Introduction to Error Analysis



Introduction to Error Analysis




For reaching the requirements concerning the standards a maximum failure rate is not allowed to exceed. Especially developers and employees that specify the safety conditions of products and systems are responsible for those calculations.


In order to fulfil the requirements laid down by the standards the maximum failure rate stipulated for the safety system or device must not be exceeded. This requires calculations proving the low error rate. This training unit is directed particularly towards developers and staff in production who specify, manufacture or use safety products or systems.

Introduction to  statistical mathematics

  • - Probability
  • - Random values, permutation
  • - Functions of distribution (binomial and Poisson distribution)
  • - Standard distribution, Gauss distribution, condition with dependent distribution

Representation of parameters

Critical values for safety assessment

Examples of calculation

Typical applications

Areas of use

  • - Calculation using EXCEL
  • - Calculation using SISTEMA

Procedures of malfunctions and parameters

  • - Calculation of MTBF
  • - Calculation of λ values

Error propagation

Residual errors and requirement profiles

SIL classification (according to IEC 61508)

Performance level (according to DIN EN ISO 13849)

Models of failures

  • - Worst case, typical case, best case
  • - MTBF values, FIT, λ values

Markov analyses

  • - Stable conditions, topologies
  • - Inter-operation probability

Safety principles

  • - Safety-related bus systems
  • - Fail-safe principles, techniques
  • - Architectures with 2 channels, architectures with multi-channels

Principles for safety and availability

Calculations using IEC 61508

  • - Diagnostic coverage
  • - Common mode failures
  • - Failure probability

Calculations for special structures (IEC 61508)

  • - Safety and availability
  • - 1 out of 2 systems
  • - 2 out of 3 systems
  • - Multiple redundancy systems


  • - Aviation
  • - Railway technology
  • - Light curtains and scanners
  • - Machines and plants