. Jr.,(2000). ¡§Robustness to non normality and
    autocorrelation of individual control charts¡¨. J. Statist. Computat. Simul. 66:145-187.
    26. Stoumbos, Z. G., Sullivan, J. H.,(2002). ¡§Robustness to non normality of the
    multivariate EWMA control chart¡¨. J. Qual. Technol. 34:260-276.
    27. Vermaat, M.B., Does, R.J.M.M., Bisgaard, S.,(2008). ¡§EWMA control chart limits for first- and second-order autoregressive processes¡¨. Quality and Reliability Engineering International 24, 573-584.
    28. Wilson, E. B., and Hilferty, M. M., (1931), ¡§The Distribution of Chi-Squares,¡¨
    Proceedings of the National Academy of Sciences, 17, 684-688.
    29. Yakowitz, S.,(1979a). ¡§A nonparametric Markov model for daily river flow¡¨. Water Resources Research, 15, 1035-1043.
    30. Yakowitz, S.,(1979b). ¡§Nonparametric estimation of Markov transition functions¡¨.
    Ann. Statist.7, 671-679.
    31. Zhang, N. F.,(1998). ¡§A Statistical Control Chart for Stationary Process Data¡¨.
    Technometrics, 40(1), 24-38.
    Advisor
  • Ying-chieh Yeh(¸­­^³Ç)
  • Files
  • 984206027.pdf
  • approve immediately
    Date of Submission 2011-07-18

    [Back to Results | New Search]


    Browse | Search All Available ETDs

    If you have dissertation-related questions, please contact with the NCU library extension service section.
    Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.