# Relaxed Rule-Based Learning for Automated Predictive Maintenance: Proof of Concept
## 1 Introduction
However, the dataset resulting from removal of the rows covered by \(R_{1}\) is smaller that the original dataset and, more importantly, is 'distorted' by a non-uniform removal of instances. As a result, learning of \(R_{2}\) in this distorted dataset becomes more difficult than in the original one. In case of more than two rules to be learned, this difficulty becomes even more pronounced. One way to address the above deficiency is somehow to assign weights to direct the RL algorithm towards considering instances that have not been covered. The main two approaches doing that are _weighted covering_[2] and _boosting_[4]. The weighted covering [2] attempts to generalize the SeCo method as follows. We can see SeCo as a method that assigns weight 1 to the instances not yet covered by the existing rules and 0 to the instances that are covered. Then new rules are sought over instances of non-zero weight. Weighted covering uses more flexible methods of weights assignment. The related heuristics are organized so as to choose heavier instances and this creates as a result a 'fuzzy' version of SeCo. It is important to note that whatever way the weights are assigned, the part of the dataset covered by the existing rules will be discriminated against the instances that are not yet covered. In other words the distortion of the dataset as presented in Example 2 will still be present in case of weighted covering. The boosting method [5] is a theoretical approach whose purpose is to show that a reasonable but not very accurate learning algorithm can undergo several rounds of retraining to learn a concept with an arbitrary degree of accuracy. The idea applied to RL [4] is that the learning algorithm first produces a single rule and then, as a result of boosting, new rules are added to the collection. In this paper we propose an alternative rule learning approach considering instances that have already been covered by the previous rules. We call this approach _Relaxed Separate-and-Conquer_ (RSC). In particular, when a new rule is formed, _it is required to cover at least one instance not covered by the previous rules_. This means that already covered instances are not excluded (like in the case of separate-and conquer) nor are they discriminated against (like in the case of weighted covering). However, the algorithm is forced to look not only at the already covered instances, but also elsewhere. The proposed RSC approach _generalizes_ both SeCo and weighted covering. In particular, any reasonable rule growing heuristic for SeCo or weighted covering can be simulated by an appropriate rule growing heuristic for the RSC method. Also, the rule growing heuristic can control 'tree-likeness' of the rules and hence can simulate any DT algorithm. More technical details related to the generalization are provided in Section 2.1 (Theorem 1). In addition in this subsection we propose Conjecture 1 formalising the intuition outlined in Example 2 regarding the advantage of RSC over SeCo. In this paper we apply the RSC method in the area of failure prediction of complex manufacturing machines. These sophisticated machines are equipped with a series of sensors and actuators that provide a combination of real-time data about the state of machines (performance) and product state (quality) during the production process. The attributes of the dataset correspond to sensors and the values of the attributes are respective sensor readings. The binary outcome column is interpreted as an alarm (outcome 1) or no alarm (outcome 0). The purpose of the failure prediction is to notify the operator of a forthcoming failure. Therefore, there is no point to learn rules whose outcome is 0. That is all the rules learned by a method we are going to present have 1 (an alarm) as the outcome. This allows to introduce the following two simplifications. 1. The outcome can be omitted. Therefore, each rule can be presented as a conjunction of (attribute, interval) pairs. 2. Since all the rules have outcome 1, conflicting predictions between overlapping rules cannot occur.