# Fault Detection, Diagnosis, and Prognosis of a Process Operating under Time-Varying Conditions
## 2 Literature Review
Predicting the health status trend of a piece of machinery allows expansion of the topic and context of decision making. It presents and reveals the possibility of adapting decision making, evaluating it in different time horizons [34]. In general, according to the existing literature, it is possible to state that extremely time-variable processes, regardless of the selected technique, are difficult to understand, and the prognostic analysis implemented is clearly affected [35]. This issue is still considered an open point in the literature, since many contributions and approaches focus only on the analysis of static operating conditions [36]. So, considering the management of machinery degradation, a lot of research is emerging and developing, all supported by an evident increase in the quality of sensors and monitoring techniques of machinery conditions. In general, however, some limitations in this regard are still evident and to be managed. One of these is the impossibility, in some contexts, to make run-to-failure machines operate, resulting in the lack of a sufficiently large historical failure dataset for subsequent analysis. This relates, then, to the need to focus prognosis analyses on specific variables that have greater predictive power with respect to degradation trends, so that accurate prognosis analyses can be achieved, reducing the inclusion of unnecessary information in the model [37]. In conclusion, the analyzed literature reveals the points of interest and innovation of the proposed contribution. First of all, the topic of the prognosis and the residual useful life of the machinery is still the starting point and the focus of extensive and heated debates, with a growing need for new contributions to this matter. Secondly, the type of process analyzed, i.e., an operating process under varying conditions over time, has many interesting facets but also numerous difficulties in the management of maintenance and data analysis, with greater repercussions on the topic of prognosis. This type of process, given the countless implicit difficulties, is currently less debated and has obtained fewer results than more linear and static processes. Ultimately, a final interesting point concerns the considered technique, CVA, and the approach proposed. On one hand, the use of CVA in this type of process is innovative because, as previously mentioned, multivariate statistics techniques still have limitations in such contexts. On the other hand, the proposedapproach is important for its dual role in fault detection and in the prognosis in conjunction with contribution plots and machine learning. Considering the results obtained in the previous contribution, the approach is innovative and even leaner than those that suggest intrinsic changes to CVA. The main contributions of this study to the research community are summarized as follows:  
1. This study applies state-of-the-art process control and machine learning techniques to a granulator operating in the pharmaceutical sector, with the developed models being verified with real-world data, thus offering a practical solution to the monitoring of the granulation process. 2. Unlike existing studies where fault prognosis was carried out relatively independent from fault detection, this study evaluates the influence of fault detection on prognosis by adding a connecting step between the two. The results show that the CVA-based contribution analysis can facilitate fault prognosis.