# Ingegneria Gestionale | Statistics and Safety of Production Systems

## Ingegneria Gestionale Statistics and Safety of Production Systems

 0612600017 DIPARTIMENTO DI INGEGNERIA INDUSTRIALE EQF6 INDUSTRIAL ENGINEERING AND MANAGEMENT 2019/2020

 OBBLIGATORIO YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2016 PRIMO SEMESTRE
 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
 MAURIZIO GUIDA1 T CARMINE NOVELLINO2 T
Objectives
THE AIM OF THE COURSE IS TWOFOLD: INTRODUCING THE BASIC NOTIONS OF THE PROBABILITY THEORY, IN ORDER TO MODEL AND ANALYSE RANDOM PHENOMENA TYPICALLY OBSERVED IN THE REAL WORLD AND, IN PARTICULAR, IN THE ENVIRONMENT AND INDUSTRY, AND PROVIDING THE MAIN TECHNIQUES FOR STATISTICAL INFERENCE AND DECISION MAKING.

KNOWLEDGE AND UNDERSTANDING: BASIC NOTIONS OF PROBABILITY AND COMBINATORIAL CALCULUS. RANDOM VARIABLES. DESCRIPTIVE AND INFERENTIAL STATISTICS. LINEAR REGRESSION ANALYSIS. DESIGN OF EXPERIMENTS (DOE) AND ANALYSIS OF VARIANCE (ANOVA).

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

PERSONAL JUDGMENTS: ABILITY TO SELECT THE MOST APPROPRIATE METHOD TO ANALYSE 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 BASIC MATHEMATICS IS REQUIRED, AS GUARANTEED BY THE MATHEMATICS I COURSE.
Contents
•ELEMENTS OF PROBABILITY THEORY AND COMBINATORIAL CALCULUS. AXIOMS OF PROBABILITY. CONDITIONAL PROBABILITY AND INDEPENDENCE. TOTAL PROBABILITY THEOREM. BAYES THEOREM. COMBINATORIAL CALCULUS. (HOURS: LESSONS/EXERCISES/LABORATORY 4/2/-)
•RANDOM VARIABLES. DEFINITION OF A RANDOM VARIABLE (R.V.) AND ITS PROBABILITY DISTRIBUTION AND PROBABILITY DENSITY FUNCTION. MEAN AND VARIANCE OF A R.V.. FUNCTIONS OF A 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 (HOURS 7/4/-)
•DESCRIPTIVE STATISTICS. POPULATION AND SAMPLE. RANDOM SAMPLE. FREQUENCY AND RELATIVE FREQUENCY DISTRIBUTION FOR DISCRETE AND CONTINUOUS VARIABLES. HISTOGRAMS. STATISTICAL POSITION INDEXES: SAMPLE MEAN, MEDIAN, MODE. STATISTICAL DISPERSION INDEXES: SAMPLE VARIANCE, SAMPLE STANDARD DEVIATION, RANGE. (HOURS 3/1/-)
•ELEMENTS OF INFERENTIAL STATISTICS. BASIC CONCEPTS OF INDUCTIVE REASONING. POINT AND INTERVAL ESTIMATION OF POPULATION PARAMETERS. HYPOTHESIS TESTING. TYPE I AND TYPE II RISKS. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE MEAN OF A NORMAL POPULATION IN CASE OF BOTH KNOWN AND UNKNOWN VARIANCE. STUDENT T DISTRIBUTION. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE VARIANCE OF A NORMAL POPULATION. CHI-SQUARED DISTRIBUTION. (HOURS 10/5/-)
•DESIGN OF EXPERIMENTS(DOE) AND ANALYSIS OF VARIANCE (ANOVA). BASIC CONCEPTS AND DEFINITIONS OF DOE. COMPLETELY RANDOMIZED DESIGN. RANDOMIZED BLOCK DESIGN. LATIN SQUARES. FULL FACTORIAL DESIGN. PARTITION OF TOTAL VARIABILITY. ONE WAY AND TWO WAY ANOVA. RESIDUAL ANALYSIS. (HOURS 10/5/-)
•LINEAR REGRESSION ANALYSIS. ASSOCIATION AMONG VARIABLES: CORRELATION COEFFICIENT. SIMPLE LINEAR REGRESSION MODEL. LEAST SQUARES ESTIMATION METHOD. GOODNESS-OF-FIT MEASURES: COEFFICIENT OF DETERMINATION. MULTIPLE LINEAR REGRESSION. STEPWISE PROCEDURE FOR CHOOSING THE BEST REGRESSION MODEL. (HOURS 6/3/0)
Teaching Methods
The course consists of in front lessons (44 h) and activities in Lab (16 h) for a total amount of 60 hours which are worth 6 credits.
The practical activities will focus on the carrying out of analytical methods used for the assessment of chemical, physical parameters that affect the safety and quality of a food product.
Attendance at the lectures is strongly recommended.
Verification of learning
THE GOAL OF THE FINAL EXAM IS THE EVALUATION OF THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, TO ESTIMATE UNKNOWN MODEL PARAMETERS, TO MAKE DECISION ON THE BASIS OF HYPOTHESES TESTING, TO STUDY THE EFFECTS OF PRIMARY FACTORS ON PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA AND TO ASSESS SIMPLE EMPIRICAL MODELS FOR THEM. FURTHERMORE, THE PERSONAL JUDGEMENT, THE COMMUNICATION SKILLS AND THE LEARNING ABILITIES ARE ALSO EVALUATED.

THE FINAL EXAM CONSISTS OF A WRITTEN TEST WHICH AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE, SUCH AS: 1) BASIC PROBABILITY EVALUATIONS; 2) BASIC STATISTICAL INFERENCE AND DECISION MAKING; 3) BASIC ANOVA AND LINEAR REGRESSION ANALYSES. THE WRITTEN TEST IS EVALUATED ON THE BASIS OF THE CORRECTNESS OF THE APPROACH AND THE RESULTS ACCORDING TO A SCORE, EXPRESSED OUT OF THIRTY. THE “INSUFFICIENT” SCORE IMPLIES THE WRITTEN TEST REPETITION.

AFTER THE WRITTEN TEST, STUDENTS MAY ASK TO DO AN ORAL INTERVIEW, TOO. THIS INTERVIEW WILL BE ADDRESSED TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. IN SUCH CASE, THE WRITTEN TEST WILL CONTRIBUTE FOR 60% TO THE FINAL SCORE, WHILE THE ORAL INTERVIEW FOR 40%. AN ORAL INTERVIEW THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST, TOO.

The sufficiency is obtained if the candidate demonstrates the ability to select the methods to be used, to write correctly the model equations and at least to select the correct path to their solution.
The excellence is obtained when the candidate is able to face out successfully even aspects of the topic not analyzed during the course.
The final grade depends from the level of exposition and from the confidence shown with the course’s topics, and with the methods, the uses of which have been shown during the course.
Texts
LECTURE NOTES ON PROBABILITY AND COMBINATORIAL CALCULUS (IN ITALIAN).
S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO.

COMPLEMENTARY BOOKS
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 