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

• Published in: International journal of production research Vol. 49; no. 7; pp. 1937 - 1955
• Main Authors: Kuo, Chang-Hsin, Tsai, Jhy-Cherng
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.04.2011; Taylor & Francis; Taylor & Francis LLC
• Subjects: Accuracy; Applied sciences; Assemblies; Assembly lines; Computer simulation; Exact sciences and technology; Mathematical analysis; Mathematical models; mean shift; Mechanical engineering. Machine design; Monte Carlo simulation; Normal distribution; Resultants; Specifications; Standard deviation; statistical tolerance analysis; Studies; Tolerances; truncated normal distribution; Monte Carlo method; Integration; Statistical analysis; mean shift; Statistical moment; Tolerance analysis; Gaussian distribution; Mean drift; accuracy; statistical tolerance analysis; Modeling; Engineering design; Uniform distribution; Statistical computation; Truncated shape; Standard deviation; Dimensional tolerance; truncated normal distribution; Analytical solution; Assembly
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207541003639634

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.