Optimal design of systems with standby dependencies

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 Vee 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 Vee 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 Vee 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.