System Reliability and Clinical Experiments

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

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.

Requirements:

Syllabus of lectures:

Outline:

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:

Study materials:

Key references:

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

Willey, 2004.

[2] L. Xing, G. Levitin and Ch. Wang, Dynamic System Reliability: Modelling and Analysis of Dynamic and

Dependent Behaviors, John Wiley & Sons 2019

[3] I.B. Frenkel, A. Karagrigoriou, A. Lisnianski and A.V. Kleyner, Applied Reliability Engineering and Risk

Analysis:Probabilistic Models and Statistical Inference, John Wiley & Sons 2013

Recommended references:

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

[5] Lange N, et al., Case Studies in Biometry, Wiley, 1994.

[6] Kovalenko I.N., Kuznetsov N.Y., Pegg P.A., Mathematical Theory of Reliability of Time Dependent Systems with

Practical Applications, Wiley, 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: