High performance reliability analysis of phased mission systems

Systems often operate over a set of time periods, known as phases, in which their reliability structure varies and many include both repairable and nonrepairable components. Success for such systems is defined as the completion of all phases, known as a phased mission, without failure. An example of such a system is an aircraft landing gear system during a flight. The Binary Decision Diagram (BDD) method provides the most efficient solution to the unreliability of non-repairable systems whilst for repairable systems Markov or other state-space based methods have been most widely applied. For systems containing both repairable and non-repairable components the repairable modelling methods are normally used, despite having far higher computational expense than the non-repairable methods, since only they are able to handle the dependencies involved. This paper introduces improvements to the BDD method for analysing non-repairable systems as well as an entirely new method that utilises a new modelling technique involving both BDD and Markov techniques. Introduction Many real world systems operate in phased missions where the reliability structure varies over consecutive time periods, known as phases, which must be completed without failure. Typical examples include aircraft flights and nuclear power station safety systems. Calculating the reliability of a mission is computationally expensive particularly if the system has components that are repairable and/or have multiple failure modes. Increased solution efficiency is an important goal as it increases the size of problem that can be analysed and increases the possibilities for performing importance measure and real time analysis. Reliability engineering research has developed methods that allow the mission reliability to be found from the set of fault trees describing the system reliability in terms of component level failures for each phase, along with the component level failure probabilities (or failure probability time distributions). Two key areas in which progress has focused is in widening the scope of the techniques so that they are applicable to a larger range of system types and improving the efficiency of analysis to increase the size of system that can be analysed and reduce computational effort. The earliest phased mission analysis methods involved the direct manipulation of the fault trees. In the first known work, Esary and Zhiehms [1] introduced a fault tree based method to transform a phased mission into an equivalent single phased mission. Each component basic event in the phase fault trees is replaced by an OR gate with the performance of the component up to and including that phase as inputs. The transformed phase fault trees are then combined into a single fault tree