# Relaxed Rule-Based Learning for Automated Predictive Maintenance: Proof of Concept
## 1 Introduction
The failure prediction task explored in this paper is an important method of _Predictive Maintenance_ (PdM). PdM is a set of techniques helping engineers to organize maintenance based on actual information about forthcoming failures [6]. The main aim of PdM is to reduce operating costs of two other maintenance strategies [6]: (1) Run-to-Failure (R2F) where corrective maintenance is performed only after the occurrence of failures; and (2) Preventive Maintenance (PvM) where equipment checks are performed at fixed periods of time. PdM also prolong the useful life of the equipment [7] and optimize the use and management of assets [8]. PdM uses predictive techniques, based on continuous machine monitoring, to decide when maintenance is needed to be performed. Two main approaches to the design of PdM software are Discrete-Event Simulation [9] and ML. The ML approach is based on prediction of future performance based on historical data. Large volumes of past performance data have been collected in large enterprises. With the advent of modern ML approaches, the analysis of these data can provide very useful information about the future performance. There are many results applying ML to the past performance data of the equipment, see surveys [10; 11; 12] for comprehensive overviews. The existing ML methodologies for PdM are based on methods such as Support Vector Machines [6; 13; 14; 15; 16; 17; 18], \(k\)-Nearest Neighbors [6; 13; 16], Artificial Neural Networks and Deep Learning [16; 19; 20], stochastic processes [21], K-means [13; 16; 22], Bayesian reasoning [23]. Ensemble methodologies where several methods are used and the weighted average of their predictions are reported in e.g. [24; 25; 26]. Rule-based methods are rather under-represented in PdM. DT based methods have been proposed in e.g., [16; 27; 28]. _Random Forests_ (RF) based methods have been used in e.g., [29; 30; 31]. The use of more generic rule-learning such as SeCo is even more limited in the area of PdM: we are only aware of work [32] (thanks to the anonymous reviewer for bringing this paper to our attention). Our paper reports a progress towards further exploration of the potential of rule learning in the area of PdM. In the context of failure prediction, we report the following technical results. 1. We present a generic framework forming a collection of rules according to the RSC approach. In particular, this framework allows implementation of a wide range of heuristics. 2. We present one particular heuristic that aims to maximize the precision of the newly formed rule as well as the coverage of the positive instances that are not covered by the previous rules. 3. We present empirical investigation of the resulting rule learner. In particular, we compare the RSC approach with a DT based and SeCo rule learners on two domains: 1. A randomly generated dataset simulating alarms caused by small number of factors. 2. A real industrial dataset collected from a machine which manufactures the plastic bottle caps. This dataset records alarms occurred in this machine and the associated sensor readings. In both cases the RSC algorithm significantly outperforms the DT based rule learner and SeCo method using the same heuristic. The RSC produces a set of rules that is smaller and much more accurate DT based and SeCo rule learners. We conclude that the RSC is a promising approach deserving further investigation. The rest of the paper is organized as follows. In Section 2 we describe the Relaxed Separate-and-Conquer (RSC) rule learning approach and provide its theoretical justification. In Section 3 we provide the experiments. Section 4 concludes the paper.