In engineering design projects, components are often outsourced to contractors. For steam turbines, this includes piping system, which must not distort the turbine casing due to forces and moments applied at the flanges. Given the complex forces in multiple directions, determining critical load cases analytically poses significant challenges. To address this, a statistical approach defines allowable force limits, ensuring structural integrity. A transfer function for casing displacements was developed by analyzing unit forces and moments on each pipe, enabling the combined response to mixed forces using a spreadsheet model based on linear elastic behavior. This tool validated through finite element analysis (FEA), was further optimized with Monte Carlo simulations, offering a fast and cost-effective alternative to traditional deterministic FEA approach. The approach maximizes permissible loads while maintaining casing integrity, streamlining analysis and design processes.