# Machine Failure Prediction Using Survival Analysis
## 2 Related Work  
Despite the abundance of statistical methods that can be used, survival analysis is conceptually largely aligned with the study of predicting the failure of a machine [16]. Kaplan-Meier curves and the COX regression model have been employed in similar research to determine the relationship between the survival time of a subject and one or more prognostic variables. In [17], the SMED (single-minute exchange of die) philosophy and survival analysis are used to reduce transition times. In this research, the COX model is also used to identify the significance of causes of time loss. The proposed methodology predicts activity times, considering only the characteristics that were identified as significant toward transition times, which is defined as a limitation by the authors. Similarly, the model proposed in [18] follows a gradual Bayesian approach to model failure using the tree-like accident theory and the Bayesian survival analysis model to predict the probability of survival for welded pipes. Using Bayesian, Kaplan-Meier, and Weibull curves, the authors construct staged Bayesian distribution, which is then used to make predictions about the time-to-failure of the pipes. Weibull distribution is also used in [19] to predict the life of battery cells, combined with the exponential, log-normal, and log-logistic distributions to create an accelerated failure time (AFT) parametric survival model. In this research, the authors concluded that low values of prediction error could be achieved by only using a small number of variables on the proposed model. The authors assert that this discovery holds significant value in their research, as their model yielded a total decrease of 40% in the root mean square error (RMSE). A limitation of this study is that the authors relied on only two datasets to support their findings, without exploring the use of other datasets. In [10], an LSTM approach is presented for the remaining life prediction of machines. The proposed approach leverages the advantages of LSTMs in capturing temporal dependencies in sensor data while also effectively handling missing data. The authors conducted experiments on a real-world dataset of a milling machine and evaluated the performance of their novel approach in comparison to various baseline methods. The results indicate that the LSTM-based approach surpasses the other methods in accurately predicting the machine's health status and effectively capturing its dynamic behavior. Out of the variety of models tested, the bidirectional-LSTM model had a total RMSE value of 15.42 cycles, outperforming all other models, such as deep convolutional neural network (DCNN) (18.44 cycles); support vector regressor (SVR) (20.96 cycles); multilayer perceptron (MLP) (20.84 cycles); bidirectional recurrent neural network (BD-RNN) (20.04 cycles); and a classic LSTM (18.07 cycles). Similarly, the authors of [11] proposed a semi-supervised deep architecture for predicting the remaining useful life (RUL) of turbofan engines. The model uses both labeled and unlabeled data to enhance its performance and reduce the need for extensive labeled data. It involves a combination of a convolutional neural network (CNN) and a LSTM network that work in tandem to extract features and capture the temporal dependencies of the input data. The model was evaluated on the C-MAPSS dataset and compared against several state-of-the-art methods, achieving superior performance in terms of both RUL prediction accuracy and mean absolute error. Specifically, the model proposed by the authors yielded superior RMSE results for most of the subsets that it tested, with the value of 12.10 on the FD003 subset being the lowest, while also providing the best prediction result on all of them (FD001: 231, FD002: 3366, FD003: 251, FD004: 2840). A limitation of the study, as stated by the authors, is the use of a piece-wise linear degradation model, which does not account for the individual degradation patterns of each engine in each subset.