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Monitoring of Short Series of Dependent Observations Using a XWAM Control Chart

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Frontiers in Statistical Quality Control 12

Abstract

Many different control charts have been proposed during the last 30 years for monitoring processes with autocorrelated observations (measurements). The majority of them are developed for monitoring residuals, i.e., differences between the observed and predicted values of the monitored process. Unfortunately, statistical properties of these chart are very sensitive to the accuracy of the estimated model of the underlying process. In this chapter we consider the case when the information from the available data is not sufficient for good estimation of the model. Therefore, we use the concept of model weighted averaging in order to improve model prediction. The novelty of the proposed XWAM control chart consists in the usage of computational intelligence methodology for the construction of alternative models, and the calculation of their weights.

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References

  • Akaike, H. (1978). Time series analysis and control through parametric model. In D. F. Findley (ed.), Applied Time Series Analysis. New York: Academic Press

    Google Scholar 

  • Albers, W., & Kallenberg, C. M. (2004). Estimation in Shewhart control charts: Effects and corrections. Metrika, 59, 207–234.

    Article  MathSciNet  Google Scholar 

  • Alwan, L. C., & Roberts, H. V. (1988). Time-Series Modeling for statistical process control. Journal of Business & Economic Statistics, 6, 87–95.

    Google Scholar 

  • Apley, D. W., & Chin, C. (2007). An optimal filter design approach to statistical process control. Journal of Quality Technology, 39, 93–117.

    Article  Google Scholar 

  • Apley, D. W., & Lee, H. C. (2008). Robustness comparison of exponentially weighted moving-average charts on autocorrelated data and on residuals. Journal of Quality Technology, 40, 428–447.

    Article  Google Scholar 

  • Berndt, D. J., & Clifford, J. (1994). Using dynamic time warping to find patterns in time series. In AAAI-94 Workshop on Knowledge Discovery in Databases (pp. 359–370).

    Google Scholar 

  • Box, G. E. P., Jenkins, G. M., & MacGregor, J. F. (1974). Some recent advances in forecasting and control, part II. Journal of the Royal Statistical Society, Series C, 23, 158–179.

    Article  MathSciNet  Google Scholar 

  • Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2008). Time Series Analysis. Forecasting and Control (4th ed.). Hoboken, NJ: J.Wiley.

    Google Scholar 

  • Brockwell, P. J., & Davis, R. A. (2002). Introduction to Time Series and Forecasting (2nd ed.). New York: Springer.

    Google Scholar 

  • Chakraborti, S. (2000). Run length, average run length and false alarm length of Shewhart X-bar chart: Exact derivations by conditioning. Communications in Statistics – Simulations and Computations, 29, 61–81.

    Article  Google Scholar 

  • Chin, C.-H., & Apley, D. W. (2006). Optimal design of second-order linear filters for control charting. Technometrics, 48, 337–348.

    Article  MathSciNet  Google Scholar 

  • De Ketelaere, B., Hubert, M., & Schmitt, E. (2015). Overview of PCA-based statistical process-monitoring methods for time-dependent, high-dimensional data. Journal of Quality Technology,47, 318–335.

    Article  Google Scholar 

  • Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. Hoboken, NJ: J. Wiley

    Book  Google Scholar 

  • Hryniewicz, O., & Katarzyna Kaczmarek-Majer (2016a). Bayesian analysis of time series using granular computing approach. Applied Soft Computing Journal, 47, 644–652.

    Article  Google Scholar 

  • Hryniewicz, O., & Katarzyna Kaczmarek-Majer (2016b). Monitoring of short series of dependent observations using a control chart approach and data mining techniques. In Proceedings of the International Workshop ISQC 2016, Helmut Schmidt Universität, Hamburg (pp. 143–161).

    Google Scholar 

  • Jiang, W., Tsui, K., & Woodall, W. H. (2000). A new SPC monitoring method: The ARMA chart. Technometrics,42, 399–410.

    Article  Google Scholar 

  • Köksal, G., Kantar, B., Ula, T. A., & Testik, M. C. (2008). The effect of Phase I sample size on the run length performance of control charts for autocorrelated data. Journal of Applied Statistics, 35, 67–87.

    Article  MathSciNet  Google Scholar 

  • Kramer, H., & Schmid, W. (2000). The influence of parameter estimation on the ARL of Shewhart type charts for time series. Statistical Papers, 41, 173–196.

    Article  MathSciNet  Google Scholar 

  • Lu, C. W., & Reynolds, M. R. Jr. (1999). Control charts for monitoring the mean and variance of autocorrelated processes. Journal of Quality Technology, 31, 259–274.

    Article  Google Scholar 

  • Maragah, H. D., & Woodall, W. H. (1992). The effect of autocorrelation on the retrospective X-chart. Journal of Statistical Computation and Simulation, 40, 29–42.

    Article  Google Scholar 

  • Montgomery, D. C., & Mastrangelo, C. M. (1991). Some statistical process control methods for autocorrelated data (with discussion). Journal of Quality Technology, 23, 179–204.

    Article  Google Scholar 

  • Runger, G. C. (2002). Assignable causes and autocorrelation: Control charts for observations or residuals? Journal of Quality Technology, 34, 165–170.

    Article  Google Scholar 

  • Schmid, W. (1995). On the run length of Shewhart chart for correlated data. Statistical Papers, 36, 111–130.

    Article  MathSciNet  Google Scholar 

  • Vasilopoulos, A. V., & Stamboulis, A. P. (1978). Modification of control chart limits in the presence of data correlation. Journal of Quality Technology, 10, 20–30.

    Article  Google Scholar 

  • Wang, X., Mueen, A., Ding, H., Trajcevski, G., Scheuermann, P., & Keogh, E. (2013). Experimental comparison of representation methods and distance measures for time series data. Data Mining and Knowledge Discovery, 26, 275–309.

    Article  MathSciNet  Google Scholar 

  • Wardell, D. G., Moskowitz, H., & Plante, R. D. (1994). Run-length distributions of special-cause control charts for correlated processes (with disscussion). Technometrics, 36, 3–27.

    Article  MathSciNet  Google Scholar 

  • Yashchin, E. (1993). Performance of CUSUM control schemes for serially correlated observations. Technometrics, 35, 37–52.

    Article  MathSciNet  Google Scholar 

  • Zhang, N. F. (1997). Detection capability of residual chart for autocorrelated data. Journal of Applied Statistics, 24, 475–492.

    Article  MathSciNet  Google Scholar 

  • Zhang, N. F. (1998). A statistical control chart for stationary process data. Technometrics, 40, 24–38.

    Article  MathSciNet  Google Scholar 

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Correspondence to Olgierd Hryniewicz .

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Hryniewicz, O., Kaczmarek-Majer, K. (2018). Monitoring of Short Series of Dependent Observations Using a XWAM Control Chart. In: Knoth, S., Schmid, W. (eds) Frontiers in Statistical Quality Control 12. Frontiers in Statistical Quality Control. Springer, Cham. https://doi.org/10.1007/978-3-319-75295-2_13

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