Optimal design of systems with standby dependencies

Abstract

The technique of fault tree analysis is commonly used to assess the probability of failure of industrial systems. The fault tree represents the failure logic of the system in an inverted tree structure and has the advantage that it provides very good documentation of the way that the failure logic was developed. During the analysis of a fault tree the component failures or basic events are assumed to occur independently. When this condition is not satisfied, as in the case of standby systems for example, alternative approaches such as Markov methods can be used. Constructing the state transition diagram required for a Markov model is not such an intuitive process for engineers as fault tree construction, since state transition diagrams do not readily document the failure logic process. This paper introduces a new gate into the fault tree diagram, which enables the reliability analyst to incorporate standby dependencies. The analysis of the fault tree is then performed by identifying the sections of the fault tree which conform to the usual requirements of independence and those which do not. Using a combination of conventional fault tree analysis methods with Markov methods, the analysis of the tree is performed by computer code in a manner that is transparent to the analyst. A similar approach has been developed for the analysis of systems with sequential failures represented by a PRIORITY AND gate on the fault tree diagram. With these extended fault tree capabilities in place, the technique has been embedded within an optimization framework to get the best system performance for systems where failures are dependent. Copyright © 1999 John Wiley & Sons, Ltd.

Quality and Reliability in Top-event Estimation: Quantitative Fault Tree Analysis in Case of Dependent Events

“…In some situations, assumption of independence will lead to unrealistic results; furthermore, the beginning of the FTA and some dedicated software packages are based on Kinetic Tree Theory (Veseley, 1970). This theory may be considered as the conventional fault tree formulation and one of the main assumptions is that basic events occur independently (Andrews and Dugan, 1999;Ridley and Andrews, 1999); for examples in the case of independent events, see Høyland and Rausand (1994, Ch. 4).…”

“…One of the main features to be dealt with is the representation of the complex system through a logic diagram (tree), i.e., the definitions of the basic events (components) and the computation of the top-event, which represents the probability of the system failure; further details can be consulted in Høyland and Rausand (1994), Kovalenko et al (1997), and Birolini (2010). In the literature, dependencies in FTA are studied in-depth by considering specific dependencies and features, such as sequential failures (Ridley and Andrews, 1999) or static and dynamic sections of the Fault Tree (Andrews and Dugan, 1999). Our efforts are directed towards analyzing specific sources of variations for the top-event.…”

How dependent basic events with interval‐valued probabilities affect fault tree analysis

“…Researches show that neglecting dependence between BEs will results in a large deviation of the TE probability 36,37 . Ridley and Andrews 38 pointed out that two situations frequently arise in engineering systems, which render the assumption of BE independence inappropriate: sequential events and standby systems. Sequential events are represented by the FT with a priority AND gate in most cases.…”

Probability and Frequency Derivation Using Dynamic Fault Trees

“…In addition, there exist several approaches that interest directly to solve DFT by calculating the probability of its top event (TE). The first idea is to convert DFT into its corresponding Markov chain model (MC) , which is subjected to the well‐known problem of the state space explosion , even if the modularization algorithm is used . Temporal Bayesian Network (TBN) is an alternative approach to solve DFT and gives various information about the system failure mechanism.…”