# Fault Inference of Electronic Equipment Based on Multi-State Fuzzy Bayesian Network
## 1 Introduction  
Electronic equipment has been widely used in industrial, military, and civil systems. Faults in electronic equipment degrade the performance of systems greatly. In order to guarantee normal operation and repair faults quickly, fault diagnosis and fault prognosis of electronic equipment have become a major topic of research [1; 2]. Fault inference refers to knowledge-based approaches of fault diagnosis [3; 4], which based on the fault state, correlation relationship, and fault propagation mode of modules of electronic equipment--the model is established to express the variable state, and then the correlation relationship is described. Multi-source information were fused, forward reliability and inverse module fault probability inference are carried out. Fault inference is employed to estimate the health of the whole system and circuit module by collecting and processing the necessary data information of electronic equipment, and instructing the tester to carry out condition based maintenance. In engineering applications, the automatic test and diagnosis system (ATDS) of the electronic equipment has been developing rapidly. High system integration and having overlapping modules, presents great difficulties for ATDS [5]. In the existing test program set, bootstrap program for fault test developed based on logic relationship of electric modules and on account of graph theory by integrating diagnose technology of fault tree, which is a graphical method for developing hierarchical relationships of parent-child nodes of electronic modules. This provides guidance of expert-type tests for non-expert engineering technicians, so as to rapidly locate faults and improve efficiency of diagnosis. Because of adverse operating environment of electronic equipment, presence of various types of uncertain information in the test and multiple fault modes, the traditional qualitative and quantitative fault inference methods are not suitable for fault inference of complex electronic equipment. The inference algorithm of the Bayesian network (BN) based on graph theory and probability theory can be used for bidirectional inference [6], namely, it can reason reliability of the system from root nodes to leaf nodes and weak linkage of the system from leaf nodes to root nodes. Therefore, it is widely used in fields such as cancer prediction [7], travel planning [8], classification of traditional Chinese medicine [9], and fault diagnosis [10; 11; 12; 13; 14]. In practical engineering applications, a system not only shows two states, i.e., normal or fault state, but also generally includes multiple fuzzy states. For this reason, BN is promoted and applied in reliability analysis on multi-state systems [15; 16]. In the circuit system, there may be a large parameter, a smaller parameter soft fault or a short-circuit, open-circuit hard fault, which is to say, the fault state is a multi-state system. The study of multi-state Bayesian inference is a necessary path for the practical application of circuit fault diagnosis. BN has been used in transient and intermittent fault diagnosis of electronic equipment [17; 18], the application of multi-state BN inference in fault diagnosis of electronic equipment is not found in the relevant literature, especially the research of the multi-state BN with fuzziness in the test diagnostic process of electronic equipment. Because there are multiple test indicators with different membership degrees of states for electronic modules and test samples are limited, statistical data are fuzzy. This paper is motivated by the problem of electronic equipment multi-state fault inference. Existing approaches do not involve the fuzziness in multi-test indicators of test points, prior probability, and conditional probability of electronic equipment. This paper suggests a multi-state fault inference model (FRM) of electronic modules based on fuzzy BN, so as to extend the bootstrap program for testing fault probability in the existing test program set.