funcharts: regr_cc_fof – R documentation

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regr_cc_fof

Functional Regression Control Chart

Description

It builds a data frame needed to plot the Functional Regression Control Chart introduced in Centofanti et al. (2020), based on a fitted function-on-function linear regression model. The training data have already been used to fit the model. A tuning data set can be provided that is used to estimate the control chart limits. A phase II data set contains the observations to be monitored with the built control charts.

Usage

regr_cc_fof(
  object,
  mfdobj_y_new,
  mfdobj_x_new,
  mfdobj_y_tuning = NULL,
  mfdobj_x_tuning = NULL,
  alpha = list(T2 = 0.025, spe = 0.025)
)

Arguments

`object`	A list obtained as output from `fof_pc`, i.e. a fitted function-on-function linear regression model.
`mfdobj_y_new`	An object of class `mfd` containing the phase II data set of the functional response observations to be monitored.
`mfdobj_x_new`	An object of class `mfd` containing the phase II data set of the functional covariates observations to be monitored.
`mfdobj_y_tuning`	An object of class `mfd` containing the tuning data set of the functional response observations, used to estimate the control chart limits. If NULL, the training data, i.e. the data used to fit the function-on-function linear regression model, are also used as the tuning data set, i.e. `mfdobj_y_tuning=object$pca_y$data`. Default is NULL.
`mfdobj_x_tuning`	An object of class `mfd` containing the tuning data set of the functional covariates observations, used to estimate the control chart limits. If NULL, the training data, i.e. the data used to fit the function-on-function linear regression model, are also used as the tuning data set, i.e. `mfdobj_x_tuning=object$pca_x$data`. Default is NULL.
`alpha`	A named list with two elements, named `T2` and `spe`, respectively, each containing the desired Type I error probability of the corresponding control chart. Note that at the moment you have to take into account manually the family-wise error rate and adjust the two values accordingly. See Centofanti et al. (2020) for additional details. Default value is `list(T2 = 0.025, spe = 0.025)`.

Value

A data.frame containing the output of the function control_charts_pca applied to the prediction errors.

References

Centofanti F, Lepore A, Menafoglio A, Palumbo B, Vantini S. (2020) Functional Regression Control Chart. Technometrics. <doi:10.1080/00401706.2020.1753581>

Examples

library(funcharts)
data("air")
air <- lapply(air, function(x) x[1:100, , drop = FALSE])
fun_covariates <- c("CO", "temperature")
mfdobj_x <- get_mfd_list(air[fun_covariates],
                         n_basis = 15,
                         lambda = 1e-2)
mfdobj_y <- get_mfd_list(air["NO2"],
                         n_basis = 15,
                         lambda = 1e-2)
mfdobj_y1 <- mfdobj_y[1:60]
mfdobj_y_tuning <- mfdobj_y[61:90]
mfdobj_y2 <- mfdobj_y[91:100]
mfdobj_x1 <- mfdobj_x[1:60]
mfdobj_x_tuning <- mfdobj_x[61:90]
mfdobj_x2 <- mfdobj_x[91:100]
mod_fof <- fof_pc(mfdobj_y1, mfdobj_x1)
cclist <- regr_cc_fof(mod_fof,
                      mfdobj_y_new = mfdobj_y2,
                      mfdobj_x_new = mfdobj_x2,
                      mfdobj_y_tuning = NULL,
                      mfdobj_x_tuning = NULL)
plot_control_charts(cclist)

funcharts

Functional Control Charts

v1.0.0

GPL-3

Authors

Christian Capezza [cre, aut], Fabio Centofanti [aut], Antonio Lepore [aut], Alessandra Menafoglio [aut], Biagio Palumbo [aut], Simone Vantini [aut]

Initial release