funcharts (version 1.7.0)

RoMFCC_PhaseI: Robust Multivariate Functional Control Charts - Phase I

Description

It performs Phase I of the Robust Multivariate Functional Control Chart (RoMFCC) as proposed by Capezza et al. (2024).

Usage

RoMFCC_PhaseI(
  mfdobj,
  mfdobj_tuning = NULL,
  functional_filter_par = list(filter = TRUE),
  imputation_par = list(method_imputation = "RoMFDI"),
  pca_par = list(fev = 0.7),
  alpha = 0.05
)

Value

A list of the following elements that are needed in Phase II:

• T2 the Hotelling's T2 statistic values for the Phase I data set,

• SPE the SPE statistic values for the Phase I data set,

• T2_tun the Hotelling's T2 statistic values for the tuning data set,

• SPE_tun the SPE statistic values for the tuning data set,

• T2_lim the Phase II control limit of the Hotelling's T2 control chart,

• spe_lim the Phase II control limit of the SPE control chart,

• tuning TRUE if the tuning data set is provided, FALSE otherwise,

• mod_pca the final RoMFPCA model fitted on the Phase I data set,

• K = K the number of selected principal components,

• T_T2_inv if a tuning data set is provided, it returns the inverse of the covariance matrix of the first K scores, needed to calculate the Hotelling's T2 statistic for the Phase II observations.

• mean_scores_tuning_rob_mean if a tuning data set is provided, it returns the robust location estimate of the scores, needed to calculate the Hotelling's T2 and SPE statistics for the Phase II observations.

Arguments

mfdobj

A multivariate functional data object of class mfd. A functional filter is applied to this data set, then flagged functional componentwise outliers are imputed in the robust imputation step. Finally robust multivariate functional principal component analysis is applied to the imputed data set for dimension reduction.

mfdobj_tuning

An additional functional data object of class mfd. After applying the filter and imputation steps on this data set, it is used to robustly estimate the distribution of the Hotelling's T2 and SPE statistics in order to calculate control limits to prevent overfitting issues that could reduce the monitoring performance of the RoMFCC. Default is NULL, but it is strongly recommended to use a tuning data set.

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").

pca_par

A list with an argument fev, indicating a number between 0 and 1 denoting the fraction of variability that must be explained by the principal components to be selected in the RoMFPCA step. All the other arguments of this list are passed as arguments to the function rpca_mfd in the RoMFPCA step. All the arguments that are not passed take their default values. See rpca_mfd for all the arguments and their default values. Default value is list(fev = 0.7).

alpha

The overall nominal type-I error probability used to set control chart limits. Default value is 0.05.

Author

C. Capezza, F. Centofanti

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)
mfdobj <- get_mfd_list(air, n_basis = 5)
nobs <- dim(mfdobj$coefs)[2]
set.seed(0)
ids <- sample(1:nobs)
mfdobj1 <- mfdobj[ids[1:100]]
mfdobj_tuning <- mfdobj[ids[101:300]]
mfdobj2 <- mfdobj[ids[-(1:300)]]
mod_phase1 <- RoMFCC_PhaseI(mfdobj = mfdobj1,
                            mfdobj_tuning = mfdobj_tuning)
phase2 <- RoMFCC_PhaseII(mfdobj_new = mfdobj2,
                         mod_phase1 = mod_phase1)
plot_control_charts(phase2)
}