edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 2 18 all tasks are non-preemptive or some tools can be used to execute only one task at a time. All these requirements, encoded in a machine-readable form using languages of constraints or mixed integer programming, are stored in a knowledge base. Every time a schedule must be computed, e.g., a new job arrives or a tool/engineer is idle, the system automatically generates an instance comprising the updated sets of jobs, tools, and engineers. Next, the instance is provided together with the knowledge base to a solver, and intelligent algorithms find a schedule. Machine learning approach. The main issue with the simple scheduling problem above is that an arbitrary FA job cannot be easily represented as a sequence of tasks. In many cases, the next task in a sequence is defined by the findings of an engineer while executing previous ones. Because there are many different special cases, experts are unable to list them all in a knowledge base and maintain this list over time. Instead, an expert uses machine learning methods to acquire this knowledge directly from data. Nevertheless, the application of such methods cannot be done completely automatically. Experts must use their knowledge about the domain to collect representative data describing various jobs, define a learning method and its objectives, and execute the training procedure. Given an observation comprising a sequence of tasks and data recorded during their execution, a trained model predicts the next task in the sequence. In addition, for many machine learning approaches experts must annotate the data with labels indicating the required outputs of a model. The annotation process might be quite costly, but it enables an additional knowledge transfer from experts to an AI system and, thus, often results in a better performance of trained models. Hybrid. As can be seen from the examples above, both approaches must be combined in a hybrid one to solve real-world problems appearing in the FA domain. However, the creation of such hybrid systems is still a field of active research[10] and, therefore, it is hard to give their systematic overview. Nevertheless, in the remainder of the paper, we provide hints about their possi- ble applications. SYMBOLIC METHODS One of the main hypotheses behind the symbolic methods assumes that any intelligent system represents and reasons about the world using symbols.[11] This family of methods originates in the attempts of Ancient Greece philosophers to establish laws of thought by formalizing principles of human reasoning. Thus, the syllogisms of Aristotle provided rules allowing for the derivation of correct conclusions out of correct premises. These rules showed that human decision-making can be automated, thus, initiating the study of logic. Over the centuries, logicians turned this field into a mathematically founded study of knowledge representation and reasoning, which ended up in the development of computer systems in the late 1960s that could, in principle, solve any problem represented in logic notation.[12] In the next two decades, a pure logicist approach to symbolic AI was extended with the development of heuristic search methods to create expert systems.[13] Equipped with encoded knowledge and powerful heuristic search algorithms, Deep Blue was able to beat Garry Kasparov in 1996. However, soon it was realized that the maintenance of large knowledge bases and logic-based reasoning differentiating only between true and false statements is insufficient to solve many real-world problems. Therefore, researchers started to extend symbolic methods with methods able to handle uncertainty, like fuzzy logic[14] or probabilistic reasoning,[15] as well as with learning capabilities, like version Fig. 3 Sample workflows of AI methods.
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