Raliability Theory 0800-TNIEZ

The lecture conveys knowledge of the basic concepts of reliability theory and engineering. Students receive basic knowledge of the following topics:
- Basic definitions in probability theory of random processes and statistics: set of elementary events, probability, conditional probability, σ-body, independent events, total probability theorem, Bayes' theorem.
- Random variable: concept of probabilistic space, discrete and continuous random variables, one-dimensional, multidimensional. Study of the relationship of random variables.
- Distributions of a discrete random variable: Bernoulli distribution, Poisson distribution.
- Basic concepts in reliability theory: the concept of system life, reliability, distributions and damage intensity functions.
- Properties of the distributant, mean values, central moments, covariance and correlation coefficient.
- Determination of parameters of n-dimensional random variables: correlation, means, variances and covariances of discrete and continuous n-dimensional random variables.
- Distributions of continuous random variables: Gaussian distribution.
- Mathematical models of the uptime of objects: lifetime distributions, including exponential distribution, gamma distribution, Weibull distribution. Parameters of distributions, determination of lifetimes and variances in distributions.
- Fitting parameters of distributions to sample data. Effect of parameters on the condition of a technical object, bathtub curve. Applications of the Weibull distribution.
- Reliability structure of systems: simple and complex. Reliability of serial and parallel structure.