B025500 - INDUSTRIAL STATISTICS

Italian

The course is based on the following learning items:
1) Introduction, basic notation
2) Descriptive statistics
3) Probability
4) Statistical inference
5) Linear regression model

Sheldon M. Ross. Introduction to Probability and Statistics for Engineers and Scientists. Apogeo, Milano, 2003

Knowledge
Knowledge of descriptive statistics for preliminary data analysis (cc1). Knowledge of probability axioms (cc1). Knowledge of inferential procedures (cc1). Knowledge of the main probability models to assess random variables in the industrial context (cc6). Knowledge of the theoretical principles of inference and of statistical methods with application to the industrial context (cc6). Knowledge of inferential methods for hypothesis testing oriented to problem solving in a cross-disciplinary contexts (cc7). Knowledge of statistical models for strategical analysis in business and industrial contexts. Knowledge of weakness of the statistical methods for the analysis of real data (cc9).

Capability of applying knowledge
Capability for solving issues of probability, parametric estimation and hypothesis testing through the inferential statistical techniques (ca1). Capability for solving issues of management engineering through the application of statistical models in uncertainty frameworks (ca1, ca3). Capability for the selection of suitable statistical methodologies for industrial engineering problem solving (ca5). Capability for the application of knowledge in probability and inference for the analysis of cross-disciplinary random events (ca8).

Mathematics

Teaching activity is mainly based on frontal classes (with slides), furthermore an optional working group activity is planned (see “Altre informazioni” section for details) aimed (i) to establish knowledge of theoretical topics and (i) to apply such knowledge in the context of management and industrial engineering. During frontal classes the R statistical software is briefly introduced to show how to generate random sample from probability distributions, the probability distribution convergence (central limit theorem), the estimators properties and the linear model estimation.
Full teaching material (slide, information, tutorial, example of written exams) is available in Moodle.

Working group activity for students attending the course (optional): some exercises, assigned one/two weeks in advance to group of students, are developed during frontal classes.

Assessment methods are based on a written exam including exercises with varying difficult levels, including challenging exercises to reward excellent students. Rewards are also considered for students who joined the working group activity (see “Altre informazioni” section for details). Knowledge about R software is not under assessment.

Introduction to statistics. Sampling data. Notation. Principal descriptive statistical indicators, graphical representations, frequency tables, sampling statistics. Average and variability indicators. Cumulative function and histogram. Chebyshev inequality. Sample linear correlation, covariance.
Introduction to probability. Sample space, union and intersection of events, conditional events. Probability axioms. Classical, frequentist and Bayesian approach to probability. Marginal, joint and conditional probability. Bayes theorem. Independence. Discrete and continuous random variables. Probability function, probability density function, cumulative probability function. Expected value and variance. Linear combination of independent/non-independent random variables. Covariance. Discrete probability models: uniform, Bernoulli, binomial, Poisson, negative binomial, ipergeometric. Continuous probability models: uniform, Gaussian, exponential, chi-square, gamma, F-Fisher, t-Student. Introduction to inference. Random sampling. Sample statistics, sample mean and variance; sample proportion and their distributions. Central limit theorem. Parametric estimation, maximum likelihood estimators. Confidence interval for mean in Gaussian population in case the variance is known-unknown. Confidence interval for variance in Gaussian population in case the mean is known-unknown. Confidence interval for Bernoulli parameter for large samples. Confidence interval for difference of mean and proportion in two independent samples. Confidence interval for prediction of Gaussian variables. Efficiency of estimators. Bayesian estimators. Hypothesis testing, significant level, type I and type II error, power of a test. Hypothesis testing for the mean in case the variance is known/unknown. Hypothesis testing for the variance in case the mean is known/unknown. Hypothesis testing for the proportion in large samples. Hypothesis testing for the mean and the proportion difference in two independent samples. p-value. Linear regression models, maximum likelihood estimators. Confidence intervals and hypothesis testing for model parameters and prediction.