Reliability and Quality (FSI-SSJ-A)

Academic year 2025/2026
Supervisor: Ing. Pavel Hrabec, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:

The aim of the course is to familiarize Mathematical Engineering majors with reliability theory methods for modeling and evaluating the reliability of technical systems, with mathematical statistics methods for process quality control. Students will gain essential knowledge in the crucial fields of reliability theory and quality control, empowering them to use computer modeling to identify significant quality attributes of technical systems and processes using statistical data.
Learning outcomes and competences:
 
Prerequisites:

Knowledge of basic and advanced methods of probability theory and mathematical statistics is assumed (statistical hypothesis testing, maximum likelihood estimation).
Course contents:

The course is concerned with basics of the reliability theory and quality control methods: functional and numerical characteristics of lifetime, selected probability distributions, statistical methods for analyses of lifetime data, process capability analysis, control charts, measurement system analysis. Practice datasets will be analyzed using the software Minitab.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Credit conditions: active participation during classes
Conditions for passing the exam: mastering practical examples on a PC, meaning adequate (oral) discussion of software otputs.
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture Interval estimates in technical practice.
Hypothesis testing in technical practice.
Measurement system analysis.
Stability and capability of the process.
Basic concepts of object reliability.
Functional and numerical characteristics of reliability.
Probability distribution of time to failure.
Estimates for uncensored and censored selections.
    Computer-assisted exercise

MSA for continuous data
MSA for attributes
Process stability (control charts)
Process capability
Process capability for nonnormally distributed data
Functional and numerical characteristics of reliability
Censoring, nonaprametric reliability analysis (Kaplan-Meier)
Probability distribution of time to failure and their likelihood.
Parametric analysis of reliability, likelihood ratio test
Competing failure mode model for reliability
Demostration and estimation test plans
Accelerated life testing.
Literature - fundamental:
1. Montgomery, Douglas C.:Introduction to Statistical Quality Control /New York :John Wiley & Sons,2001. 4 ed. 796 s. ISBN 0-471-31648-2
2. Ireson, Grant W. Handbook of Reliability Engineering and Management.Hong Kong :McGraw-Hill,1996. 1st Ed. nestr. ISBN 0070127506
3.

Kalbfleisch, J. D., & Prentice, R. L. (c2002). The statistical analysis of failure time data (2nd ed). Wiley-Interscience.
4.

Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. John Wiley.
Literature - recommended:
1. Kupka, K.: Statistické řízení jakosti, , 0
2. Militký, J.: Statistické techniky v řízení jakosti, , 0
3. Linczényi, A.: Inžinierska štatistika, , 0
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-MAI-A full-time study --- no specialisation -- Cr,Ex 4 Compulsory-optional 2 2 W
N-AIM-A full-time study --- no specialisation -- Cr,Ex 4 Elective 2 2 W