Description:

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.

Contents:

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.

Recommended literature:

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.

Keywords:

Reliability function, hazard rate, Weibull distribution, component systems, asymptotic methods, censoring, applications, clinical trials.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar