Even when all manufactured parts for an assembly are produced within limits, these parts still may not assemble properly if the assembly tolerance analysis was inadequately performed. Naturally occurring shifts in a process can produce biased distributions which can result in increased assembly problems and a greater number of rejects than anticipated. The most common methods of analysis of assembly tolerance buildup are worst case and root sum squares. The limitations of each of these methods are discussed and a simple new method is proposed which accounts for expected bias. This new method includes both worst case and root sum squares as extreme cases.