A Multivariate CUSUM Chart Handling Auto- and Cross-correlated Observations
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Published
Jul 14, 2017
Kyu Young Lee
Chuljin Park
Mi Lim Lee
Abstract
Multivariate CUSUM charts have been widely used as statistical-process-control tools to detect out-of-control states of monitoring variables. Most of earlier studies regarding multivariate CUSUM charts assume that observations of monitoring variables are independent or correlated with a limited structure. In this paper, we suggest a multivariate CUSUM chart that can handle the observations auto- and cross-correlated. The chart estimates its control limit
analytically and captures small mean shifts faster when compared to existing charts.
##plugins.themes.bootstrap3.article.details##
Keywords
PHM
References
Arkat, J., Niaki, S. T. A., & Abbasi, B. (2007). Artificial neural networks in applying MCUSUM residuals charts for AR (1) processes. Applied Mathematics and Computation, 189(2), 1889-1901.
Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.
Healy, J. D. (1987). A note on multivariate CUSUM procedures. Technometrics, 29(4), 409-412.
Issam, B. K., & Mohamed, L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process. Applied mathematics and computation, 201(1), 565-574.
Jiang, W., Han, S. W., Tsui, K. L., & Woodall, W. H. (2011). Spatiotemporal surveillance methods in the presence of spatial correlation. Statistics in Medicine, 30(5), 569-583.
Kalgonda, A. A., & Kulkarni, S. R. (2004). Multivariate quality control chart for autocorrelated processes. Journal of Applied Statistics, 31(3), 317-327.
Kim, S. B., Jitpitaklert, W., Park, S. K., & Hwang, S. J. (2012). Data mining model-based control charts for multivariate and autocorrelated processes. Expert Systems with Applications, 39(2), 2073-2081.
Lee, M. L., Goldsman, D., Kim, S. H., & Tsui, K. L. (2014). Spatiotemporal biosurveillance with spatial clusters: control limit approximation and impact of spatial correlation. IIE Transactions, 46(8), 813-827.
Loredo, E. N., Jearkpaporn, D., & Borror, C. M. (2002). Model‐based control chart for autoregressive and correlated data. Quality and Reliability Engineering International, 18(6), 489-496.
Noorossana, R., & Vaghefi, S. J. M. (2006). Effect of autocorrelation on performance of the MCUSUM control chart. Quality and Reliability Engineering International, 22(2), 191-197.
Pignatiello, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of quality technology, 22(3), 173-186.
Rogerson, P. A., & Yamada, I. (2004). Monitoring change in spatial patterns of disease: comparing univariate and multivariate cumulative sum approaches. Statistics in Medicine, 23(14), 2195-2214.
Woodall, W. H., & Ncube, M. M. (1985). Multivariate CUSUM quality-control procedures. Technometrics, 27(3), 285-292
Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.
Healy, J. D. (1987). A note on multivariate CUSUM procedures. Technometrics, 29(4), 409-412.
Issam, B. K., & Mohamed, L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process. Applied mathematics and computation, 201(1), 565-574.
Jiang, W., Han, S. W., Tsui, K. L., & Woodall, W. H. (2011). Spatiotemporal surveillance methods in the presence of spatial correlation. Statistics in Medicine, 30(5), 569-583.
Kalgonda, A. A., & Kulkarni, S. R. (2004). Multivariate quality control chart for autocorrelated processes. Journal of Applied Statistics, 31(3), 317-327.
Kim, S. B., Jitpitaklert, W., Park, S. K., & Hwang, S. J. (2012). Data mining model-based control charts for multivariate and autocorrelated processes. Expert Systems with Applications, 39(2), 2073-2081.
Lee, M. L., Goldsman, D., Kim, S. H., & Tsui, K. L. (2014). Spatiotemporal biosurveillance with spatial clusters: control limit approximation and impact of spatial correlation. IIE Transactions, 46(8), 813-827.
Loredo, E. N., Jearkpaporn, D., & Borror, C. M. (2002). Model‐based control chart for autoregressive and correlated data. Quality and Reliability Engineering International, 18(6), 489-496.
Noorossana, R., & Vaghefi, S. J. M. (2006). Effect of autocorrelation on performance of the MCUSUM control chart. Quality and Reliability Engineering International, 22(2), 191-197.
Pignatiello, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of quality technology, 22(3), 173-186.
Rogerson, P. A., & Yamada, I. (2004). Monitoring change in spatial patterns of disease: comparing univariate and multivariate cumulative sum approaches. Statistics in Medicine, 23(14), 2195-2214.
Woodall, W. H., & Ncube, M. M. (1985). Multivariate CUSUM quality-control procedures. Technometrics, 27(3), 285-292
Section
Regular Session Papers