1 Background and Legacy

The teaching of Statistics in the Faculty of Engineering at University of Naples Federico II was born in the late 1960s from the creative intuition of Prof. Luigi G. Napolitano, at that time Director of the Institute of Aerodynamics. Thanks to this, some years later, a student of Prof. Napolitano, Pasquale Erto, would become the first Full Professor of Statistics in Italy having a degree in Engineering.

In the fall of 1968, Prof. Napolitano proposed to do the MS thesis in Applied Statistics to one of his most devoted students of the Gasdynamics course and to choose a topic in either Reliability or Quality Control. Although understandably surprised by topics so far from those typical of Gasdynamics, the student chose the former on the spur of the moment (figuring that Reliability was, among the two, the topic closest to Mechanical Design, his other passion after Thermodynamics). It was precisely in 1968 that Prof. Napolitano expressed the firm conviction that it was now essential to introduce the teachings of Probability and Statistics in the Faculty of Engineering. Stubbornly he promoted multiple initiatives, even to the point of delivering himself a first course in Statistics, aimed at members of the Faculties of Engineering and Economics. Meanwhile, the thesis student in Reliability (future Prof. Pasquale Erto) graduated by discussing the thesis Statistical Evaluation of the Reliability of Components of Mechanical Systems. Obviously unable to find a placement in the Institute of Aerodynamics, he migrated to the C.N.R. Engine Institute in 1970. Here, he had the opportunity to cultivate his “unusual” studies, to continue collaborating with Prof. Napolitano as well as to accumulate a significant collection of books and journals.

After having been Professor in Charge of the first course in Italy of Reliability Theory, at the University of Calabria in the academic year 1974–1975, in the following academic years 1975–1984 Prof. Erto was in charge of Reliability and Quality Control at our Faculty of Engineering where then, in 1985, he assumed the position of Associate Professor of Reliability Theory joining to the Institute of Gasdynamics. In 1990, he became a Full Professor of Statistics and was enrolled in the Faculty of Sociology of the University of Catania. The following year, on July 23, 1991, Prof. Napolitano died prematurely in Estes Park (Colorado, US) leaving an indelible mark on the scientific education of all his students. In 1993, Prof. Erto was awarded the first position of Full Professor of Statistics and Calculus of Probability in the history of our Faculty of Engineering. As a natural and expected decision, he was assigned to the Aerospace field to complete a bumpy road that had begun about twenty years earlier in the visionary mind of the late Prof. Napolitano.

During this long journey, Prof. Erto never ceased to be involved in his activity with other young people who, with undoubted courage and passion, faced academic paths no less bumpy than his. To this cohort belong also some professors who then continued their careers in non-statistical areas of our Department. As the in-homogeneity with the traditional disciplinary fields of Statistics persisted, the young group of Statisticians working in our Faculty of Engineering, promoted and obtained in 1999 the establishment in Italy of the scientific-disciplinary sector SECS-S/02 (formerly S01B) “Statistica per la Ricerca Sperimentale e Tecnologica”.

More recently, attracted by the Applied Engineering Statistics activities of this department, the original group of Statisticians has been joined by other very young researchers who have undoubtedly already shown that they know how to employ the cultural heritage, received from those who preceded them, to achieve even more ambitious research and teaching goals.

2 Main Research Programmes

The main research programmes faced by the SECS-S/02 research group at the University of Naples Federico II in the last decade are described below. More details about these research activities as well as other research topics addressed by the Statistics for Engineering Research (SFERe) group are available at www.sfere.unina.it.

2.1 Stochastic Modelling of Degradation Processes and Their Use in Reliability and Maintenance

This research activity focuses on stochastic degradation models and their use in reliability and maintenance. Interest in degradation models in reliability and maintenance is mainly motivated by the fact that many technological units are subjected during their operating life to a gradual degradation process which, in the long run, causes an inevitable situation of failure. These units are typically assumed to fail as soon as their degradation level exceeds an assigned threshold. Consequently, their lifetime can be defined as the first passage time of the degradation process beyond the threshold. Modelling the degradation process of these units can be twofold useful, in fact, it allows estimating their lifetime distribution from degradation data, even in the absence of failures, as well as performing condition-based (i.e., degradation-based) estimates of the remaining useful life, that can be used to plan condition-based maintenance activities. The challenge, in this case, is being able to properly use all the available data and pieces of information and formulate models that have a simple structure (to encourage their use in practical settings) and are statistically tractable (i.e., whose parameters can be easily estimated from data that are usually available in the applications). The main objectives of this research activity are the formulation of (i) new degradation models [1, 2]; (ii) strategies that allow to account for the presence of observable and non-observable forms of heterogeneity (i.e., models with covariates and random effect) [1, 3]; (iii) models and computational strategies that allow the analysis of data affected by measurement errors (e.g., perturbed models, particle filtering) [3, 4]; (iv) classical and Bayesian estimation procedures and related computational techniques (e.g., EM, MCMC algorithm) [3]; (v) prognostic tools (e.g., residual reliability and remaining useful life); (vi) condition-based/predictive/prescriptive/adaptive maintenance strategies [5, 6].

2.2 Software Reliability Growth Modeling

This research path has the ultimate goal of modelling software reliability growth which, in the last decade, has revealed one of the main research topics in statistics, operational research, and computer science. Interest in software reliability growth models (SRGMs) is justified because they can support decision-making in many software development activities to determine when a particular level of reliability is likely to be attained, and to estimate the number of initial or remaining faults in software. The generalized inflection S-shaped software reliability growth model proposed in [7] contributes to advancing the field of software reliability analysis by proposing a powerful and adaptable model that caters to the needs of both practitioners and researchers, by combining the strengths of existing models while introducing the ability to model nonmonotonic failure rate per fault functions.

2.3 Natural Risk Assessment and Mitigation

This research activity aims at developing statistical tools useful for the management and prevention of natural risk. Specific objectives of this research activity are (i) the formulation of statistical tools and techniques for natural (mainly seismic and hydrogeological) hazard assessment [8,9,10]; (ii) the prediction of damages produced by natural events [11, 12]; (iii) the formulation of early warning/short-term forecasting strategies [10, 12]; (iv) the formulation of decision-making strategies useful for risk mitigation and prevention [10, 12].

Moreover, this research line addresses also the development of unbiased graphical estimators of location-scale distribution parameters, with an application to Pozzuoli’s bradyseism earthquake data. The advantage of graphical estimation lies in its ability to facilitate statistical understanding and communication with non-statisticians through visual inspection and model fit evaluation [13].

2.4 Statistical Learning and Monitoring of Complex Data from Industrial Processes

The realm of high-performance computational capabilities of modern Industry 4.0 has made feasible the acquisition of massive and complex amounts of data that are well represented as mathematical objects at different levels of complexity, from scalar quantities to vectors, curves, surfaces, and manifolds. These pose new challenges in the development of methods that, to really add value to the industrial practice, must be also interpretable, i.e., able to support human decisions based on it in a transparent way. Interpretability [14] is in fact the key issue of the statistical learning and monitoring techniques developed by this group, according to its background and legacy. The main challenges faced through this research line with the higher acknowledged impact on industrial practice are presented in the following.

The first is based on the extension of traditional statistical learning techniques, such as regression and clustering, to data observed in the form of profiles, i.e., functions varying over a continuum. Along this line, novel and more interpretable estimators for functional regression coefficient functions [15, 16] as well for functional cluster analysis are developed [17]. These methods are then applied to map a resistance spot welding (RSW) process in the automotive industry where online sensor data in the form of profiles could be used in place of destructive off-line tests. Moreover, an extended version of regression stacking is developed to address the forecasting of electricity demand at the individual household level for future grid management systems [18].

The second challenge is the development of methods that, to the best possible extent, are insensible to the presence of anomalous observations, which almost always affect the analysis of industrial data and the relative process monitoring, especially in complex and high-dimensional settings. On this path, the well-known analysis of variance method is extended in a non-parametric framework able to mitigate the influence of outliers, ensuring more accurate and reliable data interpretation in real-world applications such as the additive manufacturing process [19].

The same applies to statistical process monitoring (SPM), which represents the third challenge, where a novel approach, called the robust multivariate functional control chart (RoMFCC), is developed for the multivariate profile monitoring of an RSW process when functional outliers contaminated at least one multivariate functional component. The RSW process was also the motivating case study for the development of efficient monitoring schemes, named adaptive multivariate functional EWMA (AMFEWMA) control chart. Within the SPM challenge and the activities of the industrial engineering department, the SFERe group was called to develop a real-time monitoring procedure for \(\text {CO}_2\) emissions in maritime transportation and integrate information, usually available, on mission profile and operating conditions in the form of functional data [20,21,22]. To improve flexibility, the use of artificial neural networks (NNs) is also explored for the SPM of multiple stream processes (MSPs) through functional and non-functional multivariate data and is applied to signals characterizing systems of railway passenger vehicles. When instead the aim is only the performance comparison of two processes, which often arises in industrial production, a Bayesian control chart is developed for monitoring the ratio of Weibull percentiles [23,24,25].

The fourth challenge contributes to the application of process capability indices with mathematical criticism and remedies for the right design of lot sample size and critical acceptance value in variable sampling inspection schemes [26, 27].

Based on the aforementioned research lines, we list the main R packages and Python libraries developed by the research group, emphasizing their pivotal role in advancing this field and promoting research reproducibility: [R] funcharts; sasfunclust; rofanova; slasso; [Python] NN4MSP; NN4OCMSP.

2.5 Statistical Methods for the Evaluation of Automotive and Aircraft Seat Comfort

This research aims to develop statistical methods for planning and analyzing experiments in physical or virtual reality to diagnose and improve automotive and aircraft seating comfort. New comfort indexes based on seat interface pressure have been proposed as a good proxy of overall subjective comfort perceptions [28, 29].

2.6 Quality of Subjective Evaluations Expressed as Ratings or Preferences

This research proposes a metrological approach to assess the quality of subjective evaluations. In the absence of a gold standard for defining the reproducibility and the repeatability of subjective judgements, the agreement between ratings [30, 31] and the similarity between preferences are proposed as useful tools for measuring the rater’s evaluative performance [32]. Through extensive Monte Carlo simulation studies, the statistical behaviour of the suggested repeatability and reproducibility measures has been investigated under different scenarios in order to provide recommendations for their correct use [33, 34].

2.7 Evaluation of Classifier Predictive Performance

The evaluation of classifier predictive performance is a relevant issue in order to assess the results of the classification process as well as to obtain a datum that must be optimized by tuning classifier parameters. In this research, the behaviour of several measures of classifier predictive performance is investigated under different class imbalance conditions [35]. The effects of class imbalance on the behaviour of the investigated classifier performance measures are assessed by comparing the performance of several machine learning algorithms in real case studies as well as with artificial datasets [36].

2.8 Deep Learning for Smart and Sustainable Agriculture

The research aims to exploit machine learning and deep learning methods to develop tools for accurate yield prediction and plant disease detection. The proposed strategies have shown higher predictive performance with respect to the conventional strategies based on destructive sampling and visual inspections, providing flexible tools that can be deployed as an aid for the sustainable management of farming activities with a positive impact on sustainability in terms of reduction of product waste, costs, labour and time.