funcharts (version 1.8.1)

RoMFCC_PhaseII_casewise: Robust Multivariate Functional Control Charts - Phase II (casewise version)

Description

It performs Phase II of the Robust Multivariate Functional Control Chart (RoMFCC) for casewise outlier detection, computing Hotelling's T2 and SPE monitoring statistics according to the methodology proposed by Capezza et al. (2024).

Usage

RoMFCC_PhaseII_casewise(mfdobj_all_imp, mod_phaseI_casewise)

Value

A data.frame with as many rows as the number of multivariate functional observations in the phase II data set and the following columns:

• one id column identifying the multivariate functional observation in the phase II data set,

• one T2 column containing the Hotelling T2 statistic calculated for all observations,

• one column per each functional variable, containing its contribution to the T2 statistic,

• one SPE column containing the SPE statistic calculated for all observations,

• T2_lim gives the upper control limit of the Hotelling's T2 control chart,

• SPE_lim gives the upper control limit of the SPE control chart

Arguments

mfdobj_all_imp

A multivariate functional data object of class mfd, containing the concatenation of the fully imputed training and tuning sets to be monitored for casewise outliers.

mod_phaseI_casewise

Output obtained by applying the function RoMFCC_PhaseI_casewise to perform Phase I. See RoMFCC_PhaseI_casewise

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.

Examples

if (FALSE) {
library(funcharts)
set.seed(0)
dat <- 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)
mfdobj <- get_mfd_list(dat$X_mat_list, n_basis = 5)
mfdobj_training <- mfdobj[1:333, ]
mfdobj_tuning <- mfdobj[334:1000, ]
ff_training <- functional_filter(mfdobj = mfdobj_training)
ff_tuning <- functional_filter(mfdobj = mfdobj_tuning)
x_imp_training <- RoMFDI(mfdobj = ff_training$mfdobj)
x_imp_tuning <- RoMFDI(mfdobj = ff_tuning$mfdobj)
X_imp_training <- x_imp_training[[1]]
X_imp_tuning <- x_imp_tuning[[1]]
out_phase1_casewise <- RoMFCC_PhaseI_casewise(
  mfdobj_imp = X_imp_training,
  mfdobj_imp_tuning,X_imp_tuning
)
mfd_all_imputed <- rbind_mfd(X_imp_training, X_imp_tuning)
out_phase2_casewise <- RoMFCC_PhaseII_casewise(
  mfdobj_all_imp = mfdobj_all_imputed,
  mod_phaseI_casewise = out_phase1_casewise
)
plot_control_charts(out_phase2_casewise)
}