Engineering statistics

• Industry Engineering, Semester 1, position 2

The objectives of the course are to familiarize students with the basics of statistical methods used in industrial practice. The first step involves analyzing the characteristics of the data. The focus of the course is on identifying the problem, choosing the appropriate method through defined procedures and drawing conclusions, both mathematical and engineering. On the basis of engineering conclusions, the results are interpreted and appropriate engineering decisions are made.

After passing the exam, students are expected to know how to use: 1. statistical methods for objective problem solving in practice, 2. to draw the necessary conclusions using parametric and non-parametric research that includes hypothesis testing, one-way and two-way analysis of variance, simple and multiple regression and correlation, the 3rd goal of learning and practicing is correct problem setting, 4. determining the methodology of problem solving based on the results of descriptive statistics 5. implementing the appropriate statistical procedure defined by the steps of the procedure 6. correct engineering interpretation of the obtained results, with knowledge of their mathematical interpretation and 7. Getting to know the programming language R.

Theoretical teaching of the following statistical areas: basic concepts of statistics, graphical presentation of data, descriptive statistics of data through the determination of basic statistics, parametric confidence intervals, parametric hypothesis tests for the mean, difference between means, variance, ratio of variances - for large and small samples, as well as for proportion and ratio of proportions. In addition, the bases for making decisions based on the p level of the test. Non-parametric tests including the test of functional dependence (Kolmogorov), tests of comparison of two distributions (Kolmogorov-Smirnov, Mann-Whitney, median test, median difference test and Darling Anderson test). Parametric analysis of variance which refers both to the basic parametric models of one-factor analysis of variance and to two-factor analysis of variance, as well as to the available non-parametric methods for its analysis. Regression tests include single and multiple linear regression and correlation, as well as their modifications, for parametric tests. Nonparametric tests including one-factor nonparametric analysis of variance, determination of the degree of curve using Cherbyshev polynomials, and correlation tests between data for nonparametric statistics.

Practical teaching follows theoretical teaching with tasks aimed at identifying the problem, identifying the method for solving the problem, setting the problem, implementing the appropriate procedure for solving the problem and making appropriate conclusions. Students are trained to program problem-solving procedures using programming in appropriate software environments.. In addition, special attention is paid to training students to use specially created tables for the application of parametric and non-parametric hypothesis tests. Special attention will be paid to training students to use tables to identify parametric confidence intervals, and especially parametric hypotheses, setting up an algorithm for solving problems and using tables to choose a hypothesis testing procedure, as well as making correct conclusions based on the obtained results. Exercise tasks are done by calculation, they are partially solved on computers, using appropriate software packages.

according to the curriculum of the industrial engineering department

Before each class of lectures and exercises, students receive handouts and other necessary materials in electronic form. If necessary, students receive materials in advance that will be needed for monitoring and active participation in classes. Radojević, S, Veljković Z, Quantitative methods, CD, MF

Total assigned hours: 75

New material: 25
Elaboration and examples (recapitulation): 5

Auditory exercises: 10
Laboratory exercises: 20
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 3
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 10
Test: 0
Final exam: 2

Activity during lectures: 5
Test/test: 40
Laboratory practice: 25
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 30

Radojević, S, Veljković Z, Quantitative methods, Faculty of Mechanical Engineering in Belgrade, 2012.; Montgomery, DC, Runger, GC Applied Statistics and Probability for Engineers, Fourth Edition, Wiley, 2007