Industries are constantly seeking ways to avoid corrective maintenance in order to reduce costs. Performing regular scheduled maintenance can help to mitigate this problem, but not necessarily in the most efficient way. In many real-life applications, one wants to predict the future failure time of equipment or devices that are expensive, or with long lifetimes, to save costs and/or time. In this paper, the statistical prediction was studied using the classical and Bayesian approaches based on a unified hybrid censoring scheme. Two prediction schemes were used: (1) a one-sample prediction scheme that predicted the unobserved future failure times of devices that did not complete the lifetime experiments; and (2) a two-sample prediction scheme to predict the ordered values of a future independent sample based on past data from a certain distribution. We chose to apply the results of the paper to the Burr-X model, due to the importance of this model in many fields, such as engineering, health, agriculture, and biology. Point and interval predictors of unobserved failure times under one- and two-sample prediction schemes were computed based on simulated data sets and two engineering applications. The results demonstrate the ability of predicting the future failure of equipment using a statistical prediction branch based on collected data from an engineering system.