Statistical Tolerance Analysis Based on Beta Distributions

Statistical tolerance analysis is being studied extensively. Normal distributions have been traditionally assumed in tolerance analysis; however, little evidence has been found to support that assumption in the real world. In fact, beta distributions are found to be suited for modeling manufacturing processes because of the flexibility in fitting various shapes of distribution. In this paper, a method called the beta distribution approximation method (BDAM) is developed and applied to solve tolerance analysis problems. In the formulation of the BDAM, a beta distribution is employed to model a manufacturing process. The resultant distribution obtained from adding up a number of beta distributions is approximated with a beta distribution. A validation process of the BDAM is carried out and the results are found to be promising. An example is provided to illustrate the BDAM application. Observations are made to conclude the paper.