AMFCC_PhaseII: Phase II of the Adaptive Multivariate Functional Control...
In funcharts: Functional Control Charts

AMFCC_PhaseII

R Documentation

Phase II of the Adaptive Multivariate Functional Control Chart (AMFCC).

Description

This function implements the monitoring phase (Phase II) of the Adaptive Multivariate Functional Control Chart.

Usage

AMFCC_PhaseII(data = NULL, mod_Phase_I, ncores = 1)

Arguments

data

a data frame with the testing data with the following columns:

      var: vector of the variable indexes.

      curve: vector of the curve indexes.

      timeindex: vector of the time indexes corresponding to given elements of \code{grid}.

      x: concatenated vector of the observed curves.

mod_Phase_I

a list with the output of the Phase I.

ncores

number of cores to use for parallel computing

Value

A list containing the following arguments:

ARL: The average run length (ARL) for the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions.
ARL_cont: The average run length for the contribution to the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions.
statistics: A matrix with the values of the Hotelling T^2-type statistics for each observation and parameter combination.
contributions: A list where each element is a matrix with the contributions to 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.
p_values_combined_cont: A list where each element is a list of two elements containing the contribution to 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.
CL_cont: The control limits for the contribution to the monitoring statistics obtained with the Fisher omnibus and Tippett combining functions.

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)

funcharts documentation built on April 3, 2025, 7:47 p.m.