Centrifugal pumps are critical assets in oil refineries, many of which handle hazardous fluids that are flammable and pose potential environmental and health risks. Ensuring their proper maintenance and operation within design parameters is essential to prevent breakdowns and minimize industrial incidents. To understand their Mean Time Before Failures (MTBF) is critical in managing these assets, which is impacted by a number of different factors. While many studies explore the physical and experimental failure mechanisms of these pumps and their components, the relative impact of each factor is rarely quantified for rotating machinery in predictive models.

This paper highlights the key variables used for predicting the Mean Time Between Failures (MTBF) of centrifugal pumps by using four distinct methods. The first three approaches utilize Cox Proportional Hazards Models (PHM), while the final one relies on Machine Learning (ML) techniques. The first approach applies the partial Likelihood Ratio (LR) χ2 test, while the second and third approaches use a Lasso and Bayesian process to shrink the regression coefficients and rank the variables accordingly. Finally, the fourth method assesses the relative influence of the variables using a Random Forest (RF) model. A set of 27 potential predictors of 675 pumps in an oil refinery is analyzed using these methods. These predictors are grouped into six categories: mechanical design, hydraulics, sealing, vibrations, lubrication, and maintenance history. The results aim to improve maintenance actions, maximize equipment lifespan, and ensure reliable operation.

Predictive reliability, or the ability to anticipate the failure probability of a system or component, is essential to extend the useful life of assets, prevent breakdowns, and minimize industrial incidents. Centrifugal pumps are among the most important assets in oil and gas applications, and their reliability is critical to operational availability and safety. As a result, predictive reliability strategies have increasingly been applied to these systems in recent years to enhance performance and reduce unplanned failures. Many studies have investigated the failure mechanisms of centrifugal pumps, and several time-to-failure predictive models have been developed, but the relative impact of the variables affecting their expected life is rarely quantified. Different methods often have significant variability in their results, due to method definitions, model behavior, and data-related factors like collinearity, sampling noise, and interactions. This paper addresses the issue by quantifying the influence of key variables through the application of four different methods. Three are based on statistical techniques: partial Likelihood Ratio (LR) χ2 analysis, Bayesian coefficient magnitudes, and the variable inclusion order in Lasso regression applied to a Cox Proportional Hazards Model (PHM). The fourth method employs a Machine Learning (ML) technique, permutation importance applied to a Random Survival Forest (RSF) model. As a robustness check of the RSF model, a gradient boosting survival model was fitted. SHAP values were also computed for both ML models and compared with permutation importance scores to assess the stability and consistency of variable-importance rankings. The procedure was implemented on a real-world dataset from an oil refinery, consisting of 675 pumps with a set of 27 potential predictors. Both ordinal and weighted rankings were computed, with weighted rankings providing deeper insights than ordinal rankings by capturing the relative differences between variables. Lasso and Bayesian Cox exhibited the highest variability in these rankings, while the RSF method showed the lowest variability (mean inter-quartile range: 2.7) and the strongest correlation (0.787) with the average ranking across models. Maintenance work orders consistently emerged as the most influential predictor of MTBF followed by pumped fluid, discharge pressure, and manufacturing year. To address variability, the Copeland–Llull voting method was applied to individual and aggregated rankings, reducing dispersion and improving robustness. Bootstrap resampling further quantified uncertainty and confirmed the stabilizing effect of this technique. Although minor changes occurred in variable ordering, key predictors remained dominant. Grouping variables into six categories revealed maintenance as the most impactful category followed by operating conditions. Overall, this approach enhances ranking stability and provides actionable insights for reliability analysis.

Prognostics and Health Management (PHM) is critical for predicting the Remaining Useful Life (RUL) of systems, a key enabler of Predictive Maintenance (PdM). This paper reviews state-of-the-art data-driven prognostic models, emphasizing four essential characteristics: uncertainty, robustness, interpretability, and feasibility. While traditional research has focused on enhancing RUL prediction accuracy, this review argues that these additional characteristics are equally vital for addressing the demands of PHM applications.

The review examines Machine Learning (ML) techniques, stochastic models, and Bayesian filters (BFs), analyzing their strengths, limitations, and trade-offs. ML models excel in accuracy but often lack robust uncertainty quantification and adaptability across varying operational conditions. Stochastic models demonstrate greater robustness and feasibility, performing reliably with limited or variable data. Bayesian filters provide high interpretability and do not require run-to-failure data but face challenges in adapting to diverse environments.

To bridge these gaps, this paper proposes a structured Model Evaluation Framework that integrates users’ specific needs with key model characteristics identified in the review. By quantifying the importance of the four characteristics, the framework enables systematic evaluation and selection of prognostic models.

The findings underscore the need for advancements in uncertainty quantification, adaptive methods to improve robustness, and enhanced interpretability to meet practical and regulatory requirements. While current models offer valuable insights, further improvements are necessary to unlock their full potential for PHM and PdM applications, ensuring more reliable and actionable predictions.

This paper presents the use of proportional hazards regression models for predicting the Mean Time Between Failures (MTBF) of centrifugal pumps in the oil and gas industry. To that end, a dataset collected over 8 years including both design and operational variables from 675 pumps in an oil refinery was used to fit statistical models. Parametric and non-parametric transformations and restricted cubic splines were used to fit the covariates, thereby relaxing linearity assumptions and potentiating predictors with strong nonlinear effects on the outcome. Standard Principal Component Analysis (PCA) and sparse robust PCA methods were used for data reduction to simplify the fitted models and minimize overfitting. Models fitted with sparse robust PCA on non-parametrically transformed variables using an additive variance stabilizing (AVAS) method are suggested for further investigation. The complexity of the fitted models was reduced by 85% while at the same time providing for a more robust model as indicated by an improvement of the calibration slope from 0.830 to 0.936 with an essentially stable Akaike information criterion (AIC) (0.34% increase).

Prognostics and Health Management (PHM) is a multidisciplinary framework that provides vital information to operators to ensure maximum system uptime and system safety. It does this by estimating the current and future condition (health) of engineering systems and providing decision support. In recent years, PHM has evolved from being a post hoc maintenance support tool to an essential system that should be integrated throughout all stages of the equipment lifecycle. This chapter describes the essential steps of how PHM can be used in the design and manufacturing of future aircraft. There are many benefits in adopting and evaluating PHM in the design stage. This includes a system that is ultimately easier to monitor and maintain, has better logistics, has reduced overall costs, and has less unplanned downtime. As such, it is argued here that PHM should be designed together with the aircraft. Therefore, this chapter proposes a methodology that includes PHM considerations at all stages of aircraft design. By promoting the integration of these disciplines − PHM, engineering design and manufacturing −, we hope to contribute to more reliable and safe aircraft that can achieve more cost-effective operations and a more sustainable future. 

Prognostics and Health Management (PHM) plays a key role in predicting the Remaining Useful Life (RUL) of systems, which is essential for enabling decision-making for Predictive Maintenance (PdM) and operations. While most research has traditionally focused on improving the accuracy of RUL predictions, this paper argues that four essential characteristics, uncertainty, robustness, interpretability, and feasibility, are key for real-world PHM applications. This study explores these characteristics through a comparative analysis of two data-driven models (DDMs): the probabilistic Bidirectional Long Short-Term Memory (BiLSTM) model and the Adaptive Hidden Semi-Markov Model (AHSMM). Deep Learning (DL) models such as the BiLSTM often achieve high prediction accuracy but struggle with uncertainty quantification and adaptability across varying operating conditions. In contrast, stochastic models like AHSMM offer stronger robustness and feasibility, performing well even with limited or noisy data. Using the C-MAPSS dataset, the models are evaluated through the lens of the four proposed characteristics. This more holistic approach clarifies each model’s strengths, limitations, and practical trade-offs in PHM settings. The findings highlight that while accuracy remains important, focusing solely on it can overlook critical factors that affect model performance in real operational environments. Balancing all four characteristics is essential for deploying reliable and effective decision-making for predictive maintenance and operations.

PHM continues to show its value by improving operational efficiencies, increasing safety, reducing downtime, and decreasing cost of operations. PHM technologies are therefore not only being deployed as retrofit solutions but are being integrated into new systems as standard practice. Deployment covers areas such as medical equipment, nuclear power plants, aeronautics applications, oil and gas, mining, and many others. As the impact of PHM increases, it is imperative to also consider the potential vulnerabilities that are being exposed. Hackers have famously used Supervisory Control and Data Acquisition (SCADA) and Programmable Logic Controller (PLC) systems to sabotage industrial facilities. As such, it is important to understand the exposure to malfeasance to ensure that PHM does not end up being the enabling mechanism for unauthorized access to the system it is meant to keep in running order. It is also important to understand the measures that need to be taken to avoid or respond to an attack. These range from extensive penetration testing to conducting extensive counter-social engineering training, setting up a PHM-specific CERT plan and team in place. This paper discusses various threats that are emerging and that may have to be considered when designing a PHM solution. Additionally, the NIST cybersecurity framework is discussed in the context of PHM. Finally, this paper looks at the diagnostic capabilities of PHM systems to detect cyber security attacks and to contain these threats.

Accurately estimating a Health Index (HI) from condition monitoring data (CM) is essential for reliable and interpretable prognostics and health management (PHM) in complex systems. In most scenarios, complex systems operate under varying operating conditions and can exhibit different fault modes, making unsupervised inference of an HI from CM data a significant challenge. Hybrid models combining prior knowledge about degradation with deep learning models have been proposed to overcome this challenge. However, previously suggested hybrid models for HI estimation usually rely heavily on system-specific information, limiting their transferability to other systems. In this work, we propose an unsupervised hybrid method for HI estimation that integrates general knowledge about degradation into the convolutional autoencoder’s model architecture and learning algorithm, enhancing its applicability across various systems. The effectiveness of the proposed method is demonstrated in two case studies from different domains: turbofan engines and lithium batteries. The results show that the proposed method outperforms other competitive alternatives, including residual-based methods, in terms of HI quality and their utility for Remaining Useful Life (RUL) predictions. The case studies also highlight the comparable performance of our proposed method with a supervised model trained with HI labels.

Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) the incompleteness of physics-based models and (2) the limited representativeness of the training dataset for data-driven models. Combining the advantages of these two approaches while overcoming some of their limitations, we propose a novel hybrid framework for fusing the information from physics-based performance models with deep learning algorithms for prognostics of complex safety-critical systems. In the proposed framework, we use physics-based performance models to infer unobservable model parameters related to a system’s components health by solving a calibration problem. These parameters are subsequently combined with sensor readings and used as input to a deep neural network, thereby generating a data-driven prognostics model with physics-augmented features. The performance of the hybrid framework is evaluated on an extensive case study comprising run-to-failure degradation trajectories from a fleet of nine turbofan engines under real flight conditions. The experimental results show that the hybrid framework outperforms purely data-driven approaches by extending the prediction horizon by nearly 127%. Furthermore, it requires less training data and is less sensitive to the limited representativeness of the dataset as compared to purely data-driven approaches. Furthermore, we demonstrated the feasibility of the proposed framework on the original CMAPSS dataset, thereby confirming its superior performance.

Gearbox fault diagnosis is expected to significantly improve the reliability, safety and efficiency of power transmission systems. However, planetary gearbox fault diagnosis remains a challenge due to complex responses caused by multiple planetary gears. Model-based gearbox fault diagnosis techniques extract hand-crafted features from sensor data based on underlying physics and statistical analysis, which are not effective in extracting spatial and temporal features automatically. While deep learning methods such as convolutional neural network (CNN) enable automatic feature extraction from multiple sensor sources, they are not capable of extracting spatial and temporal features simultaneously without losing critical feature information. To address this issue, we introduce a novel deep neural network based on bidirectional-convolutional long short-term memory (BiConvLSTM) networks to determine the type, location, and direction of planetary gearbox faults by extracting spatial and temporal features from both vibration and rotational speed measurements automatically and simultaneously. In particular, a CNN determines spatial correlations between two measurements within one time step automatically by combining signals collected from three accelerometers and one tachometer. Long short-term memory (LSTM) networks identify temporal dependencies between two adjacent time steps. By replacing input-to-state and state-to-state operations in the LSTM cell with convolutional operations, the BiConvLSTM can learn spatial correlations and temporal dependencies without losing critical features. Experimental results have shown that the BiConvLSTM network can detect the type, location, and direction of gearbox faults with higher accuracy than conventional deep learning approaches such as CNN, LSTM, and CNN-LSTM.