Reliability Analysis Based on Aleatory and Epistemic Uncertainty Using Binary Decision Diagrams

The development of a mathematical model is an important step in reliability analysis. However, initial data are often not clearly defined, and some necessary information about the system’s behavior may be missing. Most mathematical models in reliability analysis primarily address aleatory uncertainty. However, recently, many problems in reliability analysis increasingly need to take into consideration epistemic uncertainty. Therefore, methods for developing mathematical models based on uncertain initial data should be refined to account for both aleatory and epistemic uncertainties. This is particularly true for models that represent a system using binary decision diagrams (BDDs). This paper proposes a new method for constructing a system’s mathematical model in the form of a BDD based on incomplete and uncertain data. Machine learning approaches and principles are employed in this method to account for the epistemic uncertainty of the initial data. A fuzzy classifier, specifically a fuzzy decision tree (FDT), is used to build a BDD from epistemically uncertain data. The use of a tree-based classifier allows simplifying the transformation between FDT and BDD.