Meaning
Statistical analysis method that calculates the total expected variation in a mechanical assembly by combining the individual component tolerances as the square root of the sum of their squares ensures realistic assembly requirements. This approach, known as root-sum-square tolerance stack-up, assumes that it is highly unlikely that all parts will simultaneously be at their extreme limit of size. By applying this statistical model, battery pack designers can specify looser, less expensive tolerances for individual components while still ensuring that the assembled pack fits together correctly.
Sourcing departments benefit from this method because it lowers component manufacturing costs and increases supplier yield rates.
Statistical Principle
The method is based on the normal distribution of manufacturing variations, where most parts fall close to the nominal dimension and very few are at the extreme limits. In a linear stack of components, such as a series of cells in a module, the statistical variation is much smaller than the absolute worst-case sum of all tolerances. By summing the squares of the individual tolerances and taking the square root, engineers calculate a realistic three-sigma boundary for the assembly dimension.
This approach prevents over-dimensioning of the housing or the use of unnecessarily high-precision manufacturing processes.
Design Application
When designing the mechanical enclosure for a large prismatic battery pack, the stack-up of cell thicknesses must be carefully analyzed. If worst-case analysis were used, the enclosure would have to be excessively large, leaving unused space in most assemblies. Using this statistical calculation allows engineers to design a more compact, space-efficient housing that is optimized for weight and volume.
Sourcing managers use this analysis to align supplier specifications with the mechanical design limits of the pack, ensuring high assembly yield.
Sourcing Impact
By avoiding over-toleranced parts, purchasing teams can source from a wider range of qualified suppliers who utilize standard manufacturing processes. This competition lowers the unit cost of components such as cell spacers, holders, and structural endplates. The method also reduces the number of assembly line failures caused by parts that do not fit together, further improving production efficiency and lowering waste.