Reliability and clinical experiments

Lecturer:

Václav Kůs (gar.)

Tutor:

Václav Kůs (gar.)

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. The techniques are illustrated and tested within practical examples originating from lifetime material experiments and clinical trials.

Requirements:

Basic course of Calculus and Probability (in the extent of the courses 01MAA3-4 or 01MAB3-4, 01PRA1 nebo 01PRST held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Reliability function, mean time before failure, Mills ratio, systems with monotone hazard rate and their characteristics. 2. Exponential distribution, Poisson process, Weibull disttribution and its flexibility, asymptotics for minimum time before failure, serial-parallel systems, Gumbel distribution. 3. Generalized Gamma and Erlang distribution, Rayleigh distribution. 4. Component systems reliability analysis, serial and parallel systems, pivotal decomposition. 5. Lifetime data - censoring (type I, type II, random, mixed), maximum likelihood and Bayesian estimates of the systems under censoring. 6. Nonparametric approach, Kaplan-Meier estimate of reliability, Nelson?s estimate of cumulative hazard rate. 7. Applications to the data from clinical research, case studies in biometry, particular data processing.

Syllabus of tutorials:

Study Objective:

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

Abilities: Orientation in various stochastic time-dependent systems and their properties.

Study materials:

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

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

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

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: