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).

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) χ ² 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.

Excessive vibrations in rotating machinery accelerate wear and component failures, causing undesired downtime in industrial plants. To assess the severity of these vibration levels, ISO 10816-7 classifies pump condition into four zones. Zone A represents good condition, Zone B is acceptable for long-term operation, Zone C is generally suitable only for limited operation, and Zone D corresponds to vibration levels that may cause machine damage. However, these qualitative classifications do not quantify how vibration severity relates to equipment reliability. This paper addresses that gap for rotodynamic pumps by integrating standardized vibration severity levels within a reliability framework based on Proportional Hazards Models (PHMs). The models were fitted with observational field data from an oil refinery using the Mean Time Between Failures (MTBF) as the reliability outcome. From the resulting survival curves, reliability is summarized by the median predicted life (B50), defined as the time at which the predicted survival probability reaches 0.5. This measure can be estimated within the observed follow-up without extrapolating the censored tail of the survival curve. The model achieved a concordance of 0.870 and was then used to estimate B50 across a range of vibration levels, holding the remaining operating conditions constant. The analysis indicated an association between the vibration levels and the predicted life, consistent with the severity considerations set by the ISO standards. The results showed a 62.5% decrease in mean predicted B50 from Zone A to Zone D. Within the 0–6 mm/s RMS range, which contained 95% of the observed vibration data, prediction uncertainty remained comparatively low, whereas it increased at higher vibration levels as data density decreased. Across speed and power groups, at a given vibration level, higher rotating speeds and higher installed power are associated with higher predicted lives. American Petroleum Institute (API) 610 between-bearings pumps showed higher predicted reliability than horizontal overhung and vertical overhung OH6 configurations. By providing a quantitative mapping from ISO severity levels to predicted equipment life and its practical implications for reliability-oriented maintenance planning, the proposed approach adds numerical resolution to current standards and supports more informed, data-driven maintenance and reliability decisions for centrifugal pumps.