Vba implementation of binary decision diagram for fault tree analysis
Seungil Jung, Delio Ricardo · NCSU Libraries Repository (North Carolina State University Libraries) · 2017
This paper presents the Visual Basic Application (VBA) implementation of the Binary Decision Diagram (BDD) that encodes the truth table representation of a Boolean function.The developed VBA tool provides an integrated risk analysis environment where the risk analyst uses familiar Excel spreadsheet tabs as a convenient vehicle to provide key inputs to backbone VBA modules.First, basic event definitions, associated descriptions and failure probabilities are provided, followed by system fault trees constructed therein to represent contributing causes to a top failure event.The fault tree is then converted to the corresponding BDD, which is subsequently solved to produce minimal cutsets (qualitative) and to calculate the top event probability using three methods (quantitative): rare event approximation, minimal cutset upper bound (MCUB) and exact probability calculation.Importance measures are calculated as part of the quantification process as well.Key algorithms involved in all these operations are implemented in a suite of VBA modules embedded in an Excel file named "VBA_BDD_PRA_Analyzer_R00.xlsm".One interesting feature of the developed tool is its capability to visualize the obtained BDD structure in an Excel spreadsheet.This enables the risk analyst to see how the system Boolean function of the top event is represented in the truth table via BDD.The risk analyst can visually trace various BDD paths leading to the top event failure that define minimal cutsets.Last, but not least, the developed program is a convenient educational tool the risk analysis can carry and play with to gain an enhanced understanding of how fault trees are solved to obtain qualitative insights as well as quantitative risk values, without being restricted by availability of commercial grade risk analysis software packages.All it takes is Microsoft Excel.Illustrative applications include the qualitative and quantitative analysis of an example fault tree, followed by the use of the developed tool for combining fragilities for seismic PRA applications.