Page 445 - Marine Structural Design
P. 445
Chapter 23 Basics of Structural Reliability 42 1
23.4 Component Reliability
The concepts introduced in Section 23.3 are mainly for the reliability evaluation at component
level, which means that the concern is on the failure probability for problems modeled by a
single limit state function. A component reliability is the basis for structural reliability analysis
since all marine structures are composed of components.
23.5 System Reliability Analysis
23.5.1 General
This section deals with the formulation and evaluation of the failure probability in the
problems where more than one limit state function must be considered, i.e. system reliability
analysis.
A system is generally composed of many elements where each element may have one or more
failure modes described by their individual limit state finctions. Moreover, a system may have
many failure modes, where each system failure mode may be due to the failure of one element
only or due to the failure of several elements jointly.
Series and parallel systems are the two fundamental types of systems from which any system
can be built.
23.5.2 Series System Reliability
A system is called series system if the system is in a state of failure whenever any of its
elements fails. Such systems are often referred to as weakest-link systems. A typical example
of this is the marine pipeline or risers.
The failure probability of a series system can be formulated as the probability of union of
failure events. For a system with m failure elements defined by their safety margins MI, the
probability of failure can be formulated as
(23.24)
where, Q,, is the m-dimensional standard normal distribution function, p=[p~, p~ ...I is the
vector of reliability indices for the m failure elements, and p is the corresponding correlation
matrix.
To demonstrate the reliability calculation of series system, an example is given in Section
23.11.
23.5.3 Parallel System Reliability
A parallel system fails when all elements in the system fail. For a parallel system all elements
have to fail for system failure to occur. The failure probability can be formulated as the
intersection of the element failure events
