8
th
Lecture: Time Variant Reliability Analysis
Aim of the present lecture
The aim of the present lecture is to introduce the problem of time variant reliability analysis
and to outline approaches for its solution. In specific, time variant reliability problems are
considered by the introduction of the Poisson process and the Normal process. For the
Poisson process it is shown how approximations for the time variant reliability problem may
be established provided that the mean out-crossing rate can be assessed. Some solutions to
the assessment of the mean out-crossing rate are then provided for special cases of Normal
processes. Thereafter, the problem is considered where the reliability problem involves not
only uncertainties which may be represented by random processes but also random sequences
and time invariant random variables. Finally some situations are discussed where it is
possible to approach time variant reliability problems by methods of time invariant reliability
analysis. Based on the introduced material in this lecture the students should acquire
knowledge and skills in regard to:
How does a time variant reliability problem differ from a time invariant reliability
problem?
How are filtered and spike Poisson processes defined and what are their characteristics?
How may the time till failure be assessed for events following a Poisson process?
What is a Normal process and how is it defined?
What is a mean out-crossing rate and how may it be calculated for Normal processes?
What is the purpose/content of Rice’s formula?
How may non-ergodic random variables and random sequences be taken into account in
time variant reliability analysis?
When and in what way may simplifications of time variant reliability problems be
introduced?