## 8 Summary and Outlook  
This work identified important papers and techniques used in the field of state of the art equipment maintenance systems based on a bibliometric analysis. The latter covers temporal, geographical, author-related, and technique-related issues. For this analysis, we used search strings from contemporary maintenance methods to extract sets of papers from an academic database.  
This work provides an overview on maintenance strategies on one hand and serves as a schema to categorize future research results on the other by providing look-up tables for research fields and techniques. The techniques, which were mostly identified by keywords, indicate how researchers approach the topic of _state of the art equipment maintenance systems_. Furthermore, each research field is represented by the most important paper, whose importance is determined by the number of citations. The collection of lead documents extracted from different search strings is not comparable due to different time periods and research fields.  
We further introduced an importance measure to compare the papers by standardizing their properties and by expressing their relevance in a more cluster-independent way. The weighting of each parameter needed for calculating of the importance measure can be chosen by the conductor of the analysis. Therefore, this procedure is adaptive and can be reused in other bibliometric analyses. Since _state of the art equipment maintenance systems_, mainly represented by predictive maintenance, constitute a growing research field, it is important to stay informed about the current research. This work allows for the classification of emerging works as well as for the comparison with existing literature. As shown, the topic of equipment maintenance systems consists of many different research fields and various applied techniques. For our future work, we will focus our research on modular predictive maintenance applications. These applications, in turn, need to scale up with an increasing number of sensors, as particularly required in the context of the Internet of Things. We will evaluate the integration of the revealed techniques into new equipment maintenance systems modules. Finally, further research will emphasize the modular design of predictive maintenance applications to support scaling applications and flexible procedures.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
AHP Analytic Hierarchy Process  
FA Frequency Analysis  
FEA Finite Element Analysis  
IR Infrared  
MCO Maintenance Cost Optimization  
MPC Model Predictive Control  
RCA Root Cause Analysis  
SVM Support Vector Machine  
To understand how clustering works, the computation of the _second-order similarities_ will be explained. First, all the terms of title, abstract, and author keywords are combined and preprocessed. This procedure includes _stemming_ (reducing words to their word stem), removing _storwords_ (like _the, a..._), and _filtering_ special characters. Let \(f_{im}\) be the frequency of a term \(t\) in document \(m\), while \(N\) represents the total number of documents and the number of documents containing \(t\) is denoted as \(j_{i}\). The resulting weight of terms is called _TF-IDF_:  
\[w_{tm}=f_{tm}*log\Bigg{(}\frac{N}{n_{t}}\Bigg{)} \tag{1}\]  
By summing up the second-order weights and applying Salton's Cosine for two documents \(m\) and \(p\), with several terms \(k\), we receive the _first-order similarity_:  
\[s_{mp}=\frac{\sum_{i=1}^{k}w_{im}\cdot w_{ip}}{\sqrt{\sum_{i=1}^{k}w_{im}^{2}} \cdot\sqrt{\sum_{i=1}^{k}w_{ip}^{2}}} \tag{2}\]  
To have a connection among all documents, we execute the cosine index once more and obtain the second-order similarity matrix \(s_{2,mp}\), which is filtered in a final step with the \(k\)-nearest-neighbour method.  
\[s_{2,mp}=\frac{\sum_{j=1}^{N}s_{jm}\cdot s_{jp}}{\sqrt{\sum_{j=1}^{N}s_{jm}^{2 }}\cdot\sqrt{\sum_{j=1}^{N}s_{jp}^{2}}} \tag{3}\]