Ana Debón

Comparing risk of failure models in water supply networks using ROC curves

Abstract The problem of predicting the failure of water mains has been considered from different perspectives and using several methodologies in engineering literature. Nowadays, it is important to be able to accurately calculate the failure probabilities of pipes over time, since water company profits and service quality for citizens depend on pipe survival; forecasting pipe failures could have important economic and social implications. Quantitative tools (such as managerial or statistical indicators and reliable databases) are required in order to assess the current and future state of networks. Companies managing these networks are trying to establish models for evaluating the risk of failure in order to develop a proactive approach to the renewal process, instead of using traditional reactive pipe substitution schemes. The main objective of this paper is to compare models for evaluating the risk of failure in water supply networks. Using real data from a water supply company, this study has identified which network characteristics affect the risk of failure and which models better fit data to predict service breakdown. The comparison using the receiver operating characteristics (ROC) graph leads us to the conclusion that the best model is a generalized linear model. Also, we propose a procedure that can be applied to a pipe failure database, allowing the most appropriate decision rule to be chosen.

Modelling and forecasting mortality in Spain

Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism. Most methods used in dynamic tables are parametric, apply traditional mortality laws and then analyse the evolution of estimated parameters with time series techniques. Our contribution consists in extending and applying Lee-Carter methods to Spanish mortality data, exploring residuals and future trends.

Modelling residuals dependence in dynamic life tables: A geostatistical approach

The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on RxR. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded into a nonseparable covariance structure. The estimated structure is then used for prediction of mortality rates, and goodness-of-fit testing is performed through some cross-validation techniques. Comments on validity and interpretation of the results are given.

Mathematical methodology to obtain and compare different embryo scores

In Vitro Fertilization (IVF) units need to decrease multiple pregnancies without affecting their overall success rate. In this study we propose a mathematical model to evaluate an embryos potential ability to implant in the uterus. Embryos are graded by the embryologist based on the number of blastomeres, evenness of growth and degree of fragmentation. Therefore, the following variables were considered: number of blastomeres produced by division of the egg after fertilisation (blastomeres), symmetry and fragmentation of the embryo (grade). This model evaluates the embryos assigning them a score which represents their quality. The main result derived from this model is the estimation of the significant improvement in the implantation rate due to the increase in blastomere values and the decrease in grade factor values. But the increase from two-three to four produces more improvement in the implantation rate than two-three to five-six blastomeres.First, statistical models were used to study embryo traceability from transfer to implantation and to evaluate the effect of the quality of the embryos (embryo score) and womens age on implantation potential. This score was obtained by making predictions from the fitted model which was used to rank embryos in terms of implantation potential. Then we totalled the scores of embryos that had been transferred to each woman for obtaining the Embryo Quality Index (EQI). In addition, we studied the effects of EQI and womens age on pregnancy. Finally, statistical techniques such as Receiver Operating Characteristics (ROC) and bootstrap procedures were used to assess the accuracy of this model. This embryo score is a quick, efficient and accurate tool to optimise embryo selection for transfers on the second day after fertilisation. This tool is especially useful for transfers involving non-top embryos.

Fault diagnosis and comparing risk for the steel coil manufacturing process using statistical models for binary data

Abstract Advanced statistical models can help industry to design more economical and rational investment plans. Fault detection and diagnosis is an important problem in continuous hot dip galvanizing. Increasingly stringent quality requirements in the automotive industry also require ongoing efforts in process control to make processes more robust. Robust methods for estimating the quality of galvanized steel coils are an important tool for the comprehensive monitoring of the performance of the manufacturing process. This study applies different statistical regression models: generalized linear models, generalized additive models and classification trees to estimate the quality of galvanized steel coils on the basis of short time histories. The data, consisting of 48 galvanized steel coils, was divided into sets of conforming and nonconforming coils. Five variables were selected for monitoring the process: steel strip velocity and four bath temperatures. The present paper reports a comparative evaluation of statistical models for binary data using Receiver Operating Characteristic (ROC) curves. A ROC curve is a graph or a technique for visualizing, organizing and selecting classifiers based on their performance. The purpose of this paper is to examine their use in research to obtain the best model to predict defective steel coil probability. In relation to the work of other authors who only propose goodness of fit statistics, we should highlight one distinctive feature of the methodology presented here, which is the possibility of comparing the different models with ROC graphs which are based on model classification performance. Finally, the results are validated by bootstrap procedures.

Risk Scoring Models for Trade Credit in Small and Medium Enterprises

Trade credit refers to providing goods and services on a deferred payment basis. Commercial credit management is a matter of great importance for most small and medium enterprises (SMEs), since it represents a significant portion of their assets. Commercial lending involves assuming some credit risk due to exposure to default. Thus, the management of trade credit and payment delays is strongly related to the liquidation and bankruptcy of enterprises. In this paper we study the relationship between trade credit management and the level of risk in SMEs. Despite its relevance for most SMEs, this problem has not been sufficiently analyzed in the existing literature. After a brief review of existing literature, we use a large database of enterprises to analyze data and propose a multivariate decision-tree model which aims at explaining the level of risk as a function of several variables, both of financial and non-financial nature. Decision trees replace the equation in parametric regression models with a set of rules. This feature is an important aid for the decision process of risk experts, as it allows them to reduce time and then the economic cost of their decisions.

A minimally invasive methodology based on morphometric parameters for day 2 embryo quality assessment

The risk of multiple pregnancy to maternal-fetal health can be minimized by reducing the number of embryos transferred. New tools for selecting embryos with the highest implantation potential should be developed. The aim of this study was to evaluate the ability of morphological and morphometric variables to predict implantation by analysing images of embryos. This was a retrospective study of 135 embryo photographs from 112 IVF-ICSI cycles carried out between January and March 2011. The embryos were photographed immediately before transfer using Cronus 3 software. Their images were analysed using the public program ImageJ. Significant effects (P < 0.05), and higher discriminant power to predict implantation were observed for the morphometric embryo variables compared with morphological ones. The features for successfully implanted embryos were as follows: four cells on day 2 of development; all blastomeres with circular shape (roundness factor greater than 0.9), an average zona pellucida thickness of 13 µm and an average of 17695.1 µm² for the embryo area. Embryo size, which is described by its area and the average roundness factor for each cell, provides two objective variables to consider when predicting implantation. This approach should be further investigated for its potential ability to improve embryo scoring.

Modelling the failure risk for water supply networks with interval-censored data

Abstract In reliability, sometimes some failures are not observed at the exact moment of the occurrence. In that case it can be more convenient to approximate them by a time interval. In this study, we have used a generalized non-linear model developed for interval-censored data to treat the life time of a pipe from its time of installation until its failure. The aim of this analysis was to identify those network characteristics that may affect the risk of failure and we make an exhaustive validation of this analysis. The results indicated that certain characteristics of the network negatively affected the risk of failure of the pipe: an increase in the length and pressure of the pipes, a small diameter, some materials used in the manufacture of pipes and the traffic on the street where the pipes are located. Once the model has been correctly fitted to our data, we also provided simple tables that will allow companies to easily calculate the pipe׳s probability of failure in a future.

Detecting spatio-temporal mortality clusters of European countries by sex and age

BackgroundMortality decreased in European Union (EU) countries during the last century. Despite these similar trends, there are still considerable differences in the levels of mortality between Eastern and Western European countries. Sub-group analysis of mortality in Europe for different age and sex groups is common, however to our knowledge a spatio-temporal methodology as in this study has not been applied to detect significant spatial dependence and interaction with time. Thus, the objective of this paper is to quantify the dynamics of mortality in Europe and detect significant clusters of mortality between European countries, applying spatio-temporal methodology. In addition, the joint evolution between the mortality of European countries and their neighbours over time was studied.MethodsThe spatio-temporal methodology used in this study takes into account two factors: time and the geographical location of countries and, consequently, the neighbourhood relationships between them. This methodology was applied to 26 European countries for the period 1990-2012.ResultsPrincipally, for people older than 64 years two significant clusters were obtained: one of high mortality formed by Eastern European countries and the other of low mortality composed of Western countries. In contrast, for ages below or equal to 64 years only the significant cluster of high mortality formed by Eastern European countries was observed. In addition, the joint evolution between the 26 European countries and their neighbours during the period 1990-2012 was confirmed. For this reason, it can be said that mortality in EU not only depends on differences in the health systems, which are a subject to national discretion, but also on supra-national developments.ConclusionsThis paper proposes statistical tools which provide a clear framework for the successful implementation of development public policies to help the UE meet the challenge of rethinking its social model (Social Security and health care) and make it sustainable in the medium term.

Mortality forecasting in Colombia from abridged life tables by sex

BackgroundAn adequate forecasting model of mortality that allows an analysis of different population changes is a topic of interest for countries in demographic transition. Phenomena such as the reduction of mortality, ageing, and the increase in life expectancy are extremely useful in the planning of public policies that seek to promote the economic and social development of countries. To our knowledge, this paper is one of the first to evaluate the performance of mortality forecasting models applied to abridged life tables.ObjectiveSelect a mortality model that best describes and forecasts the characteristics of mortality in Colombia when only abridged life tables are available.Data and methodWe used Colombian abridged life tables for the period 1973–2005 with data from the Latin American Human Mortality Database. Different mortality models to deal with modeling and forecasting probability of death are presented in this study. For the comparison of mortality models, two criteria were analyzed: graphical residuals analysis and the hold-out method to evaluate the predictive performance of the models, applying different goodness of fit measures.ResultsOnly three models did not have convergence problems: Lee-Carter (LC), Lee-Carter with two terms (LC2), and Age-Period-Cohort (APC) models. All models fit better for women, the improvement of LC2 on LC is mostly for central ages for men, and the APC model’s fit is worse than the other two. The analysis of the standardized deviance residuals allows us to deduce that the models that reasonably fit the Colombian mortality data are LC and LC2. The major residuals correspond to children’s ages and later ages for both sexes.ConclusionThe LC and LC2 models present better goodness of fit, identifying the principal characteristics of mortality for Colombia.Mortality forecasting from abridged life tables by sex has clear added value for studying differences between developing countries and convergence/divergence of demographic changes.