Marta RINALDI | Statistics and Safety of Production Systems

cod. 0612600017

STATISTICS AND SAFETY OF PRODUCTION SYSTEMS

	0612600017
	DEPARTMENT OF INDUSTRIAL ENGINEERING
	EQF6
	INDUSTRIAL ENGINEERING AND MANAGEMENT
	2025/2026

PERCORSO IN COMMON Cohort 2023/2024

	OBBLIGATORIO
	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2018
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
1	STATISTICA E SICUREZZA DEI SISTEMI PRODUTTIVI
	SECS-S/02	6	60	LESSONS	BASIC COMPULSORY SUBJECTS
2	STATISTICA E SICUREZZA DEI SISTEMI PRODUTTIVI
	ING-IND/17	6	60	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	MASSIMILIANO DE IULIIS1 T Curriculum
	MARTA RINALDI2 Curriculum

	Objectives
	Knowledge and understanding of: Definitions of random variables and main distributions and their moments; evaluation of probability of events; inference and decision on a statistical basis; analysis of variance and linear regression analysis. Ability to apply knowledge and understanding The student will be able to solve problems involving the evaluation of probability of events, the estimation of unknown parameters and the verification of hypotheses regarding non-deterministic phenomena, the identification and application of simple empirical models for the quantitative analysis of physical and/or technological phenomena. In a design context, the student will be able to identify the variables for which it is necessary to use the tools of statistical analysis and apply such tools. Autonomy of judgment The student will be able to apply methods and tools to analyze the effect of different factors on a phenomenon of interest and make quantitative comparisons between them. Communication skills The student will be able to present both orally and in writing a topic related to the probabilistic evaluation of a random phenomenon. Will be able to present the topics of statistical data analysis in a correct and exhaustive manner. Learning ability The student will be able to apply the knowledge acquired to contexts different from those presented during the course. The student will be able to use different sources for the in-depth study of the methodologies introduced in the course. The student will be able to use methods and tools to plan the collection of data in order to allow objective analyses of the problem discussed.

Knowledge and understanding of:
Definitions of random variables and main distributions and their moments; evaluation of probability of events;
inference and decision on a statistical basis; analysis of variance and linear regression analysis.

Ability to apply knowledge and understanding
The student will be able to solve problems involving the evaluation of probability of events, the estimation of unknown parameters and the verification of hypotheses regarding non-deterministic phenomena, the identification and application of simple empirical models for the quantitative analysis of physical and/or technological phenomena.

In a design context, the student will be able to identify the variables for which it is necessary to use the
tools of statistical analysis and apply such tools.

Autonomy of judgment
The student will be able to apply methods and tools to analyze the effect of different factors on a
phenomenon of interest and make quantitative comparisons between them.

Communication skills
The student will be able to present both orally and in writing a topic related to the probabilistic evaluation of a
random phenomenon. Will be able to present the topics of statistical data analysis in a correct and exhaustive manner.

Learning ability
The student will be able to apply the knowledge acquired to contexts different from those presented during the course. The student will be able to
use different sources for the in-depth study of the methodologies introduced in the course.
The student will be able to use methods and tools to plan the collection of data in order to allow objective analyses of the problem discussed.

	Prerequisites
	TO ACHIEVE THE SET OBJECTIVES, BASIC MATHEMATICAL KNOWLEDGE AND SET THEORY ARE REQUIRED. PREREQUISITES: MATHEMATICS I.

	Contents
	- INTRODUCTION TO STATISTICS, DESCRIPTIVE STATISTICS, ORGANIZATION AND DESCRIPTION OF DATA, POSITION AND DISPERSION INDEXES, GRAPHICAL REPRESENTATION OF DATA, CHEBYSHEV INEQUALITY, NORMAL SAMPLES, BIVARIATE SAMPLE SETS, CORRELATION COEFFICIENT AND REGRESSION LINE (THEORY, EXERCISE, LABORATORY) (4,2,0) - ELEMENTS OF PROBABILITY CALCULATION: DEFINITION OF PROBABILITY, VENN DIAGRAMS AND EVENT ALGEBRA, AXIOMS OF PROBABILITY, CONDITIONAL PROBABILITY, TOTAL PROBABILITY THEOREM, BAYES FORMULA, INDEPENDENT EVENTS (6,3,0) RANDOM VARIABLES: DISCRETE AND CONTINUOUS VARIABLES, VECTORS OF RANDOM VARIABLES, JOINT DISTRIBUTION OF RANDOM VARIABLES, EXPECTED VALUE AND VARIANCE, COVARIANCE OF RANDOM VARIABLES, MOMENT GENERATING FUNCTION, WEAK LAW OF LARGE NUMBERS (6,3,0) - MODELS OF RANDOM VARIABLES: BERNOULLI AND BINOMIAL VARIABLES, POISSON AND HYPERGEOMETRIC VARIABLES, UNIFORM, GAUSSIAN AND EXPONENTIAL VARIABLES, DISTRIBUTIONS DERIVED FROM THE NORMAL DISTRIBUTION: CHI-SQUARE, STUDENT'S T, FISHER'S F (6,3,0) - SAMPLING DISTRIBUTIONS: SAMPLE MEAN, CENTRAL LIMIT THEOREM, SAMPLE VARIANCE, DISTRIBUTION OF STATISTICS OF NORMAL POPULATIONS, DISTRIBUTION OF STATISTICS RELATING TO THE PROPORTION IN A POPULATION (6,3,0) - PARAMETRIC ESTIMATING: MAXIMUM LIKELIHOOD ESTIMATORS, CONFIDENCE INTERVALS OF THE MEAN FOR KNOWN AND UNKNOWN VARIANCE, CONFIDENCE INTERVALS FOR NORMAL DISTRIBUTION, FOR THE DIFFERENCE OF THE MEAN, FOR THE VARIANCE, FOR THE MEAN OF A PROPORTION, FOR THE MEAN OF AN EXPONENTIAL DISTRIBUTION (6,3,0) - HYPOTHESIS TESTING: INTRODUCTION TO THE PROBLEM, SIGNIFICANCE LEVELS, HYPOTHESIS ON THE MEAN OF A POPULATION (KNOWN AND UNKNOWN VARIANCE), HYPOTHESIS ON THE EQUALITY OF THE MEAN, HYPOTHESIS ON THE VARIANCE OF A NORMAL POPULATION, HYPOTHESIS ON A PROPORTION, HYPOTHESIS ON THE MEAN OF A POISSON DISTRIBUTION. (6,3,0)

Contents

- INTRODUCTION TO STATISTICS, DESCRIPTIVE STATISTICS, ORGANIZATION AND DESCRIPTION OF DATA, POSITION AND DISPERSION INDEXES, GRAPHICAL REPRESENTATION OF DATA, CHEBYSHEV INEQUALITY, NORMAL SAMPLES, BIVARIATE SAMPLE SETS, CORRELATION COEFFICIENT AND REGRESSION LINE (THEORY, EXERCISE, LABORATORY) (4,2,0)
- ELEMENTS OF PROBABILITY CALCULATION: DEFINITION OF PROBABILITY, VENN DIAGRAMS AND EVENT ALGEBRA, AXIOMS OF PROBABILITY, CONDITIONAL PROBABILITY, TOTAL PROBABILITY THEOREM, BAYES FORMULA, INDEPENDENT EVENTS (6,3,0)
RANDOM VARIABLES: DISCRETE AND CONTINUOUS VARIABLES, VECTORS OF RANDOM VARIABLES, JOINT DISTRIBUTION OF RANDOM VARIABLES, EXPECTED VALUE AND VARIANCE, COVARIANCE OF RANDOM VARIABLES, MOMENT GENERATING FUNCTION, WEAK LAW OF LARGE NUMBERS (6,3,0)
- MODELS OF RANDOM VARIABLES: BERNOULLI AND BINOMIAL VARIABLES, POISSON AND HYPERGEOMETRIC VARIABLES, UNIFORM, GAUSSIAN AND EXPONENTIAL VARIABLES, DISTRIBUTIONS DERIVED FROM THE NORMAL DISTRIBUTION: CHI-SQUARE, STUDENT'S T, FISHER'S F (6,3,0)
- SAMPLING DISTRIBUTIONS: SAMPLE MEAN, CENTRAL LIMIT THEOREM, SAMPLE VARIANCE, DISTRIBUTION OF STATISTICS OF NORMAL POPULATIONS, DISTRIBUTION OF STATISTICS RELATING TO THE PROPORTION IN A POPULATION (6,3,0)
- PARAMETRIC ESTIMATING: MAXIMUM LIKELIHOOD ESTIMATORS, CONFIDENCE INTERVALS OF THE MEAN FOR KNOWN AND UNKNOWN VARIANCE, CONFIDENCE INTERVALS FOR NORMAL DISTRIBUTION, FOR THE DIFFERENCE OF THE MEAN, FOR THE VARIANCE, FOR THE MEAN OF A PROPORTION, FOR THE MEAN OF AN EXPONENTIAL DISTRIBUTION (6,3,0)
- HYPOTHESIS TESTING: INTRODUCTION TO THE PROBLEM, SIGNIFICANCE LEVELS, HYPOTHESIS ON THE MEAN OF A POPULATION (KNOWN AND UNKNOWN VARIANCE), HYPOTHESIS ON THE EQUALITY OF THE MEAN, HYPOTHESIS ON THE VARIANCE OF A NORMAL POPULATION, HYPOTHESIS ON A PROPORTION, HYPOTHESIS ON THE MEAN OF A POISSON DISTRIBUTION. (6,3,0)

	Teaching Methods
	THE COURSE INCLUDES 60 HOURS OF TEACHING BETWEEN LESSONS AND EXERCISES (6 CFU). IN PARTICULAR, 40 HOURS OF CLASSROOM LESSONS AND 20 HOURS OF CLASSROOM EXERCISES ARE PLANNED. ATTENDANCE IN THE TEACHING COURSES IS STRONGLY RECOMMENDED.

	Verification of learning
	THE EXAM IS AIMED AT ASSESSING AS A WHOLE: KNOWLEDGE AND ABILITY TO UNDERSTAND THE CONCEPTS PRESENTED IN THE COURSE; THE ABILITY TO APPLY SUCH KNOWLEDGE TO SOLVING PROBLEMS INVOLVING THE EVALUATION OF PROBABILITY OF EVENTS, THE ESTIMATION OF UNKNOWN PARAMETERS AND THE VERIFICATION OF HYPOTHESES CONCERNING NON-DETERMINISTIC PHENOMENA, THE IDENTIFICATION OF SIMPLE EMPIRICAL MODELS FOR THE QUANTITATIVE ANALYSIS OF PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA. THE FOLLOWING ARE ALSO ASSESSED: INDEPENDENT JUDGMENT, THE ABILITY TO PRESENT PROBLEMS IN A CLEAR AND EXHAUSTIVE FORM, AND THE ABILITY TO LEARN. THE EXAM CONSISTS OF A WRITTEN TEST, AIMED AT ASSESSING THE CANDIDATE'S SKILLS IN SETTING UP AND SOLVING TYPICAL PROBLEMS CONCERNING THE TOPICS PRESENTED IN THE COURSE, WITH PARTICULAR REFERENCE TO: 1) ANALYSIS OF A SAMPLE OF DATA: CALCULATION OF THE MAIN STATISTICAL INDICATORS AND REPRESENTATION OF DATA; 2) SOLUTION OF PROBLEMATIC SITUATIONS THAT REFER TO THE CONCEPT OF PROBABILITY AND THE DEFINITION OF RANDOM VARIABLE 3) STATISTICAL INFERENCE: CALCULATION OF ESTIMATORS, CONFIDENCE INTERVALS, DECISIONS ON A STATISTICAL BASIS; THE WRITTEN TEST IS AWARDED WITH A SCORE OUT OF THIRTY, WHICH TAKES INTO ACCOUNT BOTH THE CORRECTNESS OF THE PROBLEM LAYOUT AND THE CORRECTNESS OF THE RESULTS. AN SCORE OF “INSUFFICIENT” WILL REQUIRE THE WRITTEN TEST TO BE REPEAT. THE STUDENT MAY ALSO ASK TO TAKE AN ORAL INTERVIEW AFTER THE WRITTEN TEST. THIS INTERVIEW WILL BE MAINLY AIMED AT ASCERTAINING KNOWLEDGE OF THE SUBJECT MATTER OF THE COURSE, EVEN ON THE PARTS NOT DIRECTLY INVOLVED IN THE WRITTEN TEST, AND IT WILL BE AWARDED WITH A SCORE OUT OF THIRTY. THE OVERALL FINAL ASSESSMENT WILL BE OBTAINED BY WEIGHING THE OUTCOME OF THE WRITTEN EXAM FOR 60% AND THE OUTCOME OF THE ORAL EXAM FOR 40%. FAILURE TO PASS THE ORAL EXAM REQUIRES THE REPEATING OF THE WRITTEN EXAM. THE LEVEL OF SUFFICIENCY CORRESPONDS TO THE DEMONSTRATION OF THE ABILITY TO IDENTIFY THE METHODOLOGICAL TOOLS TO USE, TO CORRECTLY SET UP THE MODEL EQUATIONS AND TO INDICATE PATHWAYS TO SOLVE THE PROBLEM. THE LEVEL OF EXCELLENCE IS REACHED WHEN THE STUDENT SHOWS HIMSELF ABLE TO SUCCESSFULLY DEAL WITH ASPECTS OF THE PROBLEMS NOT EXPLICITLY COVERED IN CLASS. THE EVALUATION DEPENDS ON THE LEVEL OF EXPOSURE AND THE DEGREE OF CONFIDENCE SHOWN WITH THE TEACHING TOPICS AND WITH THE METHODOLOGICAL TOOLS WHOSE USE HAS BEEN DESCRIBED IN THE COURSE.

Verification of learning

THE EXAM IS AIMED AT ASSESSING AS A WHOLE: KNOWLEDGE AND ABILITY TO UNDERSTAND THE CONCEPTS PRESENTED IN THE COURSE; THE ABILITY TO APPLY SUCH KNOWLEDGE TO SOLVING PROBLEMS INVOLVING THE EVALUATION OF PROBABILITY OF EVENTS, THE ESTIMATION OF UNKNOWN PARAMETERS AND THE VERIFICATION OF HYPOTHESES CONCERNING NON-DETERMINISTIC PHENOMENA, THE IDENTIFICATION OF SIMPLE EMPIRICAL MODELS FOR THE QUANTITATIVE ANALYSIS OF PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA. THE FOLLOWING ARE ALSO ASSESSED: INDEPENDENT JUDGMENT, THE ABILITY TO PRESENT PROBLEMS IN A CLEAR AND EXHAUSTIVE FORM, AND THE ABILITY TO LEARN.

THE EXAM CONSISTS OF A WRITTEN TEST, AIMED AT ASSESSING THE CANDIDATE'S SKILLS IN SETTING UP AND SOLVING TYPICAL PROBLEMS CONCERNING THE TOPICS PRESENTED IN THE COURSE, WITH PARTICULAR REFERENCE TO: 1) ANALYSIS OF A SAMPLE OF DATA: CALCULATION OF THE MAIN STATISTICAL INDICATORS AND REPRESENTATION OF DATA; 2) SOLUTION OF PROBLEMATIC SITUATIONS THAT REFER TO THE CONCEPT OF PROBABILITY AND THE DEFINITION OF RANDOM VARIABLE 3) STATISTICAL INFERENCE: CALCULATION OF ESTIMATORS, CONFIDENCE INTERVALS, DECISIONS ON A STATISTICAL BASIS; THE WRITTEN TEST IS AWARDED WITH A SCORE OUT OF THIRTY, WHICH TAKES INTO ACCOUNT BOTH THE CORRECTNESS OF THE PROBLEM LAYOUT AND THE CORRECTNESS OF THE RESULTS. AN SCORE OF “INSUFFICIENT” WILL REQUIRE THE WRITTEN TEST TO BE REPEAT.

THE STUDENT MAY ALSO ASK TO TAKE AN ORAL INTERVIEW AFTER THE WRITTEN TEST. THIS INTERVIEW WILL BE MAINLY AIMED AT ASCERTAINING KNOWLEDGE OF THE SUBJECT MATTER OF THE COURSE, EVEN ON THE PARTS NOT DIRECTLY INVOLVED IN THE WRITTEN TEST, AND IT WILL BE AWARDED WITH A SCORE OUT OF THIRTY. THE OVERALL FINAL ASSESSMENT WILL BE OBTAINED BY WEIGHING THE OUTCOME OF THE WRITTEN EXAM FOR 60% AND THE OUTCOME OF THE ORAL EXAM FOR 40%. FAILURE TO PASS THE ORAL EXAM REQUIRES THE REPEATING OF THE WRITTEN EXAM.

THE LEVEL OF SUFFICIENCY CORRESPONDS TO THE DEMONSTRATION OF THE ABILITY TO IDENTIFY THE METHODOLOGICAL TOOLS TO USE, TO CORRECTLY SET UP THE MODEL EQUATIONS AND TO INDICATE PATHWAYS TO SOLVE THE PROBLEM.
THE LEVEL OF EXCELLENCE IS REACHED WHEN THE STUDENT SHOWS HIMSELF ABLE TO SUCCESSFULLY DEAL WITH ASPECTS OF THE PROBLEMS NOT EXPLICITLY COVERED IN CLASS.
THE EVALUATION DEPENDS ON THE LEVEL OF EXPOSURE AND THE DEGREE OF CONFIDENCE SHOWN WITH THE TEACHING TOPICS AND WITH THE METHODOLOGICAL TOOLS WHOSE USE HAS BEEN DESCRIBED IN THE COURSE.

	Texts
	APPUNTI DELLE LEZIONI. S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO. M. DE IULIIS, ESERCIZI RISOLTI DI STATISTICA E CALCOLO DELLE PROBABILITA', LIBRERIA UNIVERSITARIA TESTI DI APPROFONDIMENTO G.E.P. BOX, W.G. HUNTER, J.S. HUNTER, STATISTICS FOR EXPERIMENTERS (AN INTRODUCTION TO DESIGN, DATA ANALYSIS AND MODEL BUILDING), WILEY. N. DRAPER, H. SMITH, APPLIED REGRESSION ANALYSIS (SECOND EDITION), WILEY

Texts

APPUNTI DELLE LEZIONI.
S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO.
M. DE IULIIS, ESERCIZI RISOLTI DI STATISTICA E CALCOLO DELLE PROBABILITA', LIBRERIA UNIVERSITARIA

TESTI DI APPROFONDIMENTO
G.E.P. BOX, W.G. HUNTER, J.S. HUNTER, STATISTICS FOR EXPERIMENTERS (AN INTRODUCTION TO DESIGN, DATA ANALYSIS AND MODEL BUILDING), WILEY.
N. DRAPER, H. SMITH, APPLIED REGRESSION ANALYSIS (SECOND EDITION), WILEY

	More Information
	Teaching is provided in Italian

Lessons Timetable

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2025-10-07]

Marta RINALDI | Statistics and Safety of Production Systems