Based on the definition of Bayes post test risk,Bayes sequential and sequential truncated inspection methods have been made a study systematically,and then the project design approaches of Bayes sequential and sequential truncated inspection have also been given concisely.

In accordance with existing some hard problems in the use of sequential and sequential truncated inspection and brought the definite error to the test,optimization design of sequential and sequential truncated inspection scheme for missile test is carried out by using the method of Monte Carlo random simulation and the idea of modern optimization,and the result is satisfactory.

A class of strong convergence theorem for an arbitrarily adapted stochastic sequence without the non-decrease condition was established by using the truncation method of stochastic variables and the stop time.

By using truncation methods of random variables and Doob martingale convergence theorem,the properties of sequence of arbitrary random variables are studied,a class of strong limit theorems for sequences of arbitrary random variables is obtained under moment conditions, and some conclusions corresponded to these are generalized.

By use of truncation of random variables,the properties of sequences of arbitrary random variables are studied and a class of strong limit theorems for sequences of arbitrary random variables are discussed under moment conditions.

It is very important to select a truncating point in the truncated sequential posterior odd test (SPOT), but there is no efficient method to solve the problem up to now.