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 0-7803-9766-5/07/$25.00 ©2007 IEEE