Ingegneria Gestionale | APPLIED STATISTICS

cod. 0622600047

APPLIED STATISTICS

	0622600047
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
	EQF7
	MANAGEMENT ENGINEERING
	2022/2023

PERCORSO IN COMMON

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	SPRING SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	SECS-S/02	6	60	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	THE AIM OF THE COURSE IS TWOFOLD: INTRODUCING THE BASIC NOTIONS OF THE PROBABILITY THEORY, TO MODEL AND ANALYZE RANDOM PHENOMENA TYPICALLY OBSERVED IN THE REAL WORLD AND, IN PARTICULAR, IN THE ENVIRONMENT AND INDUSTRY, AND PROVIDING THE MAIN TECHNIQUES FOR STATISTICAL INFERENCE. KNOWLEDGE AND UNDERSTANDING: BASIC NOTIONS OF PROBABILITY AND COMBINATORIAL CALCULUS. RANDOM VARIABLES. RELIABILITY THEORY FOR REPARABLE AND NOT REPARABLE ELEMENTS IN DIFFERENT CONFIGURATIONS. APPLIED KNOWLEDGE AND UNDERSTANDING: THE ABILITY TO MODEL AND ANALYZE RANDOM EVENTS. ABILITY TO ESTIMATE UNKNOWN QUANTITIES ON A STATISTICAL BASIS AND TO MAKE A STATISTICAL DECISION. ABILITY TO IMPLEMENT SIMPLE PROBLEMS OF LINEAR REGRESSION ANALYSIS, AND ANALYSIS OF VARIANCE. PERSONAL JUDGMENTS: THE ABILITY TO SELECT THE MOST APPROPRIATE METHOD TO ANALYZE A RANDOM PHENOMENON AND THE MOST SUITABLE STATISTICAL METHOD FOR ESTIMATING MODEL PARAMETERS AND MAKING STATISTICAL DECISIONS. COMMUNICATION SKILLS: BEING ABLE TO VERBALLY EXPLAIN OR WRITE A TOPIC OF THE COURSE, BY USING SUITABLE MATHEMATICAL STATEMENTS. LEARNING SKILLS: BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE, AND TO DEEPEN THE TOPICS USING MATERIALS OTHER THAN THOSE PROPOSED FOR THE COURSE.

THE AIM OF THE COURSE IS TWOFOLD: INTRODUCING THE BASIC NOTIONS OF THE PROBABILITY THEORY, TO MODEL AND ANALYZE RANDOM PHENOMENA TYPICALLY OBSERVED IN THE REAL WORLD AND, IN PARTICULAR, IN THE ENVIRONMENT AND INDUSTRY, AND PROVIDING THE MAIN TECHNIQUES FOR STATISTICAL INFERENCE.

KNOWLEDGE AND UNDERSTANDING: BASIC NOTIONS OF PROBABILITY AND COMBINATORIAL CALCULUS. RANDOM VARIABLES. RELIABILITY THEORY FOR REPARABLE AND NOT REPARABLE ELEMENTS IN DIFFERENT CONFIGURATIONS.

APPLIED KNOWLEDGE AND UNDERSTANDING: THE ABILITY TO MODEL AND ANALYZE RANDOM EVENTS. ABILITY TO ESTIMATE UNKNOWN QUANTITIES ON A STATISTICAL BASIS AND TO MAKE A STATISTICAL DECISION. ABILITY TO IMPLEMENT SIMPLE PROBLEMS OF LINEAR REGRESSION ANALYSIS, AND ANALYSIS OF VARIANCE.

PERSONAL JUDGMENTS: THE ABILITY TO SELECT THE MOST APPROPRIATE METHOD TO ANALYZE A RANDOM PHENOMENON AND THE MOST SUITABLE STATISTICAL METHOD FOR ESTIMATING MODEL PARAMETERS AND MAKING STATISTICAL DECISIONS.

COMMUNICATION SKILLS: BEING ABLE TO VERBALLY EXPLAIN OR WRITE A TOPIC OF THE COURSE, BY USING SUITABLE MATHEMATICAL STATEMENTS.

LEARNING SKILLS: BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE, AND TO DEEPEN THE TOPICS USING MATERIALS OTHER THAN THOSE PROPOSED FOR THE COURSE.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE OBJECTIVES, A SUITABLE KNOWLEDGE OF BASICS OF PROBABILITY THEORY AND ALGEBRA OF RANDOM VARIABLES IS REQUIRED.

	Contents
	COMPLEMENTS OF PROBABILITY THEORY AND RANDOM VARIABLES. FUNCTIONS OF ONE RANDOM VARIABLE. COUPLES OF R.V.S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.S OF COMMON USE: BERNOULLI, BINOMIAL, GEOMETRIC, NEGATIVE BINOMIAL, POISSON, UNIFORM, NORMAL, LOGNORMAL, EXPONENTIAL, GAMMA, WEIBULL. (HOURS 7/3/-) BASIC ELEMENTS OF RELIABILITY THEORY. THE OPERATIVE DEFINITION OF RELIABILITY. RELIABILITY AND UNRELIABILITY FUNCTIONS. FAILURE PROBABILITY DENSITY. MEAN LIFE. MEAN RESIDUAL LIFE. HAZARD RATE AND CUMULATIVE HAZARD RATE FUNCTIONS. RELIABILITY MODELS FOR NON-REPAIRABLE UNITS: EXPONENTIAL, WEIBULL. (HOURS 7/3/-) RELIABILITY ANALYSIS OF MULTI-COMPONENT SYSTEMS. RELIABILITY BLOCK DIAGRAMS. SERIES, PARALLEL AND SERIES-PARALLEL STRUCTURES. K-OUT-OF-N PARALLEL STRUCTURES. FAULT TREE ANALYSIS. (HOURS 7/3/-) RELIABILITY AND AVAILABILITY ANALYSIS OF REPAIRABLE SYSTEMS. STOCHASTIC POINT PROCESSES. COUNTING PROCESSES. TIME TO FAILURE AND TIME BETWEEN FAILURES. MEAN NUMBER OF FAILURES. RATE OF OCCURRENCE OF FAILURES. FAILURE INTENSITY. HOMOGENEOUS POISSON PROCESS. RENEWAL PROCESS. NON-HOMOGENEOUS POISSON PROCESS. POWER LAW PROCESS. MARKOV CHAINS AND MARKOV PROCESSES. AVAILABILITY FUNCTION. STEADY-STATE AVAILABILITY AND AVERAGE AVAILABILITY. SYSTEM AVAILABILITY. (HOURS 10/5/-) STATISTICAL METHODS FOR RELIABILITY ASSESSMENT. TYPES OF RELIABILITY DATA. NON-PARAMETRIC ESTIMATION METHODS: PLOTTING POSITIONS. ANALYTICAL METHODS OF PARAMETRIC ESTIMATION: MAXIMUM LIKELIHOOD METHOD, LINEAR ESTIMATION METHODS. GRAPHICAL METHODS FOR PARAMETRIC ESTIMATION: PROBABILITY PLOTS. ESTIMATION METHODS FOR REPAIRABLE UNITS. (HOURS 10/5/-)

Contents

COMPLEMENTS OF PROBABILITY THEORY AND RANDOM VARIABLES. FUNCTIONS OF ONE RANDOM VARIABLE. COUPLES OF R.V.S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.S OF COMMON USE: BERNOULLI, BINOMIAL, GEOMETRIC, NEGATIVE BINOMIAL, POISSON, UNIFORM, NORMAL, LOGNORMAL, EXPONENTIAL, GAMMA, WEIBULL. (HOURS 7/3/-)
BASIC ELEMENTS OF RELIABILITY THEORY. THE OPERATIVE DEFINITION OF RELIABILITY. RELIABILITY AND UNRELIABILITY FUNCTIONS. FAILURE PROBABILITY DENSITY. MEAN LIFE. MEAN RESIDUAL LIFE. HAZARD RATE AND CUMULATIVE HAZARD RATE FUNCTIONS. RELIABILITY MODELS FOR NON-REPAIRABLE UNITS: EXPONENTIAL, WEIBULL. (HOURS 7/3/-)
RELIABILITY ANALYSIS OF MULTI-COMPONENT SYSTEMS. RELIABILITY BLOCK DIAGRAMS. SERIES, PARALLEL AND SERIES-PARALLEL STRUCTURES. K-OUT-OF-N PARALLEL STRUCTURES. FAULT TREE ANALYSIS. (HOURS 7/3/-)
RELIABILITY AND AVAILABILITY ANALYSIS OF REPAIRABLE SYSTEMS. STOCHASTIC POINT PROCESSES. COUNTING PROCESSES. TIME TO FAILURE AND TIME BETWEEN FAILURES. MEAN NUMBER OF FAILURES. RATE OF OCCURRENCE OF FAILURES. FAILURE INTENSITY. HOMOGENEOUS POISSON PROCESS. RENEWAL PROCESS. NON-HOMOGENEOUS POISSON PROCESS. POWER LAW PROCESS. MARKOV CHAINS AND MARKOV PROCESSES. AVAILABILITY FUNCTION. STEADY-STATE AVAILABILITY AND AVERAGE AVAILABILITY. SYSTEM AVAILABILITY. (HOURS 10/5/-)
STATISTICAL METHODS FOR RELIABILITY ASSESSMENT. TYPES OF RELIABILITY DATA. NON-PARAMETRIC ESTIMATION METHODS: PLOTTING POSITIONS. ANALYTICAL METHODS OF PARAMETRIC ESTIMATION: MAXIMUM LIKELIHOOD METHOD, LINEAR ESTIMATION METHODS. GRAPHICAL METHODS FOR PARAMETRIC ESTIMATION: PROBABILITY PLOTS. ESTIMATION METHODS FOR REPAIRABLE UNITS. (HOURS 10/5/-)

	Teaching Methods
	THE COURSE INCLUDES THEORETICAL LESSONS AND CLASSROOM NUMERICAL EXERCISES. SOME CLASSROOM EXERCISES INVOLVING SIMPLE STATISTICAL ANALYSES ARE SOLVED BY USING STATISTICAL SOFTWARE (MATLAB).

	Verification of learning
	THE AIM OF THE EXAM IS THE ASSESSMENT OF THE KNOWLEDGE AND UNDERSTANDING CONCERNING THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, ESTIMATE UNKNOWN MODEL PARAMETERS, MAKE A DECISION BASED ON HYPOTHESES TESTING, STUDY THE EFFECTS OF PRIMARY FACTORS ON PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA AND TO ASSESS SIMPLE EMPIRICAL MODELS FOR THEM. FURTHERMORE, PERSONAL JUDGMENT, COMMUNICATION SKILLS, AND LEARNING ABILITIES ARE ALSO EVALUATED. THE FINAL EXAM CONSISTS OF A WRITTEN TEST THAT AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE. THE WRITTEN TEST IS EVALUATED BASED ON THE CORRECTNESS OF THE APPROACH AND THE RESULTS ACCORDING TO A SCORE, EXPRESSED OUT OF THIRTY. AN INSUFFICIENT SCORE IMPLIES THE WRITTEN TEST REPETITION. AFTER THE WRITTEN TEST, STUDENTS MAY ASK TO FACE AN ORAL EXAM. THIS EXAM WILL BE ADDRESSED TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. IN SUCH A CASE, BOTH THE WRITTEN TEST AND ORAL EXAM WILL CONTRIBUTE 50% TO THE FINAL SCORE. AN ORAL EXAM THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST. THE MINIMUM GRADE (18/30) IS ACHIEVED BY SHOWING ENOUGH KNOWLEDGE OF ALL THE CONTENTS OF THE COURSE. THE MAXIMUM GRADE (30/30) IS GIVEN TO THE STUDENT WHO SHOWS SIGNIFICANT KNOWLEDGE OF THEORETICAL AND APPLICATION CONTENTS. FULL MARKS WITH DISTINCTION MAY BE GIVEN TO STUDENTS WHO DEMONSTRATE THAT THEY CAN APPLY THE ACQUIRED KNOWLEDGE WITH CONSIDERABLE AUTONOMY TO EXERCISES AND THEORETICAL ISSUES.

Verification of learning

THE AIM OF THE EXAM IS THE ASSESSMENT OF THE KNOWLEDGE AND UNDERSTANDING CONCERNING THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, ESTIMATE UNKNOWN MODEL PARAMETERS, MAKE A DECISION BASED ON HYPOTHESES TESTING, STUDY THE EFFECTS OF PRIMARY FACTORS ON PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA AND TO ASSESS SIMPLE EMPIRICAL MODELS FOR THEM. FURTHERMORE, PERSONAL JUDGMENT, COMMUNICATION SKILLS, AND LEARNING ABILITIES ARE ALSO EVALUATED.

THE FINAL EXAM CONSISTS OF A WRITTEN TEST THAT AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE. THE WRITTEN TEST IS EVALUATED BASED ON THE CORRECTNESS OF THE APPROACH AND THE RESULTS ACCORDING TO A SCORE, EXPRESSED OUT OF THIRTY. AN INSUFFICIENT SCORE IMPLIES THE WRITTEN TEST REPETITION.

AFTER THE WRITTEN TEST, STUDENTS MAY ASK TO FACE AN ORAL EXAM. THIS EXAM WILL BE ADDRESSED TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. IN SUCH A CASE, BOTH THE WRITTEN TEST AND ORAL EXAM WILL CONTRIBUTE 50% TO THE FINAL SCORE. AN ORAL EXAM THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST.

THE MINIMUM GRADE (18/30) IS ACHIEVED BY SHOWING ENOUGH KNOWLEDGE OF ALL THE CONTENTS OF THE COURSE. THE MAXIMUM GRADE (30/30) IS GIVEN TO THE STUDENT WHO SHOWS SIGNIFICANT KNOWLEDGE OF THEORETICAL AND APPLICATION CONTENTS.

FULL MARKS WITH DISTINCTION MAY BE GIVEN TO STUDENTS WHO DEMONSTRATE THAT THEY CAN APPLY THE ACQUIRED KNOWLEDGE WITH CONSIDERABLE AUTONOMY TO EXERCISES AND THEORETICAL ISSUES.