@MASTERSTHESIS\{IMM2012-06350,
    author       = "R. Oduk",
    title        = "Control Charts for Serially Dependent Multivariate Data",
    year         = "2012",
    school       = "Technical University of Denmark, {DTU} Informatics, {E-}mail: reception@imm.dtu.dk",
    address      = "Asmussens Alle, Building 305, {DK-}2800 Kgs. Lyngby, Denmark",
    type         = "",
    note         = "Supervised by Associate Professor Murat Kulahci, mk@imm.dtu.dk, {DTU} Informatics.",
    url          = "http://www.imm.dtu.dk/English.aspx",
    abstract     = "In the literature, traditional univariate and multivariate control charts have been designed to monitor uncorrelated variables. However, in real life the data collected in time often show serial dependency. Since this serial dependency affects the false alarm rate and the shift detection capability, traditional control charts are effected. In this research we use the {X-}chart for univariate case and Hotelling {T-}square control chart for the multivariate case. The first objective is to measure the shift detection performance of proposed methods in the combination of different autocorrelation levels and various magnitudes of shifts in the process mean. For the univariate case proposed methods are to use {X-}chart based on raw data and based on residuals. For the multivariate case, using the Hotelling {T-}square control chart based on raw data, residuals and reconstructed data with lagged variables are the proposed methods. Raw data is generated based on the univariate first order autoregressive, {AR}(1), and bivariate first order vector autoregressive, {VAR}(1), structure. The residuals are considered as an output of perfectly modelled raw data. Reconstructed data is considered as expanded data with two lagged variables. The second objective is to take autocorrelation into account by adjusting the control limits to in control {ARL} using the Hotelling {T-}square control chart based on proposed methods for the multivariate case in the combination of different autocorrelation levels and various magnitudes of shifts in the process mean. Finally, the shift detection performances of the proposed methods are compared by using average run length as performance measure."
}