AMFCC_PhaseI {funcharts} | R Documentation |
Phase I of the Adaptive Multivariate Functional Control Chart (AMFCC).
Description
This function implements the design phase (Phase I) of the Adaptive Multivariate Functional Control Chart.
Usage
AMFCC_PhaseI(
data_tra,
data_tun = NULL,
grid,
q = 30,
par_seq_list = list(10^seq(-7, 2, l = 10), c(0.5, 0.7, 0.8, 0.9, 0.99)),
alpha_diagn = 0.05,
alpha_mon = 0.05,
ncores = 1
)
Arguments
data_tra |
a data frame with the training data with the following columns:
|
data_tun |
a data frame with the tuning data with the same structure as |
grid |
The vector of time points where the curves are sampled. |
q |
The dimension of the set of B-spline functions. |
par_seq_list |
a list with two elements.
The first element is a sequence of values for the regularization
parameter |
alpha_diagn |
Type I error probability for the diagnostic. |
alpha_mon |
Type I error probability for the monitoring. |
ncores |
number of cores to use for parallel computing |
Value
A list containing the following arguments:
-
statistics_IC
: A matrix with the values of the Hotelling T^2-type statistics for each observation and parameter combination. -
p_values_combined
: A list with two elements containing the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions. -
CL
: The control limits for the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions. -
contributions_IC
: A list where each element corresponds to a variable and is a matrix with the contributions to the HotellingT^2
-type statistics for each observation and parameter combination. -
p_values_combined_cont
: A list where each element corresponds to a variable and is a list of two elements containing the contribution to the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions. -
CL_cont
: The control limits for the contribution to the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions. -
par_seq_list
: The list of the sequences of the tuning parameters. -
q
: The dimension of the set of B-spline functions. -
basis
: The basis functions used for the functional data representation. -
grid
: The vector of time points where the curves are sampled. -
comb_list_tot
: The matrix with all the parameter combinations. -
mod_pca_list
: The list of the MFPCA models for each value oflambda_s
.
Author(s)
F. Centofanti
References
Centofanti, F., A. Lepore, and B. Palumbo (2025). An Adaptive Multivariate Functional Control Chart. Accepted for publication in Technometrics.
Examples
library(funcharts)
N <- 10
l_grid <- 10
p <- 2
grid <- seq(0, 1, l = l_grid)
Xall_tra <- funcharts::simulate_mfd(
nobs = N,
p = p,
ngrid = l_grid,
correlation_type_x = c("Bessel", "Gaussian")
)
X_tra <-
data.frame(
x = c(Xall_tra$X_list[[1]], Xall_tra$X_list[[2]]),
timeindex = rep(rep(1:l_grid, each = (N)), p),
curve = rep(1:(N), l_grid * p),
var = rep(1:p, each = l_grid * N)
)
Xall_II <- funcharts::simulate_mfd(
nobs = N,
p = p,
ngrid = l_grid,
shift_type_x = list("A", "B"),
d_x = c(10, 10),
correlation_type_x = c("Bessel", "Gaussian")
)
X_II <-
data.frame(
x = c(Xall_II$X_list[[1]], Xall_II$X_list[[2]]),
timeindex = rep(rep(1:l_grid, each = (N)), p),
curve = rep(1:(N), l_grid * p),
var = rep(1:p, each = l_grid * N)
)
# AMFCC -------------------------------------------------------------------
print("AMFCC")
mod_phaseI_AMFCC <- AMFCC_PhaseI(
data_tra = X_tra,
data_tun =
NULL,
grid = grid,
ncores = 1
)
mod_phaseII_AMFCC <- AMFCC_PhaseII(data = X_II,
mod_Phase_I = mod_phaseI_AMFCC,
ncores = 1)
plot(mod_phaseII_AMFCC)
plot(mod_phaseII_AMFCC,type='cont',ind_obs=1)