Composite pipes are increasingly replacing traditional materials like steel in various industries due to their high strength-to-weight ratio. This is particularly beneficial for the oil industry, especially in drilling applications where structures face multi-axial loadings. However, the anisotropic mechanical behavior of these materials adds complexity to their analysis. Moreover, their mechanical properties are statistically variable, affecting component response and failure. To address these challenges, mathematical models are employed to analyze composite pipe performance, and statistical methods are used to assess their reliability. The primary focus is on developing a composite pipe design capable of withstanding anticipated drilling loads. This involves determining the optimal layup design and identifying first-ply failure envelopes under combined tension, torsion, and pressure using three-dimensional finite element models in ABAQUS software. Furthermore, the occurrence of delamination between layers is investigated by integrating the cohesive zone model into simulations. The reliability of composite pipes with suitable layup designs is quantified by considering the statistical variation of mechanical properties. Reliability-based first-ply failure contours are determined by analyzing the load distribution that each pipe, with specific mechanical properties, could withstand just before damage occurs. In conclusion, this work aims to develop a comprehensive understanding of composite pipe behavior under drilling conditions. By utilizing advanced modeling techniques and statistical analysis, it seeks to optimize composite pipe designs for enhanced reliability and performance in the oil industry.