Tolerance analysis looks at the relationship of design
tolerance (requirement) and manufacturing variation (process capability) to
define an optimal tolerance solution. The method of tolerance analysis will
depend upon the method of manufacture and the tolerance range within which the
parts may vary. The key concept of tolerance analysis is the interchangeability
of parts. If two parts can be switched in an assembly, they are considered to be
interchangeable. In terms of fit, these parts are considered to be the same.
Tolerance analysis will determine the limit to which these parts can vary and
still be considered interchangeable. As the tolerance range approaches zero, the
cost of manufacturing the part increases greatly. Therefore, the goal of
tolerance analysis is to generate parts with as loose a tolerance as possible to
minimize the production cost while still meeting the conditions for
interchangeability. From a producibility standpoint, maximizing design
tolerances is a necessity for a robust design.

There are several types of tolerance analysis methods
available depending upon the complexity of the assembly and how conservative the
design requirements are. Following are examples of tolerance analysis
techniques:

**Arithmetic Worse Case (AWC): **AWC analysis is a straightforward linear addition and subtraction of
worse case tolerances. From a design standpoint, AWC is the most conservative of
the techniques. It does not consider the statistical probability of interference
fit or process capability, but focuses instead on design specifications.
Generally, worse case analysis should not be used when the number of parts in
the assembly is greater than four.

**Root Sum of Squares (RSS): **RSS analysis produces less conservative results than AWC tolerance
analysis. RSS assumes that the design tolerance will fall within centered
Six-Sigma limits. This analysis exploits the manufacturing probability that a
part will tend more toward the median level of design dimension instead of the
maximum or minimum limits. It does not take into account process mean
shifts.

**Dynamic Root Sum of Squares (DRSS)** and **Static Root Sum of Squares (SRSS): **These analyses factor process mean shifts into the analysis
and, therefore, produce less conservative results than RSS. Process shifts at
the component levels can, thereby, result in fit-up problems at the assembly
level. DRSS inflates the assembly standard deviation but has little impact on
the overall assembly mean (random process mean shift). SRSS assumes sustained
mean shift conditions of each component in the assembly.

**References:**

Boyd, R. R. (1993). __Tolerance Analysis of Electronic Circuits Using MATLAB__. New York: CRC Press.

Cox, N. D. (1986). __How to Perform Statistical Tolerance Analysis, Vol. 11__.
ASQ Press.

Meadoews, J. D. (1995). __Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection__. New York: Marcel Dekker.

Zhang, H. (1997). __Advance Tolerancing Techniques__. New York: Wiley & Sons.