The article presents methods for calculating moments of order statistics from dependent and non-identically distributed discrete random variables. The researchers derived exact and approximate formulas for these moments, making it easier to calculate them numerically. They then applied these methods to find the means and second moments of order statistics from random vectors with specific distributions. Additionally, the researchers used their results in reliability theory to determine the expectations and variances of lifetimes for systems with different components. The study provides useful tools for analyzing the reliability of systems with diverse and potentially interdependent parts.