arXiv subjects

Antonio Lepore

Publications and source records attributed to Antonio Lepore.

14 recordsLinked to original sources

arXiv2026

Monitoring Covariance in Multichannel Profiles via Functional Graphical Models

Most statistical process monitoring methods for multichannel profiles focus solely on the mean and are almost ineffective when changes involve the covariance structure. Although it is known to be crucial, covariance monitoring requires estimating a much larger number of parameters, which may shift in a subtle and sparse fashion. That is, an out-of-control (OC) state may manifest with small deviations and affect only a very limited subset of these parameters. To address these difficulties, we propose a multichannel profile covariance (MPC) control chart based on functional graphical models that provide an interpretable representation of conditional dependencies between profiles. A nonparametric combination of the likelihood-ratio tests corresponding to different sparsity levels is then used to draw an overall inference and signal whether an OC state may have occurred. Between-profile relationships that are likely to have shifted are naturally identified at no additional computational cost. An extensive Monte Carlo simulation study compares the MPC control chart with state-of-the-art competitors, and a case study on monitoring multichannel temperature profiles in a roasting machine illustrates its practical applicability.

stat.ME↗

arXiv2025

An Adaptive Multivariate Functional Control Chart

New data acquisition technologies allow one to gather huge amounts of data that are best represented as functional data. In this setting, profile monitoring assesses the stability over time of both univariate and multivariate functional quality characteristics. The detection power of profile monitoring methods could heavily depend on parameter selection criteria, which usually do not take into account any information from the out-of-control (OC) state. This work proposes a new framework, referred to as adaptive multivariate functional control chart (AMFCC), capable of adapting the monitoring of a multivariate functional quality characteristic to the unknown OC distribution, by combining $p$-values of the partial tests corresponding to Hotelling $T^2$-type statistics calculated at different parameter combinations. Through an extensive Monte Carlo simulation study, the performance of AMFCC is compared with methods that have already appeared in the literature. Finally, a case study is presented in which the proposed framework is used to monitor a resistance spot welding process in the automotive industry. AMFCC is implemented in the R package funcharts, available on CRAN.

stat.ME↗

arXiv2024

Stream-Based Active Learning for Process Monitoring

Statistical process monitoring (SPM) methods are essential tools in quality management to check the stability of industrial processes, i.e., to dynamically classify the process state as in control (IC), under normal operating conditions, or out of control (OC), otherwise. Traditional SPM methods are based on unsupervised approaches, which are popular because in most industrial applications the true OC states of the process are not explicitly known. This hampered the development of supervised methods that could instead take advantage of process data containing labels on the true process state, although they still need improvement in dealing with class imbalance, as OC states are rare in high-quality processes, and the dynamic recognition of unseen classes, e.g., the number of possible OC states. This article presents a novel stream-based active learning strategy for SPM that enhances partially hidden Markov models to deal with data streams. The ultimate goal is to optimize labeling resources constrained by a limited budget and dynamically update the possible OC states. The proposed method performance in classifying the true state of the process is assessed through a simulation and a case study on the SPM of a resistance spot welding process in the automotive industry, which motivated this research.

stat.ML↗

arXiv2024

funcharts: Control charts for multivariate functional data in R

Modern statistical process monitoring (SPM) applications focus on profile monitoring, i.e., the monitoring of process quality characteristics that can be modeled as profiles, also known as functional data. Despite the large interest in the profile monitoring literature, there is still a lack of software to facilitate its practical application. This article introduces the funcharts R package that implements recent developments on the SPM of multivariate functional quality characteristics, possibly adjusted by the influence of additional variables, referred to as covariates. The package also implements the real-time version of all control charting procedures to monitor profiles partially observed up to an intermediate domain point. The package is illustrated both through its built-in data generator and a real-case study on the SPM of Ro-Pax ship CO2 emissions during navigation, which is based on the ShipNavigation data provided in the Supplementary Material.

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arXiv2024

An Adaptive Multivariate Functional EWMA Control Chart

In many modern industrial scenarios, the measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in the monitoring of the quality of a resistance spot welding process in the automotive industry through the online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and recognized as the full technological signature of the process.

stat.ME↗

arXiv2024

Functional Mixture Regression Control Chart

Industrial applications often exhibit multiple in-control patterns due to varying operating conditions, which makes a single functional linear model (FLM) inadequate to capture the complexity of the true relationship between a functional quality characteristic and covariates, which gives rise to the multimode profile monitoring problem. This issue is clearly illustrated in the resistance spot welding (RSW) process in the automotive industry, where different operating conditions lead to multiple in-control states. In these states, factors such as electrode tip wear and dressing may influence the functional quality characteristic differently, resulting in distinct FLMs across subpopulations. To address this problem, this article introduces the functional mixture regression control chart (FMRCC) to monitor functional quality characteristics with multiple in-control patterns and covariate information, modeled using a mixture of FLMs. A monitoring strategy based on the likelihood ratio test is proposed to monitor any deviation from the estimated in-control heterogeneous population. An extensive Monte Carlo simulation study is performed to compare the FMRCC with competing monitoring schemes that have already appeared in the literature, and a case study in the monitoring of an RSW process in the automotive industry, which motivated this research, illustrates its practical applicability.

stat.ME↗

arXiv2024

Robust Multivariate Functional Control Chart

In modern Industry 4.0 applications, a huge amount of data is acquired during manufacturing processes that are often contaminated with anomalous observations in the form of both casewise and cellwise outliers. These can seriously reduce the performance of control charting procedures, especially in complex and high-dimensional settings. To mitigate this issue in the context of profile monitoring, we propose a new framework, referred to as robust multivariate functional control chart (RoMFCC), that is able to monitor multivariate functional data while being robust to both functional casewise and cellwise outliers. The RoMFCC relies on four main elements: (I) a functional univariate filter to identify functional cellwise outliers to be replaced by missing components; (II) a robust multivariate functional data imputation method of missing values; (III) a casewise robust dimensionality reduction; (IV) a monitoring strategy for the multivariate functional quality characteristic. An extensive Monte Carlo simulation study is performed to compare the RoMFCC with competing monitoring schemes already appeared in the literature. Finally, a motivating real-case study is presented where the proposed framework is used to monitor a resistance spot welding process in the automotive industry.

stat.AP↗

arXiv2023

Functional Neural Network Control Chart

In many Industry 4.0 data analytics applications, quality characteristic data acquired from manufacturing processes are better modeled as functions, often referred to as profiles. In practice, there are situations where a scalar quality characteristic, referred to also as the response, is influenced by one or more variables in the form of functional data, referred to as functional covariates. To adjust the monitoring of the scalar response by the effect of this additional information, a new profile monitoring strategy is proposed on the residuals obtained from the functional neural network, which is able to learn a possibly nonlinear relationship between the scalar response and the functional covariates. An extensive Monte Carlo simulation study is performed to assess the performance of the proposed method with respect to other control charts that appeared in the literature before. Finally, a case study in the railway industry is presented with the aim of monitoring the heating, ventilation and air conditioning systems installed onboard passenger trains.

stat.ME↗

arXiv2022

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named S-LASSO, is proposed for the coefficient function of the Function-on-Function linear regression model. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating regions where the coefficient function is zero, and to smoothly estimate non-zero values of the coefficient function. The sparsity of the estimator is ensured by a \textit{functional LASSO penalty}, which pointwise shrinks toward zero the coefficient function, while the smoothness is provided by two roughness penalties that penalize the curvature of the final estimator. The resulting estimator is proved to be estimation and pointwise sign consistent. Via an extensive Monte Carlo simulation study, the estimation and predictive performance of the S-LASSO estimator are shown to be better than (or at worst comparable with) competing estimators already presented in the literature before. Practical advantages of the S-LASSO estimator are illustrated through the analysis of the \textit{Canadian weather}, \textit{Swedish mortality} and \textit{ship CO\textsubscript{2} emission data}. The S-LASSO method is implemented in the \textsf{R} package \textsf{slasso}, openly available online on CRAN.

stat.ME↗

arXiv2022

Sparse and Smooth Functional Data Clustering

A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. The proposed method is referred to as sparse and smooth functional clustering (SaS-Funclust) and relies on a general functional Gaussian mixture model whose parameters are estimated by maximizing a log-likelihood function penalized with a functional adaptive pairwise penalty and a roughness penalty. The former allows identifying the noninformative portion of domain by shrinking the means of separated clusters to some common values, whereas the latter improves the interpretability by imposing some degree of smoothing to the estimated cluster means. The model is estimated via an expectation-conditional maximization algorithm paired with a cross-validation procedure. Through a Monte Carlo simulation study, the SaS-Funclust method is shown to outperform other methods already appeared in the literature, both in terms of clustering performance and interpretability. Finally, three real-data examples are presented to demonstrate the favourable performance of the proposed method. The SaS-Funclust method is implemented in the $\textsf{R}$ package $\textsf{sasfunclust}$, available online at https://github.com/unina-sfere/sasfunclust.

stat.ME↗

arXiv2022

Real-time Monitoring of Functional Data

With the rise of Industry 4.0, huge amounts of data are now generated that are apt to be modelled as functional data. In this setting, standard profile monitoring methods aim to assess the stability over time of a completely observed functional quality characteristic. However, in some practical situations, evaluating the process state in real-time, i.e., as the process is running, could be of great interest to significantly improve the effectiveness of monitoring. To this aim, we propose a new method, referred to as functional real-time monitoring (FRTM), that is able to account for both phase and amplitude variation through the following steps: (i) registration; (ii) dimensionality reduction; (iii) monitoring of a partially observed functional quality characteristic. An extensive Monte Carlo simulation study is performed to quantify the performance of FRTM with respect to two competing methods. Finally, an example is presented where the proposed method is used to monitor batches from a penicillin production process in real-time.

stat.AP↗

arXiv2020

Adaptive Smoothing Spline Estimator for the Function-on-Function Linear Regression Model

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also on two real-data benchmark examples.

stat.ME↗

arXiv2020

Functional clustering methods for resistance spot welding process data in the automotive industry

Quality assessment of resistance spot welding (RSW) joints of metal sheets in the automotive industry is typically based on costly and lengthy off-line tests that are unfeasible on the full production, especially on large scale. However, the massive industrial digitalization triggered by the industry 4.0 framework makes available, for every produced joint, on-line RSW process parameters, such as, in particular, the so-called dynamic resistance curve (DRC), which is recognized as the full technological signature of the spot welds. Motivated by this context, the present paper means to show the potentiality and the practical applicability to clustering methods of the functional data approach that avoids the need for arbitrary and often controversial feature extraction to find out homogeneous groups of DRCs, which likely pertain to spot welds sharing common mechanical and metallurgical properties. We intend is to provide an essential hands-on overview of the most promising functional clustering methods, and to apply the latter to the DRCs collected from the RSW process at hand, even if they could go far beyond the specific application hereby investigated. The methods analyzed are demonstrated to possibly support practitioners along the identification of the mapping relationship between process parameters and the final quality of RSW joints as well as, more specifically, along the priority assignment for off-line testing of welded spots and the welding tool wear analysis. The analysis code, that has been developed through the software environment R, and the DRC data set are made openly available online at https://github.com/unina-sfere/funclustRSW/

stat.AP↗

arXiv2014

Plotting positions close to the exact unbiased solution: application to the Pozzuoli's bradeysism earthquake data

Graphical techniques are recommended for critical applications in order to share information with non-statisticians, since they allow for a visual analysis and helpful understanding of the results. However, graphical estimation methods are often underestimated because of their minor efficiency with respect to the analytical ones. Therefore, finding unbiased plotting positions can contribute to rise their reputation and to encourage their strategic use. This paper proposes a new general plotting position formula which can be as close as needed to the exact unbiased plotting positions. The ability of the new solution in estimating quantiles for both symmetrical and skewed location-scale distributions is shown via Monte Carlo simulation. An applicative example shows how the proposed formula enables to perform, with known accuracy, the graphical analysis of critical data, such as the earthquake magnitudes registered during the serious 1983-1984 bradyseismic crisis in Campi Flegrei (Italy). Moreover, the proposed formula gives a unified look at existing plotting positions and a definitive insight into plotting position controversies recently renewed in the literature.

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