6. Reliability¶
6.1. Reliability measures¶
A standard reliability measure may be chosen to be the generalized reliability index. It is defined as:
where \(P_f\) is the probability of failure
\(\Phi^{-1}(\cdot)\) is the inverse Gaussian distribution
Another equivalent reliability measure is the probability of the complement of the adverse event
The probability \(P_f\) should be calculated on the basis of the standardized joint distribution type of the basic variables and the standardized distributional formalism of dealing with both model uncertainty and statistical uncertainty.
In special situations other than the standardized distribution types can be relevant for the reliability evaluation. In such cases the distributional assumptions must be tested on a suitable representative set of observation data.
Reliability analysis principles including time-dependent reliability problems are described in Annex C.
6.2. Component reliability and system reliability¶
Component reliability is the reliability of one single structural component which has one dominating failure mode.
System reliability is the reliability of a structural system composed of a number of components or the reliability of a single component which has several failure modes of nearly equal importance. The following type of systems can be classified:
-redundant systems where the components are “fail safe”, i.e. local behaviour of one component does not directly result in failure of the structure;
-non-redundant systems where local failure of one component leads rapidly to failure of the structure.
Probabilistic structural design is primarily concerned with component behaviour. System behaviour is, however, of concern because it is usually the most serious consequence of structural failure. Therefore the likelihood of system failure following an initial component failure should be assessed. In particular, it is necessary to determine the system characteristics in relation to damage tolerance or robustness with respect to accidental events. The requirements for the reliability of the components of a system should depend upon the system characteristics.
A probabilistic system analysis should therefore be carried out to establish:
the redundancy (alternate load-carrying paths)
the state and complexity of the structure (multiple failure modes). Furher aspects on system reliability are provided in Annex C.
6.3. Methods for reliability analysis and calculation¶
The numerical value of the reliability measure is obtained by a reliability analysis and calculation method (see Annex C). The reliability method used should be capable of producing a sensitivity analysis including importance factors for uncertain parameters. The choice of the method should be in general justified. The justification can be for example based by another relevant computation method or by reference to appropriate literature.
Due to the computational complexity a method giving an approximation to the exact result is generally applied. Two fundamental accuracy requirements are:
Overestimation of the reliability due to use of an approximative calculation method shall be within limits generally accepted for the specific type of structure.
The overestimation of the reliability index should not exceed 5 % with respect to the target level.
The accuracy of the reliability calculation method is linked to the sensitivity with respect to structural dimensions and material properties in the resulting design.