autumn meeting of industrial mathematics

Symbolic Data Analysis

Symbolic Data is concerned with representing and analysing data with intrinsic variability, which is to be taken into account. In Data Mining, Multivariate Data Analysis, and classical Statistics, the elements under analysis are generally individual entities for which a single value is recorded for each variable - e.g., individuals, described by age, salary, education level, etc. But when the elements of interest are classes or groups of some kind - the citizens living in given towns; car models, rather than specific vehicles - then there is variability inherent to the data. Symbolic data goes beyond the usual data representation model, considering variables whose observed values for each element are no longer necessarily single real values or categories, but may assume the form of sets, intervals, or, more generally, distributions. In this course, we shall introduce Symbolic Data Analysis with motivating examples. We then proceed to the definition of the new variable types and introduce alternative symbolic data representations. Multivariate analysis of interval or histogram-value data will then be addressed, following different approaches, and focusing on clustering, classification, and regression approaches.

Statistical Methods for Quality and Reliability

This course provides an introduction to the fundamental concepts of quality and reliability, including key metrics and data structures used in industrial and engineering applications. It covers statistical process control techniques, with emphasis on control charts for variables and attributes, as well as their interpretation and diagnostic use in monitoring process performance. Process capability analysis is also addressed through the study of capability indices, confidence intervals, and their practical application in industry. In the area of reliability data analysis, the course explores lifetime models, censored data, parameter estimation methods, and interpretation of reliability measures. An overview of degradation modelling and accelerated life testing is included, highlighting common modelling strategies and practical examples. Throughout the course, students engage with real-world case studies and reproducible data analyses, including implementations in software such as R.