edfas.org 19 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 2 spaces, rules and decision-tree learning,[16] or inductive logic programming.[17] Symbolic AI methods are widely applied in the semiconductor industry. One of the first applications can be found in the seminal thesis of Shannon, who applied Boolean logic to analyze relay and switching circuits.[18] This work resulted in tools for the design, layout, verification, and diagnosis of semiconductors. In the FA context, the latter plays an important role in the failure localization in digital circuits. For instance, the main idea of model-based diagnosis methods[19,20] is to encode a circuit specification using some formal language and then reason about possible root causes of discrepancies between electrical outputs of a physical device with expected outputs according to its specification. Selected FA applications of diagnostic methods resulting in this work can be found in references 21-23. Similarly, rule engines were extensively used to create expert systems for FA.[24,25] The knowledge base of such systems included a set of rules encoding expert knowledge and a reasoning engine. Given data about the jobs, available resources, and results of already finished tasks, the reasoning engine deduced the next task(s) required to localize a failure. To handle uncertainty some of the recent expert systems applied graphical models, such as Bayesian networks,[26] where expert knowledge can be used to model dependencies between failures and symptoms. Next, experts can manually specify conditional probability tables of these dependencies or extract them from databases by computing how often dependent concepts appear in them together. Whenever an engineer communicates new evidence to the system, it automatically recomputes probabilities for possible failures and recommends the next steps. Another application of symbolic AI lies in the definition of FA ontologies or knowledge graphs—knowledge bases describing main FA concepts and relations between them and storing them in a machine-interpretable form.[27] Modern ontologies are a knowledge representation and reasoning approach developed in the framework of the Semantic Web initiative.[28] In many cases, an ontology en- codes knowledge and/or data of a domain using formal languages such as Resource Definition Framework Schema (RDFS) or a more expressive Web Ontology Language (OWL). In the FA case, an ontology can store a hierarchy of concepts denoting physical failures, their electrical characterizations, failure mechanisms, possible locations, available tools, or descriptions of analysis tasks and methods. For example, a part of an FA ontology, shown in Fig. 4, comprises the definition of the “Failure” concept that comprises among others two subconcepts—“Physical” and “Electrical.” The Physical concept is a general class that comprises all possible physical failures, like FusedWire, as subclasses. In addition, the ontology indicates that FusedWire has HighResistive electrical class as its exter- nal signature, and cannot have Short. An ontology brings many benefits: First, the collection of concepts stored in an ontology acts as a domain and/ or range for other AI methods. That is, they can be used to label data, such as job reports or images, and used as an output of machine learning models. As a result, FA engineers can easily and unambiguously interpret results output by AI methods since an ontology provides clear and precise definitions of all concepts that can be used in reporting by an FA lab. Second, an ontology can establish interoperability between different FA systems by providing unique identifiers of concepts and relations. For instance, two documents like a wiki page describing best practices Fig. 4 FusedWire physical failure described in the FA ontology.[27]
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