System Reliability and Clinical Experiments

The course is not on the list Without time-table
Code Completion Credits Range Language
01SKE KZ 3 2+0 Czech
Garant předmětu:
Department of Mathematics

The main goal of the subject is to provide the mathematical principles of reliability theory and techniques of survival data analysis, reliability of component systems, asymptotic methods for reliability, concept of experiments under censoring and their processing in clinical trials (life-time models). The techniques are illustrated and tested within practical examples originating from lifetime material experiments and clinical trials.


01MAS or 01PRST

Syllabus of lectures:

1. Reliability function, mean time before failure, hazard rate, conditional reliability, mean rezidual life.

2. Systems with monotone hazard rate and their characteristics, TTT transformation and its usage.

3. Binomial, exponential distribution, Poisson process, Weibull disttribution and its flexibility, practical examples.

4. Generalized Gamma and Erlang distribution, Rayleigh distribution, Inverted Gaussian, Birnbaum-Saundersův model.

5. Component systems reliability analysis, serial, parallel, k-oo-n systems, bridge systems, pivotal decomposition.

6. Repairable and renewal systems, perfect and imperfect switching.

7. Asymptotics for minimum time before failure, serial-parallel systems, Gumbel distribution.

8. Lifetime data - censoring (type I, type II, random, mixed), maximum likelihood and Bayesian estimates of the systems under censoring.

9. Nonparametric approach, Kaplan-Meier estimate of reliability, Nelson estimate of cumulative hazard rate.

10. Cox proporcional hazard model, its properties, PH assumption testing, usage, examples.

11. Applications to the data from clinical research, case studies in biometry, particular data processing.

Syllabus of tutorials:
Study Objective:


Extension of the statistical procedures for objets reliability analysis with random effects and their applications in stochastic survival tasks.


Orientation in various stochastic reliability multi-component systems and their properties.

Study materials:

Key references:

[1] Rausand M., Hoyland A., System Reliability Theory: Models, Statistical Methods, and Applications, Second Ed., Willey, 2004.

Recommended references:

[2] Kleinbaum D.G., Survival Analysis, Springer, 1996.

[3] Lange N, et al., Case studies in Biometry, Wiley, 1994.

[4] Kovalenko I.N., Kuznetsov N.Y., Pegg P.A., Mathematical theory of reliability of time dependent systems with practical applications, Wiley, 1997.

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-18
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