In Industry 4.0 factories, innovative prediction tools are adopted so that data can be systematically processed into information that can explain uncertainties and support decisions. Predictive manufacturing systems begin with acquiring data from monitored assets using appropriate sensors to extract various signals. These signals can then be integrated with historical data into extensive datasets containing a multitude of variables. Consequently, addressing the challenge of reducing dimensionality becomes of paramount importance. Dimension reduction techniques such as partial least squares (PLS) have recently gained attention to deal with the problem of big datasets with a large number of correlated variables. Standard PLS approaches confine the estimation to examining only average effects, resulting in an insufficient portrayal. In this paper, we combine the standard PLS technique with M-quantile regression. The proposed approach aims at offering a more comprehensive view of the effect of various dimensions on the degradation of etching equipment in the microchip fabrication process.

This paper addresses the critical issue of road safety and accident prevention by integrating road features, network theory, and advanced statistical models. It emphasises the importance of understanding the relationship between road infrastructure and accident risk, which impacts on various administrative stakeholders and on citizens’ safety. While existing literature focuses on road features and engineering solutions, this paper highlights the need to consider implicit spatial constraints as well. Our study builds on prior research by proposing a novel approach that merges conditional autoregressive modelling with a two-stage mixed Geographically weighted Poisson regression. This integrated methodology allows us to consider both the effect of risk factors at a global level and at a local road level. By leveraging the strengths of these two methods, we aim to capture both overarching trends and local variations of risk factors, thereby offering a comprehensive understanding of accident risk factors. Using data from the Open Street Map database, which covers the wide province of Milan in Italy, our models identify influential street characteristics, providing valuable insights for informed decision-making regarding road safety measures. Our method can be applied to any region in the world. The paper describes the models used, the dataset employed, and presents a detailed numerical analysis demonstrating the effectiveness of the approach in identifying and understanding accident risk factors within road networks. This information can help guide investments for the benefit of society.

We explore the quantification of demographic risk in accordance with the market-consistent actuarial valuation principles. Our contribution includes closed formulas for assessing the inflows and outflows of an insurance policy portfolio using a cohort approach. To maintain versatility, we address both traditional and equity-linked policies, providing a market-consistent valuation of liabilities. Subsequently, we compute the capital requirement for idiosyncratic risk (linked to accidental mortality) and systematic risk (trend risk), presenting an approach that allows consideration of the risks at cohort level. Specifically, we evaluate the minimum capital using an annual time horizon, a 99.5% confidence level, and the Value at Risk as the risk measure, developing a framework aligned with the European Solvency II regulation for insurance and reinsurance companies. Moreover, the model can be easily adapted to accommodate other regulatory frameworks, incorporating specific rules and accounting principles relevant to diverse jurisdictions worldwide. The numerical analysis and the sensitivities reveal that the accidental volatility of policyholders' deaths is influenced by the inherent characteristics of the cohort's policies, the age of policyholders, and the variability of sums insured. Furthermore, trend risk is contingent on both accidental volatility and the longevity forecasting model employed.

Within the insurance field, the digital revolution has enabled the collection and storage of large quantities of information [...]

Process capability indices are routinely used to estimate the mean-variability performance of industrial products with respect to both targets and specification limits. However, when the target variable is defined over a planar surface of a manufact, it is relevant to assess the capability of the production process locally, that is, at any spatial location of the surface, in particular if the manufact has to be split into pieces to obtain single production items. In this article, focusing on the Cpk specification introduced by Clements [Qual Prog., 22, 95-100], we suggest an approach based on additive quantile models to estimate, in a Bayesian paradigm, the index locally. We demonstrate its use in the context of the etching phase of the integrated circuit fabrication process. Since capability of etching processes is typically assessed for batches of wafers, we also propose two algorithms based on resampling to perform local capability analysis at the lot level.

Every day, insurance companies collect an enormous quantity of text data from multiple sources. We present a strategy to make beneficial use of the large amount of information available in documents by exploiting natural language processing. After a brief review of the basics of text mining, we describe a case study in which, by analyzing the accident narratives written by the researchers of the National Highway Traffic Safety Administration of the U.S. Department of Transportation, we aim to extract latent information that can be used to fine-tune policy premiums. The process involves two steps. First, we classify the reports according to the relevance of their content to determine the risk profiles of the people involved. Next, we use these profiles to create new latent risk covariates for a company’s ratemaking process. Address for Correspondence: diego.zappa@unicatt.it

Car accident causes are relevant both for insurance companies as well as for policy makers. The former are interested into the dynamics of the accidents in order to evaluate responsibilities, the latter to foster good driving behavior for the sake of social benefit, too. By using a large set of medical and police reports, and by exploiting Natural Language Processing techniques we aim at grasping latent information useful to classify them according to the relevance of their content.

Starting from the Markowitz’s formula for a portfolio we compute the solutions for three structures of dependencies and use acyclic directed graphs (DAGs) to represent the structures. Same levels of returns and volatilities are adopted for all assets in order to focus just on the role of correlations. We start with two structures of dependencies among three assets. We then compute the optimal solution for a four assets portfolio whose DAG is the superposition of the previous patterns.

In this article, we investigate the occurrence of defects in integrated circuit fabrication and show how spatial analysis can be effective in grasping and representing spatial regularities in defect patterns on the silicon supports, called wafers, used to produce microchips. Defects occurring on the wafer surface are the main cause of yield loss in the semiconductor industry; hence, to promptly detect an excess of defects and identify their spatial structure is crucial to the entire fabrication process. To address this hard-to-solve problem, this article proposes a concatenation of different methods, namely, a control chart, a clustering algorithm, and a graphical tool. First, a control chart based on the p-value of an appropriate test recognizes spatially structured defects on the wafer area. Then a clustering procedure grounded on the minimum spanning tree algorithm is adopted to identify those regions more prone to defect occurrences. Finally, alpha-shapes are employed to display their shape effectively. The suggested procedure proves to be extremely fast and effective, allowing its implementation in-line during the fabrication process. This provides a great advantage in modern microelectronics where items tend to be highly specialized and often produced in small lots. In particular, due to the Monte Carlo nature of the procedure, the control chart proposed hereafter does not require gold standard data to be set. This is particularly advantageous for small lot production, which is typically limited in time and does not permit to collect long time series of the charting statistics.

Worldwide, thousands of people die annually in highway-related crashes and millions are injured. Hence, car wrecks have very high direct social costs but also relevant indirect economic effects such as an adverse impact on the burden of hospitalization and an increased health expenditure. The analysis of car crash data has long been used as a basis for influencing highway and vehicle designs but also, and perhaps more importantly, to support local authorities in allocating resources aimed at improving road safety and making political decisions to mitigate road risks in the most exposed areas. In this paper, we show how a range of information collected from open data sources concerning the structure of the road network (road typology, traffic lights, pedestrian crossings, etc.), socio-demographical dimensions and crash history can be proficiently used for this aim. We adopt a dynamic Zero Inflated Poisson (ZIP) regression model to define two indexes. The first index, derived from the counting component of the ZIP model, measures how prone to crash risk a segment is. The other, derived by the zero component of the ZIP model, represents a measure of the likelihood of segments to not be exposed to crashes. Focussing on the city of Milan (Northern Italy), we found that the most relevant determinant of road risk proneness is crash history and that structural characteristics of the road are much more relevant than demographic information. Finally, we show how this information can be spatialized to produce maps of crash proneness and predict future spatial risk indexes.

Process capability indices are widely used to check quality standards both at the production level and for business activity. They consider the location and the deviation from specification limits and targets. The literature contains many contributions on this topic both in the univariate and the multivariate context. Motivated by a real semiconductor case study, we discuss the role of rational subgroups and the challenge they present in the computation of capability indices, especially when data refer to lots of products. In addition, our context involves a mix of problems: unilateral specification limit, nonsymmetric distribution of the data, evidence of data from a mixture of distributions, and the need to filter one component of the mixture. After solving the previous issues and because of the peculiar characteristics of semiconductor processes based on the so called “wafers,” we contribute to the literature a proposal on how to compute capability indices in the case of heteroscedastic spatial processes. With a generalized additive model, we show that it is possible to estimate a capability surface that allows the identification of regions expected to not be fully compliant with the desired quality standards.

The problem related to the identification of a change in time series trajectories plays a crucial role in many contexts. In this paper, we propose a flexible and computationally efficient procedure for turning point identification based on hypothesis testing applied to the difference between two consecutive slopes in a rolling regression framework. Along with the description of the methodology, to measure the performance of the method we have applied it to the S&P 500 Stock Index and its subsector indices. By using an in‐sample/out‐of‐sample approach we compare results with the profit/losses we could obtain by using the moving average crossover strategy. Results show that the operating signals obtained by our proposal may better enable financial analysts to make profitable decisions. Finally we present an extensive simulation study to show the weaknesses and strengths of the proposal under different expected returns and volatility scenarios.

In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analyzed by exploiting the Fisher-Lange average cost method.

We propose a model to extract significant risk spatial interactions between countries adopting the Graphical Lasso algorithm, used in graph theory to sort out spurious conditional correlations. In this context, the major issue is the definition of the penalization parameter. We propose a search algorithm aimed at the best separation of the variables (expressed in terms of conditional dependence) given an a priori desired partition. The case study focuses on Credit Default Swap (CDS) returns over the period 2009–2017. The proposed algorithm is used to estimate the spatial systemic risk relationship between Peripheral and Core Countries in the Euro Area.

The monitoring of spatial production processes typically involves sampling network to gather information about the status of the process. Sampling costs are often not marginal, and once the process has been accurately calibrated, it might be appropriate to reduce the dimension of the sampling grid. This aim is often achieved through the allocation of a brand new network of less dimension. In some cases that is not possible and it might be necessary the selection of a subgrid extracted from the original network. Motivated by a real semiconductor problem, we propose a method to extract a monitoring subgrid from a given one, based upon grid representativeness, accuracy, and spatial coverage of the subgrid and, if available, by expert knowledge of the weights to be assigned to those areas where production may need greater precision. Discussion is mainly focused on circular spatial domain, since, in microelectronics, the basic production support, called wafer, is a circle. Straightforward generalizations to different spatial domains are possible. Furthermore, conditionally upon the availability of experimental data, we check the loss of accuracy by fitting a dual mean‐variance response surface on the reduced grid. Joining the latter information and the criteria used to select the subgrid, we provide additional guidelines on how to fine‐tune the subgrid selection. Real case studies are used to show the effectiveness of the proposal.

Control limits are one of the main elements of control charts. Generally speaking, a control chart is the graphical display of a statistic regarding the quality characteristic of interest, computed from a sample randomly drawn from a process at different time instances. As natural variability is always present in a process, we expect some variability on the control chart. Excessive variability, owing to special cause events, is referred to as being due to an assignable cause. Otherwise, when only chance causes – also called common causes of variation – are operating, the process is said to be in statistical control. In order to make a decision about the status of the process, control limits are typically positioned so that under the hypothesis of no deviation in the process, a type I probability error corresponds to an economically acceptable average run length. In this article, we discuss in a general manner how to compute control limits, and give some remarks on how limits should be computed so as to reduce false out of control signals.