Description Usage Arguments Value References See Also

This function builds a data frame needed to plot
the Hotelling's T^2 and squared prediction error (SPE)
control charts
based on multivariate functional principal component analysis
(MFPCA) performed
on multivariate functional data,
proposed in Capezza et al. (2020) together with the scalar control chart
and used also to build the
functional regression control chart proposed in Centofanti et al. (2020)
(this function is used by `regr_cc_fof`

).
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_pca(
pca,
components,
tuning_data = NULL,
newdata,
alpha = list(T2 = 0.025, spe = 0.025),
limits = "standard",
seed = 0,
nfold = 5,
ncores = 1
)
``` |

`pca` |
An object of class |

`components` |
A vector of integers with the components over which to project the multivariate functional data. |

`tuning_data` |
An object of class |

`newdata` |
An object of class |

`alpha` |
A named list with two 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.

Capezza C, Lepore A, Menafoglio A, Palumbo B, Vantini S. (2020)
Control charts for
monitoring ship operating conditions and CO2 emissions
based on scalar-on-function regression.
*Applied Stochastic Models in Business and Industry*,
36(3):477–500.
<doi:10.1002/asmb.2507>

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

library(funcharts) data("air") air <- lapply(air, function(x) x[1:220, , drop = FALSE]) fun_covariates <- c("CO", "temperature") mfdobj_x <- get_mfd_list(air[fun_covariates], n_basis = 15, lambda = 1e-2) y <- rowMeans(air$NO2) y1 <- y[1:100] y_tuning <- y[101:200] y2 <- y[201:220] mfdobj_x1 <- mfdobj_x[1:100] mfdobj_x_tuning <- mfdobj_x[101:200] mfdobj_x2 <- mfdobj_x[201:220] pca <- pca_mfd(mfdobj_x1) components <- 1:which(cumsum(pca$varprop) >= .90)[1] cclist <- control_charts_pca(pca = pca, components = components, tuning_data = mfdobj_x_tuning, newdata = mfdobj_x2) plot_control_charts(cclist)

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