Reliability analysis of engineering systems conventionally represents the system state variables as precise probability distributions and generates precise estimates of the probability of system failure. It is demonstrated how this conventional approach can be extended to handle imprecise knowledge about the system state variables, represented in general as random sets, in order to generate bounds on the probability of failure. The conventional assumption of a precise limit state function is then relaxed. A new method based on linguistic covering of the state variable space with fuzzy set labels is introduced and is used to generate an imprecise limit state function from very scarce experimental data.
Keywords. Reliability analysis, imprecise failure probabilities, random sets, linguistic labels.
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Department of Civil Engineering
Dept. Engineering Mathematics
University of Bristol
Bristol BS8 1TR