Dynamic Reliability Block Diagrams VS Dynamic Fault Trees
Salvatore Distefano, PhD, Università degli Studi di Messina
Antonio Puliafito, PhD, Università degli Studi di Messina
Key Words: system reliability, dynamic systems, dynamic fault tree, dynamic reliability block diagrams
SUMMARY & CONCLUSIONS
Reliability block diagrams (RBD), and fault trees (FT) are
the most widely used formalisms in system reliability
modeling. They implement two different approaches: in a
reliability block diagram, the system is represented by
components connected according to their function or
reliability relationships, while fault trees show which
combinations of the components failures will result in a
system failure. Although RBD and FT are commonly used,
they are limited in their modeling capacity of systems that
have no sequential relationships among their component
failures. They do not provide any elements or capabilities to
model reliability interactions among components or
subsystems, or to represent system reliability configuration
changing (dynamics), such as: load-sharing, standby
redundancy, interferences, dependencies, common cause
failures, and so on. To overcome this lack, Dugan et al.
developed the dynamic FT (DFT). DFT extend static FT to
enable modeling of time dependent failures by introducing
new dynamic gates and elements. Following this way, recently
we have extended the RBD into the dynamic RBD notation.
Many similarities link the DFT and the DRBD formalisms,
but, at the same time, one of the aims of DRBD is to extend
the DFT capabilities in dynamic behavior modeling.
In the paper the comparison between DFT and DRBD is
studied in depth, defining a mapping of DFT elements into the
DRBD domain, and investigating if and when is possible to
invert the translations from DRBD to DFT. These mapping
rules are applied to an example drawn from literature to show
their effectiveness.
1 INTRODUCTION
A system is a collection of components, subsystems
and/or assemblies arranged according to a specific design in
order to achieve acceptable performance and reliability levels.
The types of components, their quantities, their qualities and
the manner in which they are arranged within the system have
a direct effect on the reliability of the system. The main
objective of system reliability [1] is the construction of a
model (life distribution) that represents the times-to-failure of
the entire system based on the life distributions of the
components, subassemblies and/or assemblies “black boxes”
from which it is composed [10].
There are many formalisms to model system reliability.
The most widely used are reliability block diagrams (RBD)
[2], and fault trees (FT) [3]. RBD and FT are graphical
representations of the system in reliability-wise or functional
logic, providing a view of the system close to the modeler,
more readable and understandable than any other formalism.
In a RBD the system is represented by subsystems or
components connected according to their function or
reliability relationship. Whereas RBD are mission success
oriented, the FT show which combinations of the component
failures will result in a system failure. FT represent the logical
relationships of ‘AND’ and ‘OR’ among different failure
events. From the expressiveness point of view it can be
affirmed that RBD and FT are substantially equivalent in
system reliability modeling [2]. A difference between the two
methodologies is in the analysis approach: while FT are
commonly analyzed by exploiting cut sets or binary decision
diagrams (BDD) [7], RBD are analyzed by applying the more
practical structure equations (series, parallel) [2]. On the other
hand, RBD and FT do not provide any elements or capabilities
to model reliability interactions among components or
subsystems, or to represent system reliability configuration
changing, aspects conventionally identified as dynamics. It
could be possible that a subsystem has some influence on
other subsystems. Examples of such interactions are: load-
sharing, standby redundancy, interference, dependence,
common cause failure. Also the configuration of a system,
considering the reliability aspects, could vary: a failed
component/subsystem could be repaired (maintenance,
reliability growth model), the system could be multi-phase,
and so on. These lacks in system reliability modeling notations
have awakened the scientific community to the need of new
formalisms. One approach adopted has been to extend the
existing formalisms with new elements to model the
(uncovered) aspects. Thus, the dynamic fault trees notation
(DFT) was born [8, 9]. DFT extend static FT to enable
modeling of time dependent failures by introducing new
dynamic gates and elements.
Inspired by the same aims and also with the intent to
improve the capability of DFT in dynamic system reliability
modeling, we have developed a new formalism derived from
RBD: the dynamic RBD (DRBD) [4, 5, 6]. DRBD formalize
the concepts of state, event and dependence, providing a logic
infrastructure to define several dynamic reliability behaviors.
The DRBD lower level approach increases the modeling
power of DFT, allowing representing of reliability aspects not
considered in DFT. An obvious next step is to establish an
analogy between DFT and DRBD objects and elements, as for
FT and RBD. But, unlike the FT and RBD case, the
correspondence between DFT and DRBD is generally not
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