funcharts (version 1.8.1)

RoAMFEWMA_PhaseI: Robust Adaptive Multivariate Functional EWMA Control Chart - Phase I

Description

It performs Phase I of the Robust Adaptive Multivariate Functional EWMA control chart (RoAMFEWMA). The procedure combines:

1. Functional cellwise outlier detection via functional_filter,

2. Robust Multivariate Functional Data Imputation (RoMFDI) via RoMFDI,

3. Casewise outliers detection via RoMFCC (RoMFCC_PhaseI_casewise and RoMFCC_PhaseII_casewise), on the imputed Phase I data,

4. AMFEWMA Phase I calibration (AMFEWMA_PhaseI) on cellwise and casewise clean data.

The resulting object can be directly used as mod_1 argument in AMFEWMA_PhaseII

Usage

RoAMFEWMA_PhaseI(
  mfdobj,
  mfdobj_tuning,
  functional_filter_par = list(filter = TRUE),
  imputation_par = list(method_imputation = "RoMFDI", n_dataset = 1),
  verbose = FALSE
)

Value

A list of the following elements:

• mod_1 object returned by AMFEWMA_PhaseI, see the value of AMFEWMA_PhaseI for a full description of its component;

• mfd_clean_training training data after complete cleaning, containing no outliers at either cellwise or casewise;

• mfd_clean_tuning tuning data after complete cleaning, containing no outliers at either cellwise or casewise;

• mfd_all_clean full Phase I clean data (training + tuning);

• idx_casewise_outliers indices of observations indetified as casewise outliers by RoMFCC Phase II;

• ff_training training set after the functional filter;

• ff_tuning tuning set after the functional filter;

• X_imp_training_1 first imputation of the training set after RoMFDI

• X_imp_tuning_1 first imputation of the tuning set after RoMFDI

• X_all_imputed training + tuning data after robust multivariate functional imputation;

• mod_RoMFCC_phaseI_casewise object returned by RoMFCC_PhaseI, see the value of RoMFCC_PhaseI_casewise for a full description of its component;

• mod_RoMFCC_phaseII_casewise object returned by RoMFCC_PhaseII, see the value of RoMFCC_PhaseII_casewise for a full description of its component;

Arguments

mfdobj

A multivariate functional data object of class mfd. This dataset is used as the Phase I training set. A functional filter is first applied to detect functional cellwise outliers; the flagged components are then imputed through a robust multivariate functional imputation procedure. The imputed data are subsequently processed by the Robust Multivariate Functional Control Chart to detect and remove functional casewise outliers. The resulting clean dataset (free of both cellwise and casewise outliers) is then used as the training set in the Phase I of the Adaptive Multivariate Functional EWMA control chart.

mfdobj_tuning

A multivariate functional data object of class mfd representing the Phase I tuning set. This dataset undergoes the same functional filtering and robust imputation steps applied to mfdobj. The filtered and imputed data are used within the Robust Multivariate Functional Control Chart to estimate tuning quantities and control limits. After casewise cleaning, the resulting clean tuning set is employed in the Phase I calibration of the Adaptive Multivariate Functional EWMA control chart.

functional_filter_par

A list with an argument filter that can be TRUE or FALSE depending on if the functional filter step must be performed or not. All the other arguments of this list are passed as arguments to the function functional_filter in the filtering step. All the arguments that are not passed take their default values. See functional_filter for all the arguments and their default values. Default is list(filter = TRUE).

imputation_par

A list with an argument method_imputation that can be "RoMFDI" or "mean" depending on if the imputation step must be done by means of RoMFDI or by just using the mean of each functional variable. If method_imputation = "RoMFDI", all the other arguments of this list are passed as arguments to the function RoMFDI in the imputation step. All the arguments that are not passed take their default values. See RoMFDI for all the arguments and their default values. Default value is list(method_imputation = "RoMFDI").

verbose

If TRUE, it prints messages about the steps of the algorithm. Default is FALSE.

Details

Among the multiple imputed datasets, the first one is used to build the cleaned training and tuning sets for AMFEWMA.

References

Capezza, C., Centofanti, F., Lepore, A., Palumbo, B. (2024) Robust Multivariate Functional Control Chart. Technometrics, 66(4):531--547, doi:10.1080/00401706.2024.2327346.

Capezza, C., Capizzi, G., Centofanti, F., Lepore, A., Palumbo, B. (2025) An Adaptive Multivariate Functional EWMA Control Chart. Journal of Quality Technology, 57(1):1--15, doi:https://doi.org/10.1080/00224065.2024.2383674.

Examples

if (FALSE) {
set.seed(0)
dat_phaseI <- simulate_data_RoMFCC(p_cellwise = 0.05,
                            p_casewise = 0.05,
                            outlier = "outlier_E",
                            M_outlier_cell = 0.03,
                            M_outlier_case = 0.01,
                            max_n_cellwise = 10)
dat_phaseII <- simulate_data_RoMFCC(OC = "OC_E",
                                    M_OC = 0.01,
                                    which_OC = 5)
mfdobj_phaseI <- get_mfd_list(dat_phaseI$X_mat_list, n_basis = 5)
mfdobj_phaseII <- get_mfd_list(dat_phaseII$X_mat_list, n_basis = 5)
mfdobj_training_phaseI <- mfdobj_phaseI[1:333, ]
mfdobj_tuning_phaseI <- mfdobj_phaseI[334:1000, ]
out_phaseI <- RoAMFEWMA_PhaseI(mfdobj = mfdobj_training_phaseI,
                               mfdobj_tuning = mfdobj_tuning_phaseI)
out_phaseII <- RoAMFEWMA_PhaseII(mfdobj_2 = mfdobj_phaseII,
                                 mod_1 = out_phaseI)
plot_control_charts(out_phaseII$cc)
}