Making full use of knowledge in manufacturing tolerance analysis combined with the beta distribution model is introduced and applied.

Considering the step by step improvement in the related knowledge and information, a dynamic and recurring method is advocated of assessing the containment with Bayes theorem and the solution is obtained to the problem in its practical application: how to set forth a prior Beta distribution.

The 8087 s instructions are estimated with beta distribution and normal distribution separately, the whole program s execution time is approximated with normal distribution after adding instruction.

Several empirical Bayes Estimations on binomial distribution;

Improvement of Stirling s formula and approximate calculation of probability of binomial distribution;

Hypothesis test in the judgement on a binomial distribution and a Poisson distribution;

Result The index of distribution of carcinoma of the stomach from 44 clans in wuwei is well above the probability space in binominal distribution (χ 2=15.

But concerning the probability of the number of core damage under the condition of multiple reactor years,it follows the binominal distribution.

In order to avoid that a small amount of field test information would be obliterated by a large amount of prior information,a Bayesian method with mixed Beta distribution was used.