An analytical computation method for statistical tolerance analysis of assemblies with truncated normal mean shift

Abstract

This paper proposes an analytical solution for fast tolerance analysis of the assembly of components with a mean shift or drift in the form of a doubly-truncated normal distribution. The assembly of components with a mean shift or drift in the form of a uniform distribution (the Gladman model) can be calculated by this method as well since the uniform distribution is a special form of the doubly-truncated normal distribution. Integration formulae of the first four moments of the truncated normal distribution are first derived. The first four moments of the resultant tolerance distribution are then calculated. As a result, the resultant tolerance specification is represented as a function of the standard deviation and the coefficient of kurtosis of the resultant distribution. Based on this method, the calculated resultant tolerance specification is more accurate than that predicted by the Gladman's model or the simplified truncated normal model. The difference between this model and the Monte Carlo method with 1,000,000 simulation samples is less than 0.5%. The merit of the proposed method is that it is fast and accurate which is crucial for engineering applications in tolerance analysis.

Keywords:

• statistical tolerance analysis
• mean shift
• truncated normal distribution
• accuracy

Acknowledgments

The authors want to express their gratitude for funding support from the National Science Council, Taiwan under contract NSC95-2221-E-005-014-MY3, with additional funding from the Mechanical Industrial Research Laboratories of the Industrial Technology Research Institute.