# Assisted-Driven Design of Customized Maintenance Plans for Industrial Plants
## 2 Methodology
### CBR Method  
The Case-Based Reasoning (CBR) method was originally pioneered by [PERSON] [30] from his research work on dynamic memory [31], in which he discovered that memory recalls solved cases as similarity patterns to solve new problems posed. In this way, he defines reasoning based on cases as \"the resolution of problems using or adapting the solutions of old problems\" [32]. Case-Based Reasoning (CBR) is an artificial intelligence paradigm that combines problem solving and learning, as established by [PERSON] [33]--that is, Case-Based Reasoning (CBR) is a method to describe a problem posed where various technologies can be used for its resolution. In this work, jCOLIBRI, developed by [PERSON] [34], has been used as a technology for the algorithmic implementation of the Case-Based Reasoning (CBR) methodology in the Java programming language [35]. In summary, the Case-Based Reasoning (CBR) method is based on the hypothesis of human reasoning, where similar problems present similar solutions; therefore, it is about solving problems by adapting solutions to problems previously solved successfully and by describing them in a similar way to the new problem raised. In this sense, it is possible to differentiate two spaces: the space of the problem posed, called the description space, and the solution space. The CBR method is described as a cyclical process, as seen in Figure 3, with four activities: Recover, Reuse, Review and Retain. Once a new problem arises, a new case is created in the description space, and the Retrieve activity makes it possible to obtain from the case base those problems that are most similar to the new case described. Figure 2: Detail of the RCM decision diagram; adapted from [29]. Once the most similar case is obtained, called the recovered case, the second activity is called Reuse--that is, the solution of the recovered case is used as an approximation of the solution of the new problem posed. This proposed solution, if necessary, is revised or better adapted to the problem initially raised, obtaining an adapted case with a new solution. If this solution is validated as good, the last activity consists of retaining the case as a new learned case and incorporating it as a new case added to the case base. As can be seen, the CBR method seeks to increase knowledge by incorporating new cases each time the CBR cycle is invoked. Of the four activities, attention is focused on the recovery activity to establish that this methodology allows for the use of different technologies to recover cases due to similarity. In this work, the Nearest Neighbor algorithm (hereafter NN) has been used to model the similarity between the new case and the existing cases in order to obtain the recovered case. kNN is the most widely used recovery method in the CBR methodology [36]; this has been evaluated as the most accurate method compared to other methodologies such as k-means clustering (k-means), FCM (Fuzzy C-Means) and SOM (Self-Organizing Map). According to [PERSON] [33], the similarity can be assessed as described in the following equation:  
\[\text{Similarity}(\text{T},\text{S})=\sum\text{f}(\text{Ti},\text{Si})\cdot \text{wi}, \tag{1}\]  
The similarity between an objective case, T, and a case of the base of cases, S, is evaluated with the similarity function, f, for the attribute, i, extending it from the first to the last, n, of each case. As can be seen in \"(1)\", it is a sum weighted by the weight, wi, that marks the importance of each attribute, i. Extending this assessment between the objective case, T, and all the cases of the case base, Sj, of those existing, m, a normalized and ordered list can be obtained from the highest to the lowest, thus configuring from the most similar cases to those least close to the target. Finally, only a group of them will be taken from the entire list, the first k most similar to the objective. In this work, a value of k = 3 has been considered, according to the recommendation of an interval comprised of 1 to 4 according to the study by [PERSON] and [PERSON] [37].