Liquefaction accounts for a large portion of the cost of liquefied natural gas (LNG), motivating significant efforts in the simulation and optimization of liquefaction processes. While most optimization studies typically assume a fixed feed stream concentration, the properties of natural gas feeds can vary in time or between different sources. This constitutes a significant exogenous uncertainty, particularly for field or offshore liquefaction facilities with limited feed-blending capabilities. This paper examines the PRICO plant as a representative mixed-refrigerant liquefaction process and presents a design optimization formulation for natural gas liquefaction processes with varying feed composition. We introduce models for the multistream heat exchanger and for the compressor that allow for the size of key equipment to be optimized along with the process operating conditions. Using a recently developed scenario-free framework for optimization under parametric uncertainty, our study provides new insights (including some counterintuitive results) concerning optimal liquefaction equipment sizing for dealing with uncertainty in feed composition.