Description Usage Arguments Value See Also Examples

This function builds a data frame needed to plot control charts for monitoring a multivariate functional covariates based on multivariate functional principal component analysis (MFPCA) and a related scalar response variable using the scalar-on-function regression control chart, as proposed in Capezza et al. (2020).

In particular, this function provides:

* the Hotelling's T^2 control chart,

* the squared prediction error (SPE) control chart,

* the scalar regression control chart.

This function calls `control_charts_pca`

for the control charts on
the multivariate functional covariates and `regr_cc_sof`

for the scalar regression control chart.

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.

1 2 3 4 5 6 7 8 9 10 11 | ```
control_charts_sof_pc(
mod,
y_test,
mfdobj_x_test,
mfdobj_x_tuning = NULL,
alpha = list(T2 = 0.0125, spe = 0.0125, y = 0.025),
limits = "standard",
seed = 0,
nfold = NULL,
ncores = 1
)
``` |

`mod` |
A list obtained as output from |

`y_test` |
A numeric vector containing the observations of the scalar response variable in the phase II data set. |

`mfdobj_x_test` |
An object of class |

`mfdobj_x_tuning` |
An object of class |

`alpha` |
A named list with three elements, named |

`limits` |
A character value.
If "standard", it estimates the control limits on the tuning
data set. If "cv", the function calculates the control limits only on the
training data using cross-validation
using |

`seed` |
If |

`nfold` |
If |

`ncores` |
If |

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 T^2 statistic calculated
for all observations,

* one column per each functional variable, containing its contribution to the T^2 statistic,

* one `spe`

column containing the SPE statistic calculated
for all observations,

* one column per each functional variable, containing its contribution to the SPE statistic,

* `T2_lim`

gives the upper control limit of the
Hotelling's T^2 control chart,

* one `contribution_T2_*_lim`

column per each
functional variable giving the
limits of the contribution of that variable to the
Hotelling's T^2 statistic,

* `spe_lim`

gives the upper control limit of the SPE control chart

* one `contribution_spe*_lim`

column per
each functional variable giving the
limits of the contribution of that variable to the SPE statistic.

* `y_hat`

: the predictions of the response variable
corresponding to `mfdobj_x_new`

,

* `y`

: the same as the argument `y_new`

given as input to this function,

* `lwr`

: lower limit of the `1-alpha`

prediction interval on the response,

* `pred_err`

: prediction error calculated as `y-y_hat`

,

* `pred_err_sup`

: upper limit of the `1-alpha`

prediction interval on the prediction error,

* `pred_err_inf`

: lower limit of the `1-alpha`

prediction interval on the prediction error.

`control_charts_pca`

, `regr_cc_sof`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
library(funcharts)
data("air")
air <- lapply(air, function(x) x[201:300, , drop = FALSE])
fun_covariates <- c("CO", "temperature")
mfdobj_x <- get_mfd_list(air[fun_covariates],
n_basis = 15,
lambda = 1e-2)
y <- rowMeans(air$NO2)
y1 <- y[1:60]
y2 <- y[91:100]
mfdobj_x1 <- mfdobj_x[1:60]
mfdobj_x_tuning <- mfdobj_x[61:90]
mfdobj_x2 <- mfdobj_x[91:100]
mod <- sof_pc(y1, mfdobj_x1)
cclist <- control_charts_sof_pc(mod = mod,
y_test = y2,
mfdobj_x_test = mfdobj_x2,
mfdobj_x_tuning = mfdobj_x_tuning)
plot_control_charts(cclist)
``` |

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