Zero-suppressed ternary decision diagram algorithm for solving noncoherent fault trees in probabilistic safety assessment of nuclear power plants

Probabilistic safety assessment (PSA) plays a critical role in ensuring the safe operation of nuclear power plants. In PSA, event trees are developed to identify accident sequences that could lead to core damage. These event trees are then transformed into a core-damage fault tree, wherein the accident sequences are represented by usual and complemented logic gates representing failed and successful operations of safety systems, respectively. The core damage frequency (CDF) is estimated by calculating the minimal cut sets (MCSs) of the core-damage fault tree. Delete-term approximation (DTA) is commonly employed to approximately solve MCSs representing accident sequence logics from noncoherent core-damage fault trees. However, DTA can lead to an overestimation of CDF, particularly when fault trees contain many nonrare events. To address this issue, the present study introduces a new zero-suppressed ternary decision diagram (ZTDD) algorithm that averts the CDF overestimation caused by DTA. This ZTDD algorithm can optionally calculate MCSs with DTA or prime implicants (PIs) without any approximation from the core-damage fault tree. By calculating PIs, accurate CDF can be calculated. The present study provides a comprehensive explanation of the ZTDD structure, formula of the ZTDD algorithm, ZTDD minimization, probability calculation from ZTDD, strength of the ZTDD algorithm, and ZTDD application results. Results reveal that the ZTDD algorithm is a powerful tool that can quickly and accurately calculate CDF and drastically improve the safety of nuclear power plants.