Mathematical models for MTTF and PFD analysis

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. Knowledge of probability theory, statistics, solving differential equations and series development is required to determine failure rates. Reliability block diagrams or Markov models can be used to determine failure probabilities and MTTF values. This requires knowledge of integral and differential calculus or matrix calculus. In the absence of reliable failure rates for the individual elements of a system from field tests, Monte Carlo simulation can be used to estimate the required parameters with corresponding 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 development (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

Prior knowledge:
Mathematics 1/2

Course number: FB16-6606

Time and place:
Fridays, 14:00-17:00, Room: 1332

Beginning:

Lecturer:

Contact:
Email to the secretary's office

Scope:
4 SWS or 6 CP

Written exam:
Date to be announced