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  "Title": "Functional Control Charts",
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  "Authors@R": "c(\nperson(\"Christian\", \"Capezza\",\nemail = \"christian.capezza@unina.it\",\nrole = c(\"cre\",\"aut\")),\nperson(\"Fabio\", \"Centofanti\", role = c(\"aut\")),\nperson(\"Davide\", \"Forcina\", role = c(\"aut\")),\nperson(\"Antonio\", \"Lepore\", role = c(\"aut\")),\nperson(\"Biagio\", \"Palumbo\", role = c(\"aut\")),\nperson(\"Alessandra\", \"Menafoglio\", role = c(\"ctb\")),\nperson(\"Simone\", \"Vantini\", role = c(\"ctb\"))\n)",
  "Description": "Provides functional control charts for statistical process\nmonitoring of functional data, using the methods of Capezza et\nal. (2020) <doi:10.1002/asmb.2507>, Centofanti et al. (2021)\n<doi:10.1080/00401706.2020.1753581>, Capezza et al. (2024)\n<doi:10.1080/00224065.2024.2383674>, Capezza et al. (2024)\n<doi:10.1080/00401706.2024.2327346>, Centofanti et al. (2025)\n<doi:10.1080/00224065.2024.2430978>, Capezza et al. (2025)\n<doi:10.48550/arXiv.2410.20138>. The package is thoroughly\nillustrated in the paper of Capezza et al (2023)\n<doi:10.1080/00224065.2023.2219012>.",
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  "Author": "Christian Capezza [cre, aut], Fabio Centofanti [aut], Davide\nForcina [aut], Antonio Lepore [aut], Biagio Palumbo [aut],\nAlessandra Menafoglio [ctb], Simone Vantini [ctb]",
  "Maintainer": "Christian Capezza <christian.capezza@unina.it>",
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    "FMRCC_PhaseII",
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    "fof_pc_real_time",
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    "get_mfd_array_real_time",
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    "get_mfd_list",
    "get_mfd_list_real_time",
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    "get_outliers_mfd",
    "get_sof_pc_outliers",
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    "inprod_mfd_diag",
    "is.mfd",
    "lines_mfd",
    "mfd",
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    "minus_mfd",
    "nbasis",
    "norm.mfd",
    "nvar",
    "OEBFDTW",
    "par.FDTW",
    "par.mFPCA",
    "par.rtr",
    "pca_mfd",
    "pca_mfd_real_time",
    "plot_bifd",
    "plot_bootstrap_sof_pc",
    "plot_control_charts",
    "plot_control_charts_real_time",
    "plot_mfd",
    "plot_mon",
    "plot_pca_mfd",
    "plus_mfd",
    "predict_fof_pc",
    "predict_sof_pc",
    "rbind_mfd",
    "regr_cc_fof",
    "regr_cc_fof_real_time",
    "regr_cc_sof",
    "regr_cc_sof_real_time",
    "RoMFCC_PhaseI",
    "RoMFCC_PhaseII",
    "RoMFDI",
    "rpca_mfd",
    "scale_mfd",
    "sim_funcharts",
    "simulate_data_fmrcc",
    "simulate_data_FRTM",
    "simulate_data_RoMFCC",
    "simulate_mfd",
    "sof_pc",
    "sof_pc_real_time",
    "tensor_product_mfd",
    "times_mfd",
    "which_ooc"
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  "_datasets": [
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      "title": "Air quality data",
      "object": "air",
      "class": [
        "list"
      ],
      "fields": [],
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
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      "page": "sub-.mfd",
      "title": "Extract observations and/or variables from 'mfd' objects.",
      "topics": [
        "[.mfd"
      ]
    },
    {
      "page": "abline_mfd",
      "title": "Add reference lines to all panels of the current multi-panel plot",
      "topics": [
        "abline_mfd"
      ]
    },
    {
      "page": "air",
      "title": "Air quality data",
      "topics": [
        "air"
      ]
    },
    {
      "page": "AMFCC_PhaseI",
      "title": "Phase I of the Adaptive Multivariate Functional Control Chart (AMFCC).",
      "topics": [
        "AMFCC_PhaseI"
      ]
    },
    {
      "page": "AMFCC_PhaseII",
      "title": "Phase II of the Adaptive Multivariate Functional Control Chart (AMFCC).",
      "topics": [
        "AMFCC_PhaseII"
      ]
    },
    {
      "page": "AMFEWMA_PhaseI",
      "title": "Adaptive Multivariate Functional EWMA control chart - Phase I",
      "topics": [
        "AMFEWMA_PhaseI"
      ]
    },
    {
      "page": "AMFEWMA_PhaseII",
      "title": "Adaptive Multivariate Functional EWMA control chart - Phase II",
      "topics": [
        "AMFEWMA_PhaseII"
      ]
    },
    {
      "page": "cbind_mfd",
      "title": "Bind variables of two Multivariate Functional Data Objects",
      "topics": [
        "cbind_mfd"
      ]
    },
    {
      "page": "cont_plot",
      "title": "Produce contribution plots",
      "topics": [
        "cont_plot"
      ]
    },
    {
      "page": "control_charts_pca",
      "title": "T2 and SPE control charts for multivariate functional data",
      "topics": [
        "control_charts_pca"
      ]
    },
    {
      "page": "control_charts_pca_mfd_real_time",
      "title": "Real-time T2 and SPE control charts for multivariate functional data",
      "topics": [
        "control_charts_pca_mfd_real_time"
      ]
    },
    {
      "page": "control_charts_sof_pc",
      "title": "Control charts for monitoring a scalar quality characteristic adjusted for by the effect of multivariate functional covariates",
      "topics": [
        "control_charts_sof_pc"
      ]
    },
    {
      "page": "control_charts_sof_pc_real_time",
      "title": "Real-time scalar-on-function regression control charts",
      "topics": [
        "control_charts_sof_pc_real_time"
      ]
    },
    {
      "page": "cor_mfd",
      "title": "Correlation Function for Multivariate Functional Data",
      "topics": [
        "cor_mfd"
      ]
    },
    {
      "page": "cov_mfd",
      "title": "Covariance Function for Multivariate Functional Data",
      "topics": [
        "cov_mfd"
      ]
    },
    {
      "page": "data_sim_mfd",
      "title": "Simulate multivariate functional data",
      "topics": [
        "data_sim_mfd"
      ]
    },
    {
      "page": "estimate_mixture",
      "title": "Performs the estimation of gaussian mixtures of regression models and gaussian mixture models. Used in FMRCC_PhaseI.",
      "topics": [
        "estimate_mixture"
      ]
    },
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      "title": "Phase I of the FMRCC",
      "topics": [
        "FMRCC_PhaseI"
      ]
    },
    {
      "page": "FMRCC_PhaseII",
      "title": "Phase II of the FMRCC",
      "topics": [
        "FMRCC_PhaseII"
      ]
    },
    {
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      "title": "Function-on-function linear regression based on principal components",
      "topics": [
        "fof_pc"
      ]
    },
    {
      "page": "fof_pc_real_time",
      "title": "Get a list of function-on-function linear regression models estimated on functional data each evolving up to an intermediate domain point.",
      "topics": [
        "fof_pc_real_time"
      ]
    },
    {
      "page": "FRTM_PhaseI",
      "title": "Phase I of the FRTM method.",
      "topics": [
        "FRTM_PhaseI"
      ]
    },
    {
      "page": "FRTM_PhaseII",
      "title": "Phase II of the FRTM method.",
      "topics": [
        "FRTM_PhaseII"
      ]
    },
    {
      "page": "functional_filter",
      "title": "Finds functional componentwise outliers",
      "topics": [
        "functional_filter"
      ]
    },
    {
      "page": "get_mfd_array",
      "title": "Get Multivariate Functional Data from a three-dimensional array",
      "topics": [
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      ]
    },
    {
      "page": "get_mfd_array_real_time",
      "title": "Get a list of functional data objects each evolving up to an intermediate domain point.",
      "topics": [
        "get_mfd_array_real_time"
      ]
    },
    {
      "page": "get_mfd_df",
      "title": "Get Multivariate Functional Data from a data frame",
      "topics": [
        "get_mfd_df"
      ]
    },
    {
      "page": "get_mfd_df_real_time",
      "title": "Get a list of functional data objects each evolving up to an intermediate domain point.",
      "topics": [
        "get_mfd_df_real_time"
      ]
    },
    {
      "page": "get_mfd_fd",
      "title": "Convert a 'fd' object into a Multivariate Functional Data object.",
      "topics": [
        "get_mfd_fd"
      ]
    },
    {
      "page": "get_mfd_list",
      "title": "Get Multivariate Functional Data from a list of matrices",
      "topics": [
        "get_mfd_list"
      ]
    },
    {
      "page": "get_mfd_list_real_time",
      "title": "Get a list of functional data objects each evolving up to an intermediate domain point.",
      "topics": [
        "get_mfd_list_real_time"
      ]
    },
    {
      "page": "get_ooc",
      "title": "Get out of control observations from control charts",
      "topics": [
        "get_ooc"
      ]
    },
    {
      "page": "get_outliers_mfd",
      "title": "Get outliers from multivariate functional data",
      "topics": [
        "get_outliers_mfd"
      ]
    },
    {
      "page": "get_sof_pc_outliers",
      "title": "Get possible outliers of a training data set of a scalar-on-function regression model.",
      "topics": [
        "get_sof_pc_outliers"
      ]
    },
    {
      "page": "inprod_mfd",
      "title": "Inner products of functional data contained in 'mfd' objects.",
      "topics": [
        "inprod_mfd"
      ]
    },
    {
      "page": "inprod_mfd_diag",
      "title": "Inner product of two multivariate functional data objects, for each observation",
      "topics": [
        "inprod_mfd_diag"
      ]
    },
    {
      "page": "is.mfd",
      "title": "Confirm Object has Class 'mfd'",
      "topics": [
        "is.mfd"
      ]
    },
    {
      "page": "lines_mfd",
      "title": "Add the plot of a new multivariate functional data object to an existing plot.",
      "topics": [
        "lines_mfd"
      ]
    },
    {
      "page": "lines.mfd",
      "title": "Add curves to an existing multivariate functional data plot",
      "topics": [
        "lines.mfd"
      ]
    },
    {
      "page": "mean.mfd",
      "title": "Mean Function for Multivariate Functional Data",
      "topics": [
        "mean.mfd"
      ]
    },
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      "page": "mfd",
      "title": "Define a Multivariate Functional Data Object",
      "topics": [
        "mfd"
      ]
    },
    {
      "page": "mFPCA",
      "title": "Mixed Functional Principal Component Analysis (mFPCA)",
      "topics": [
        "mFPCA"
      ]
    },
    {
      "page": "minus_mfd",
      "title": "Subtract multivariate functional data (and unary negation)",
      "topics": [
        "-.mfd",
        "minus_mfd"
      ]
    },
    {
      "page": "mixregfit_multivariate",
      "title": "Performs the estimation of gaussian mixtures of regression models and gaussian mixture models. Used in FMRCC_PhaseI.",
      "topics": [
        "mixregfit_multivariate"
      ]
    },
    {
      "page": "nbasis",
      "title": "Number of basis functions",
      "topics": [
        "nbasis"
      ]
    },
    {
      "page": "nobs.mfd",
      "title": "Number of observations in a multivariate functional data object",
      "topics": [
        "nobs.mfd"
      ]
    },
    {
      "page": "norm.mfd",
      "title": "Norm of Multivariate Functional Data",
      "topics": [
        "norm.mfd"
      ]
    },
    {
      "page": "nvar",
      "title": "Number of variables",
      "topics": [
        "nvar"
      ]
    },
    {
      "page": "OEBFDTW",
      "title": "Open-end/open-begin Functional Dynamic Time Warping (OEB-FDTW)",
      "topics": [
        "OEBFDTW"
      ]
    },
    {
      "page": "par.FDTW",
      "title": "Setting open-end/open-begin functional dynamic time warping (OEB-FDTW) defaults",
      "topics": [
        "par.FDTW"
      ]
    },
    {
      "page": "par.mFPCA",
      "title": "Setting mixed functional principal component analysis (mFPCA) defaults",
      "topics": [
        "par.mFPCA"
      ]
    },
    {
      "page": "par.rtr",
      "title": "Setting real-time registration step defaults",
      "topics": [
        "par.rtr"
      ]
    },
    {
      "page": "pca_mfd",
      "title": "Multivariate functional principal components analysis",
      "topics": [
        "pca_mfd"
      ]
    },
    {
      "page": "pca_mfd_real_time",
      "title": "Get a list of multivariate functional principal component analysis models estimated on functional data each evolving up to an intermediate domain point.",
      "topics": [
        "pca_mfd_real_time"
      ]
    },
    {
      "page": "plot_bifd",
      "title": "Plot a Bivariate Functional Data Object.",
      "topics": [
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