Mathematical models for MTTF and PFD analysis

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Learning objectives:
Depending on the architecture and complexity of a safety-related system or subsystem, the user has several options for calculating the various parameters. For the determination of failure rates, one needs knowledge from the fields of probability theory, statistics, solving differential equations and series expansion. Reliability block diagrams or Markov models can be used to determine failure probabilities and MTTF values. Knowledge of integral and differential calculus or matrix calculus is required for this. In the absence of assured failure rates of the individual elements of a system from field tests, Monte Carlo simulation can be used to estimate the required parameters with appropriate confidence intervals.

Learning content:
Mathematical models for MTTF and PFD analysis, probability theory, mathematical model descriptions.

The lecture is therefore divided into the following topics:

  • Vector and matrix calculus
  • Series expansion (Taylor series, Mc Laurin series, etc.)
  • Integral calculation
  • Solving differential equations
  • Statistics and probability theory
  • Setting up simple Markov models
  • Monte Carlo simulation
  • Calculation of safety parameters, such as MTTF and PFD

Mathematics 1/2

Course number: FB16-6606

Location and time:
Fridays, 14:00-17:00, Room: 1332

Start: 04/22/2016


Email to the secretary's office

4 SWS or 6 CP

Written exam:

Date to be announced