Decision Diagrams Extension Methods For Importance Measures

Importance measure is an important branch of the reliability theory, one of the basictheory of reliability engineering, and an assessment method of the important componentidentification of systems. Importance measure of complex systems is widely used inreliability design and optimization, maintenance decision, the allocation of maintenanceresources, etc. Fault tree analysis (FTA) is a traditional analysis method for reliability analysisand importance measure. And decision diagram simplifies the calculation of reliability andimportance measure by combining the same parts of path-sets and cut-sets in fault trees.Aiming at importance measure for complex systems, the author proposes decision diagramgeneration methods and decision diagram extension methods in the dissertation; the methodscan be applied in reliability analysis and importance measure for reliability system whichincluding common cause failures.The main innovations of the paper are as follows:（1）The basic decision diagram modeling methodsSince the states of components have similar meanings to the variable states in decisiondiagram, the modeling method of variables in decision diagram could be carried out bytransforming different events into the states of different variables, and the decision diagramscorresponding to the ‘AND’,‘OR’ and ‘NAND’ gates are given. Also, the decision diagramgeneration method for voter gate is proposed by summarizing and proving the patterns ofbinary decision diagram (BDD)/multi-state multi-valued decision diagram (MMDD) forbinary/multi-state (k/n (G))system. Complexity analysis shows that the proposed method ismore computationally efficient than the traditional algorithms for system.（2）Two enhanced decision diagram modeling methodsTo analyze fault trees with dependent basic events and independent components, themulti-state fault trees are divided into independent subtrees. By using a component-basedlinear-time enhanced algorithm, the multi-state multi-valued decision diagram is applied toeach subtree for modeling and reliability analysis, and the computational cost is reduced. Toanalyze the system with a new component/system serial-added or parallel-added to, anenhanced decision diagram succession method is proposed, with which generating the newBDD/MMDD over the new system is not needed. One advantage of the analytical method isthat the generation parts of original BDD/MMDD are reduced. Case studies showed that theBDD/MMDD generation of complex systems can be simplified by dividing the system intoindependent parts with the modular method and generating BDD/MMDD with the succession method.（3）An analytical method based on decision diagrams for computing importancemeasureThe application of decision diagram in Birnbaum impotance, risk achievement worth,risk reduction worth and Fussell-Vesely is discussed based on the common parts in theseimportance measures, which is effective in the important component identification of complexsystems. Complexity analysis shows that the proposed method is more computationallyefficient than the traditional algorithms for importance measure.（4）An analytical method based on common cause decision diagrams for computingimportance measureFor the complex systems considering common cause failures, a fault tree extensionmethod and a corresponding common cause decision diagram modeling method are proposed.And the calculation method of reliability and importance measure based on common causedecision diagram is discussed. Case studies show the common cause decision diagram basedmethod is more efficient in computation than traditional enumeration calculation method.