Tolerance analysis is a method used in engineering and manufacturing to assess how variations in part dimensions affect the overall performance and fit of an assembly. It helps identify acceptable limits for these variations, ensuring that parts will function together correctly despite minor discrepancies in size or shape. By applying tolerance analysis, designers can optimize the manufacturing process, reduce costs, and improve product quality. This analysis often involves statistical techniques to predict how variations will impact the final product, making it essential for industries like automotive and aerospace, where precision is critical for safety and functionality.