Statistical tolerancing

Statistical tolerancing is an analysis of the tolerance accumulation, in an assembly or system, based on process capability through assembly stack-up, performance variation and cycle time stack-up. It is also the process to identify significant and non-significant effects of subsystems or component variation. The process of tolerancing analysis is based on four steps:

1. Identify the significant characteristic.

2. Develop a model.

3. Acquire process capability data.

4. Perform tolerance analysis.

Developing model for tolerancing

Typically, there are two types of models: a) linear (such that the coefficient of xs are constants (e.g., Y = X1 + X2 + X3 -X4, 1-D stack-up tolerance; Y = X1 - X2, cost model) and nonlinear (so that the coefficient of Xs are functions of Xs (e.g., , geometric function; P = L/A, performance function; Y = X₁exp(0.5X₂X₃)). To develop a tolerancing model, we follow five steps. They are:

1. Developed from mechanical assembly tolerance model the parameters and the tolerances (using tolerance chain vector loop and/or assembly kinematics. Perhaps the most common technique to develop a tolerance chain for a one or two dimensional case is the "vector loop technique.")

2. Derived from physical principles parameters and the tolerances (engineering science, using models from surrogate data, and/or obtaining help from an expert).

3. Use computer-aided engineering (CAE) tools such as Abacus, ADAMS, Easy5, Nastran and Simulink.

4. Conduct computer experimentation and response surface using CAE.

5. Conduct hardware DOE and fit response model.