Predicting machinery failures is central to predictive maintenance, with two main paradigms commonly used to estimate time to failure: Remaining Useful Life (RUL) prediction and survival analysis (SA). However, a fair comparison between them remains challenging, as existing studies typically focus on a single paradigm or a limited set of evaluation metrics. We propose a unified evaluation framework that enables systematic comparison by transforming model outputs between RUL and SA representations, allowing the computation of any metric reported in the literature. Using this framework, we evaluate 15 models on two time-series datasets for failure prediction. Our results show that RUL models generally achieve superior predictive performance than SA. Nevertheless, SA models provide more interpretable outputs through explicit modeling of uncertainty. This work provides a practical guidance for a fair model selection in predictive maintenance.
Industry 4.0 integrates digital and physical systems, the Internet of Things (IoT), and Artificial
Intelligence (AI) to create sensor-rich manufacturing environments. Cloud and edge platforms support
automation, data collection, and real-time analytics, towards automated smart and safe industries [
PdM has been approached using various methodologies, including unsupervised anomaly detection
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Current research typically evaluates RUL and SA models in isolation [15, 16], limiting the scope of the insights obtained, while direct and fair comparisons across the two paradigms remain rare. Moreover, the widespread use of diferent evaluation metrics across studies further fragments the field, making it dificult to draw clear conclusions about relative model performance [14].
Motivated by the aforementioned challenges, we propose UniFPE, a Unified framework for Failure Prediction Evaluation for the systematic comparison of RUL and SA models. This framework enhances trustworthiness by enabling fair comparison between diferent model families—such as regressionbased RUL models and probabilistic SA models—under the same conditions. Beyond identifying bestperforming models, we also analyze the limitations of each approach in this work. Ultimately, our goal is to provide practical guidance for researchers in selecting predictive models for PdM applications.
In this paper, we make three main contributions. We propose a unified post-processing method that enables the production of both RUL estimates and ISDs from standard regression and survival analysis models. We then perform a comprehensive evaluation of 15 representative models on two time-series PdM datasets, providing a systematic comparison for the failure prediction problem. Finally, we analyze the transformation between RULs and ISDs, comparing ISD-derived RULs with regressionbased estimates and RUL-derived ISDs with those from SA models. This analysis reveals that RUL models generally provide more accurate and precise predictions approaching failure time compared to SA models.
Evaluating SA models alongside RUL models can be trivially done by applying RUL metrics after transforming the ISD into a single RUL estimate, usually by selecting a fixed probability threshold [13, 17]. In other work [18], the comparison between SA and RUL models was performed using only the C-index, which is applicable to both. Our methodology supports both C-index, but also enables a direct comparison of SA and RUL models in terms of any SA or RUL related metric. Thus, provides a more complete transformation of SA to RUL, without limiting the comparison between the two families to only ranking based metric C-index.
Remaining Useful Lifetime prediction, in the context of PdM, is typically formulated as a regression task, where, given historical failure and sensor data, the objective is to predict the time until failure. In data-driven PdM, researchers [19, 10, 11] employ established models such as XGBoost and Random Forests, as well as rule-based models [20]. Furthermore, Deep learning (DL) models designed for time-series data are also widely used [21]. In our evaluation we use and present both classical tabular and DL models.
Survival Analysis recently has seen increasing adoption in PdM applications [22], where researchers use SA models to estimate machines’ ISD [14]. The Cox proportional hazards model [23] (CoxPH), despite being introduced over half a century ago, remains one of the most widely used survival analysis models [24, 18, 25, 26, 13], suggesting that recent developments have not outperformed classical approaches in this domain. The review in [27] provides a good overview of SA models. In our evaluation we include and discuss both classical SA methods but also more recent DL models.
Our goal is to propose a unified evaluation of RUL estimation methods and SA methods for the problem of failure prediction. As failures, we consider events that cause monitored entities (e.g., machines or vehicles) to malfunction, stop operating, or break down, requiring replacement or heavy maintenance. Both RUL and SA methods leverage sensors and log data arising from continuously monitored entities, aiming to predict the time until the next failure event. While both methodologies aim to solve the same problem, they rely on diferent formalizations and provide diferent types of output. In particular, at inference time, RUL methods output a single real-valued RUL estimate, whereas SA methods produce probability curves (ISDs). In the following, we introduce the necessary notation and formally define the problem of unifying the evaluation of RUL and SA methods. This is accomplished by proposing a transformation of their outputs into both probability curves and RUL estimates.
For each entity ∈ E, where E denotes the set of entities, we observe multivariate time-series data X ∈ R× , where is the number of covariates and is the number of available timestamps for the particular entity . At timestamp , we observe x ∈ X, which represents the sensor readings produced by entity at time , with x ∈ R. Note, that depending on the underlying predictive Labeling scheme model, instead of , we may consider a sequence (or a window) of the ℎ most resent values of entity −ℎW,e c=las{sify−ℎth,ee−ℎn+ti1tie,s..i.n,tot}w.o categories, run-to-failure (RTF) marked with and censored entities. We refer to RTF entities as those that experience a failure event, which marks the end of their operational life. Respectively, We refer to censored entities as those for which data collection stops before a failure event occurs. We use the notation to indicate in which category each entity belongs. Specifically, = 1 indicates that the entity is an RTF entity and = 0 indicates that the entity is censored. For RTF entity , refers to the timestamp of the failure event, while for a diferent censored entity , corresponds to the last observed timestamp.
Then, we use the notation to denote the remaining time until the event (either failure or censoring) for entity at timestamp . Specifically, is defined as the time elapsed from timestamp until the failure time if = 1 ( = − ), or until the censoring time if = 0 ( = − ). Finally we formalise the dataset used by predictive models as = {︁(︁ {, x}= 1, ︁)}︁ , where denotes ∈E the number of available samples for entity .
RUL prediction The first family - RUL prediction - uses regression models to predict the RUL of an entity at a timestamp . Here, we impose the constraint of considering only RTF entities in the training data. Specifically, we consider the subset of the dataset = {︁{, x}= 1, }︁ , with = 1. Then, given , regression models are trained to compute the function ℱ (x; ) : R∈E → R ∼ , where represents the model’s parameters, utilizing the actual RUL labels . These models, in inference time, provide estimations of the actual (unknown) RUL ^.
Survival Analysis aims to provide the survival probability of failing entities in several future timestamps. Typically, methods in this family derive the ISD [14] of the entity, represented as a curve showing the survival probability of the entity as time progresses. In classical SA, a unique will be derived for each diferent patient based on their state. Inherently in PdM, we produce a diferent for every observation , which represents the state of the entity at each timestamp . Formally, given , the ISDs the SA models aim to learn is: ̂︀( | x) = P( > | x), ≥ 0, that characterizes the time-to-event distribution for entity at time with covariates x (or −ℎ, ). The estimation of ISDs is typically performed by maximizing a (partial or full) likelihood associated with a parametric, semi- or non-parametric survival model.
Next, we discuss evaluation metrics used to asses RUL and SA methods and present UniFPE. Specifically, we present how SA-generated ISDs can be transformed into RUL predictions, and on the other side, how RUL predictions for diferent timestamps can be converted into ISDs. Figure 1(a) illustrates how labels are derived from entities, as described in the previous section. Then Figure 1(b) provides a graphical overview of UniFPE. The figure illustrates deployed predictive models, including both RUL and SA models, all trained and validated on the same data (note that RUL models ignore censored data). It further shows how RUL predictions are converted into ISDs and how ISDs produced by SA models are translated into RUL predictions, enabling a unified evaluation of all predictive models on the test set. Finally, Table 1 summarizes the evaluation metrics used by UniFPE.
For evaluating RUL predictions, numerous metrics have been proposed [29]. A typical choice involves metrics commonly used in regression problems, which measure the distance between a prediction and the actual RUL (e.g., squared error, absolute error). However, because prediction errors become more critical as the entity approaches failure, it is often preferable to use the Mean Absolute Percentage Error (MAPE), defined as MAPE = 1 ∑︀=1 ⃒⃒⃒ ^− ⃒⃒⃒ , where is the number of samples. For example, predicting 210 days instead of 200 days yields the same absolute and squared error as predicting 12 days instead of 2 days. Yet, the latter case is far more harmful in a PdM scenario, since errors near failure carry higher risk. Instead of mean of the absolute presentage errors, someone can choose the median (MdAPE), towards robustness on outlier errors. Although we use MAPE and MdAPE as the main metrics for evaluating RUL predictions, we also compute a variety of additional metrics (refer to Table 1), all of which are provided along with our implementation.
In survival analysis, two widely used evaluation metrics are the Brier score and the Concordance index (C-index) [14]. The C-index evaluates whether a model assigns higher risk scores to entities that fail earlier. When models output an ISD, it is common to compute the C-index across time by using the ISD probability at each step as the score, yielding a C-index curve. Since the C-index is not specific to SA models, it can also be applied to RUL predictions by converting them to risk scores (e.g., using −^ ). While the C-index measures discriminative ability (capturing only the ranking of predicted risks and ignoring their calibration), the Brier score [30] evaluates both calibration and discrimination, and is defined as: BS() = 1 ∑︀=1 ︁( ( > ) − ^ ()︁) 2, where () is the predicted survival probability at time , ( > ) indicates whether the observed time-to-failure exceeds , and is the number of samples. The Brier score can also be computed across all ISD time steps, forming a curve, from which the Integrated Brier Score (IBS) summarizes performance: IBS = 1 ∫︀0 BS() .
We compute all aforementioned metrics (Brier, IBS, and C-index), and also include the best C-index across time steps and the worst Brier score (Maximum Brier Score, MBS), with primarily focus on IBS and MBS for comparing predictive models. Note that MBS is particularly useful, as IBS can be dominated by the very small (and thus good) Brier scores at early and very late time steps. These regions often behave like noise, since making reliable predictions at those stages is trivial (e.g., predicting near-certain survival at initial time steps and near-certain failure at very large time steps).
Instead of adopting a fixed threshold (e.g., 0.5) as done in [13, 17], we use a tuned threshold on the ISD that minimizes MAPE on a sampled validation set after training the SA model. A graphical representation of extracting ^ from ISD can been seen in the step b.2) of Figure 1. An SA model achieving a perfect implies that it produces ISDs with probability 1 for all times prior to the event (i.e failure) and probability 0 from the event time onward. Consequently, a model with perfect (i.e., = 0) will also achieve perfect MAPE, regardless of the use of calibrated threshold. This is because the predicted probability will always cross the decision threshold exactly at the true failure time, yielding an RUL estimate equal to the actual.
Although C-index can be directly used to evaluate RUL models, applying IBS requires first transforming RUL predictions into survival curves. A straightforward way is to rely entirely on the predicted RUL ^ and define a hard-mapped survival function () = (, ^) = {1 if < ^, 0 otherwise}. transformation provides a simple interpretation of RUL as an ISD. In the case of a perfect RUL model (with = 0), will result in Brier score and IBS equal to zero as well. But, for imperfect models, the Brier score evaluates each sample at time as either 0 or 1, meaning that the transformation favors samples with < min(, ^) or > max(, ^) and penalizes those where min(, ^) < < max(, ^). As a result, even small deviations between predicted and true RUL lead to the maximum penalty, reflecting the absence of uncertainty in the curve.
To address this limitation, we introduce a smoother transformation using the sigmoid function, inspired by its widespread use in neural networks for converting hard decisions into class probabilities [31]. A graphical demonstration of such transformation is depicted in the step b.1) step of Figure 1. The sigmoid yields an ISD corresponding to a logistic failure-time distribution centered at ^. In our evaluation, we report results using the sigmoid transformation, while providing the -based results in our repository [32].
4.1.1. Models In this section, we describe the evaluation setup used to tune and assess the performance of SA and RUL models. Subsequently, we present the PdM datasets used in our analysis, and finally, we report and discuss the results of our study. Result and implementation is available in [32]. In this study we include the following SA models. First, the Cox Proportional Hazards model (CoxPH) [23], a semi-parametric approach that estimates the efect of covariates on event times through hazard ratios. Second, the Random Survival Forests (RSF) model [33], which extends random forests to handle censored data and generate non-parametric survival functions. Third, the Recurrent Deep Survival Model (RDSM) [34], an LSTM-based architecture specifically designed to model time-dependent covariates and capture nonlinear temporal dynamics in survival predictions. Finally, we also include DeepHit [35] a non-parametric model, which leverages NN to learn the distribution of survival times directly.
For RUL estimation, we incorporate commonly used regression models for RUL prediction as well as state-of-the-art time-series regression models that have demonstrated superior performance in recent benchmarks [36]. Classical machine learning methods comprise of: i) XGBoost [37], a gradient-boosted ensemble of decision trees, ii) CatBoost [38], which incorporates ordered boosting and target statistics Censored Failure 20k 15k 10k
Censored Failure 0 200 400 600 800 Time-to-event (or RUL) 1000 0 100 200 300 400 Time-to-event (or RUL) 500 to efectively handle categorical variables, iii) TabPFN [ 39], a tabular foundation model, iv) Elastic Net regression [40], and v) Random Forests (RF) [41]. In addition, we evaluate several deep learning architectures tailored for sequence modeling, including ResNet [42], a residual convolutional network adapted for regression; InceptionTime [43], which uses multi-scale inception modules for time-series forecasting; standard CNNs [44] adapted for regression; Fully Convolutional Networks (FCN) [45], which omit pooling layers to preserve temporal resolution; LSTM-FCN [46], combining recurrent and convolutional feature extraction; and ROCKET [47], a linear model built on features generated by random convolutional kernels.
This study focuses on PdM, consequently, we have included two industrial datasets consisting of dynamic, multivariate time-series data, with ground-truth derived from failure and maintenance logs. Figure 2 depicts the distribution of the time to event labels , for both RTF ( = 1) and censored ( = 0) entities. In our evaluation, we maintain a fixed ratio of censored to RTF samples of 0.5 for both datasets.
SCANIA dataset [48] comes from the IDA 2024 Industrial Challenge and consists of telemetry and specification data from several SCANIA trucks. It includes 113 operational features, both numerical and categorical, like engine type and wheel configuration.
AZURE dataset [49] comprises hourly measurements of voltage, rotational speed, pressure, and vibration signals collected from 100 simulated machines under realistic industrial setting, provided by Microsoft Azure. In addition to the sensor readings, the dataset includes records of maintenance operations for individual machine components, failure events, corresponding to machine breakdowns, and categorical data of error states.
For both dataset we split the data into train, validation and test set. The spliting was done such that 60% of the entities belong to training set, 20% of entities belong to validation set and the ifnal 20% of entities belong to test set. In the training set we also include Censored entities which are only leverage from SA methods, which inherently have the capability of considering censored data to improve the predictions. Finally categorical features are transformed using one-hot-encoding for both datasets.
For each method, we optimize the hyperparameters (or the architecture, in the case of deep learning models) using the Mango Bayesian optimization framework [50] on the training and validation sets, while final model performance is evaluated on the test set. We perform 20 optimization steps and retain the best configuration. For RUL models, the optimization metric is MAPE, whereas for SA models it is IBS. For a fair comparison across models, the test set includes only RTF entities (i.e., entities that ultimately fail) since computing regression-based metrics requires ground-truth RUL values.
In this section, we present the results of our evaluation study. We begin by discussing the bestperforming predictive models overall and assessing the impact of the tuned thresholding strategy. We then focus specifically on the ability of the predictive models to estimate RUL and to generate valid ISDs.
Figure 3 reports the performance of RUL and SA models on the SCANIA (a) and Azure (b) datasets, evaluated using IBS and MBS (SA metrics), and MAPE and MdAPE (RUL metrics). At first glance, it is evident that regression models specifically designed for time-series data e.g., ResNet, LSTMFCN, Inception Time, FCN, consistently achieve the best performance across both metrics and datasets.
On the SCANIA dataset, considering SA metrics, SA models outperform classical tabular regression methods in terms of IBS, but are outperformed by time-series deep learning RUL models. With respect to RUL metrics, SA models exhibit performance comparable to tabular RUL models, for both MdAPE and MAPE. In the Azure dataset, time-series RUL models achieve the best results in terms of both IBS and MBS, while SA models do not surpass tabular RUL approaches. Regarding MAPE and MdAPE, time-series–based RUL models again achieve the best performance. In contrast, SA models don’t exhibit consistent behavior. Instead, performance varies across individual methods: RSF and DeepHit achieve low MdAPE values, whereas RDSM and CoxPH show performance comparable to that of tabular RUL models. Although the ranking of methods difers between SA and RUL metrics in both datasets, the overall performance trends remain consistent. An exception is observed for RSF and DeepHit in terms of MdAPE, where they are ranked higher than when evaluated using IBS. The reason for this discrepancy lies in the use of calibrated thresholds for deriving RUL estimates, as discussed in the following section.
Although RSF and DeepHit on the Azure dataset do not produce more calibrated probabilities than other methods, as reflected by their IBS scores, they assign consistent probability values at the true time of failure. Figure 4 illustrates RSF predictions for a representative entity in Azure dataset, where red markers indicate the probability assigned by each survival curve at the true failure time (i.e., the actual RUL). These values cluster around 0.77 rather than approaching zero, indicating a systematic shift in probability scale rather than random miscalibration. Because this behavior is consistent across samples, applying a calibrated threshold enables a more accurate estimation of RUL, thereby reducing the error between predicted and true RUL.
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We further evaluate the impact of tuned threshold by comparing the performance of all SA models on both datasets using a calibrated threshold versus a fixed threshold of 0.5, which is used in prior works [13, 17]. Overall, tuned threshold reduce MAPE and MdAPE by approximately 28% compared to the fixed-threshold setting, indicating that interpreting survival probabilities through dataset-specific thresholds yields more reliable RUL estimates in practice.
Taking a closer look at the model results, we observe that the main diference between high-performing models (time-series regression models), SA models, and classical regression models lies in their ability to accurately predict near-failure instances. Figure 5 presents the MdAPE achieved by each method across diferent RUL bins. To obtain this visualization, we partition the RUL labels into 10 uniformly distributed bins, such that each bin contains one-tenth of the samples. From Figure 5, we observe that all models achieve relatively good performance in the mid-range RUL regions. However, classical regression models and SA models exhibit substantial deviations from the true RUL values in the initial bins, which correspond to near-failure instances. While this behavior is also present for some time-series regression models, their relative error remains considerably lower. Overall, classical regression and SA models appear to capture the median survival behavior of entities, producing accurate predictions for middle RUL regions, but fail to adequately capture near-failure behavior.
Focusing specifically on SA models, accurately modeling near-failure instances requires producing steep survival curves, such that the probability drops sharply at the true failure time. This limitation is illustrated in Figure 6, which shows ISDs generated by the RDSM model for a vehicle in the SCANIA dataset. In the figure, the red markers denote the true RUL values for each observation. For instances far from failure, the survival probability assigned at the true RUL is near zero, which is the desired behavior. However, for instances close to failure, although the corresponding ISDs shift their mass toward earlier times, indicating higher risk, the curves are not suficiently steep. As a result, the survival probability is not close to zero at the actual RUL, leading to inaccurate RUL estimations when a threshold-based conversion is applied. This illustrates a limitation of SA models in capturing sharp transitions near failure in the examined long time-series PdM settings.
For regression models we transform RUL estimations to ISDs leveraging the sigmoid function instead of using step function , as explained in Section 3.2.4. This choice is validated by our experiments on both datasets for all 10 regression models; namely, we observe that the sigmoid transformation resulted on statistically better and than the transformation (statistical significance is measured using Wilcoxon test [51]). In particular, the sigmoid transformation achieved lower and in all cases.
The models examined in this study difer in how they convey failure risk over time. RUL models remain point-estimate predictors; however, our proposed sigmoid-based transformation allows their scalar outputs to be expressed as smooth ISDs, yielding a consistent representation of temporal risk centered at the predicted RUL. Because the sigmoid employs a fixed smoothness parameter, this representation does not vary across operating conditions (i.e., the same sigmoid transformation is applied regardless of the observed covariates). Therefore, it reflects a post-hoc uncertainty rather than instance-specific aleatoric uncertainty inferred from the data.
In contrast, SA models estimate ISDs directly as part of their training objective, providing a view of how predicted risk evolves over time. In the examined PdM cases, particularly in near-failure regimes, these models tend to produce relatively smooth survival curves, which limits the precision of RUL extraction, reflected in higher MdAPE in the lowest RUL bins (see Figure 5). Calibrated thresholds partially mitigate this efect by aligning probability levels with dataset-specific error objectives, improving RUL accuracy without altering the underlying uncertainty structure. Overall, the results expose a practical tradeof: time-series RUL models yield sharper near-failure estimates but rely on post-hoc mechanisms to express uncertainty, whereas SA models provide a more direct temporal risk representation but struggle to provide low survival probability in critical regimes. From an interpretability perspective, these diferences afect how decisively and transparently models communicate failure risk to downstream decision-makers.
In this work, we propose UniFPE for comparing RUL and SA models for failure prediction and apply it to two predictive maintenance datasets. Our results show that time-series regression models consistently outperform both SA models, including RDSM, which is specifically designed for time-dependent data, and classical regression approaches. Moreover we show that, accurate RUL predictions can yield probability curves that are more calibrated and more discriminative than ISDs produced directly by SA models. A possible explanation is that regression models have a simpler learning objective, predicting a single continuous value, in contrast to SA models which aim to estimate full survival distributions, introducing additional complexity that may limit their ability.
On the other hand, SA models inherently provide uncertainty estimation, leading to more interpretable results than RUL models. Based on our findings, two main future research directions emerge: (i) investigating how SA models can benefit from the strengths of RUL models (e.g., whether pretrained RUL models can be adapted for survival analysis tasks), and (ii) developing improved methods for transforming RUL predictions into ISDs that explicitly incorporate uncertainty, rather than relying on ifxed transformation.
During the preparation of this work, spelling and grammar checking were supported by Overleaf and Grammarly. Typing assistant software was used to improve the spelling and grammar of the existing text. The authors reviewed and edited the content as needed and take full responsibility for the publication’s content.
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