Future advances in nuclear power technologies call for enhanced operator advice and autonomous control capabilities that can leverage simpler designs and increased safety features to reduce reliance on human labor. One of the first tasks in the development of such capabilities is the formulation of symptom-based conditional failure probabilities for the plant structures, systems, and components (SSCs) of interest. The primary goal is to aid plant personnel in (1) deducing the probabilistic performance status of the monitored SSCs and (2) detecting impending faults/failures. The task of estimating conditional failure probability is a bidirectional inference problem, and a logical approach is to use the Bayesian network (BN) method. As a knowledge-based explainable artificial intelligence tool and a probabilistic graphical model, BN offers reasoning capability under uncertainty, graphical representation emulating physical behavior of the target SSC, and interpretability of the model structure and results. This paper provides a systematic overview of the BN technique and the software tools for implementing BN models, along with the associated knowledge representation and reasoning paradigm. Both operational data and expert judgment can be readily incorporated into the knowledge base of a BN model. The challenges with data availability are highlighted, and the general approach to target SSC identification is presented. The focus is on failure-prone and risk-important balance of plant assets, especially for cases with strong operator involvement. Two example case studies on the failure of (1) a centrifugal pump and (2) an electric motor are conducted to demonstrate the usefulness and technical feasibility of the proposed BN-based fault diagnostic system using an expert system shell.