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.