Robust design of dimension chain with less composing loops and higher precision requirement

Beta-distribution is used to describe the error distribution of dimension chain with less composing loops and higher precision requirement. Through fine-tune target value to make dimension chain robustness. Without decreasing tolerance of each composing loop and increasing cost of product, deviation and variance of dimension chain can be made smaller, thus dimension chain can be met more precision requirement. This method can make dimension chain to meet more precision requirement without decreasing tolerance of each composing loop. Avoid using single distribution give rise a deviation between actual error and theoretical error. The example shows that the new method can play a role in mechanical engineering.