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.

Failure process for numerical control machine with random ending method;

Fault process for turret systems of CNC lathes with random ending;

Weighted kernel estimator of nonparametric regression functions with censored data of  sequences;

Analysis of Location and Dispersion Effects in Unreplicated Factorial Experiments with Censored Data;

Based on Type-Ⅰcensored likelihood function and actual timing censored data of the machining center, the fitting of weibull model is made for time between failures of mach.

Because the normal distribution is not fit for the practical design,the truncated distribution has been presented to solve this problem,the reliability index under truncated distribution has also been calculated.

Based on stress life model and distribution theory, the stress life model of truncated distribution was set up.

The advances of random censoring data;

Fisher information matrix for random censoring model with incomplete information;

With the data of random censoring constant stress life test,the estimation of Bayes of three parameters is derived when the 3 parameter Weibull distribution is under the condition of squares loss.