Bayesian Reliability Analysis And Bayesian Statistical Decision Problems With Bridging Complex Systems, Several Conclusions

This paper contains two parts.In the first part, the Bayesian reliablity of complex systems is discussed. On the basis of our analysis to the existing research on the complex system, the related analysis methods are optimized in this paper, resulting one effective new method that the maximum entropy principle is used to analysing the systems with components are dependent each other. In this paper, the following systems are studied: the series system, the bridge system, the series-bridge system and the bridge-series system.Moreover, the above systems are discussed from the two sides: one is that the components are dependent each other; especially the other is that the components are independent each other.In the second part, the super-parametre of conjugate prior distribution Gamma is discussed from the view of maximum likelihood estimation and torque estimatation.This paper shows the method of getting its Bayesian estimation when the samples submit to homogeneous distribution and the prior distribution of parameter 6 is Pareto distribution. This paper gives the yardstick of verdicting risk function that is conservative estimation or not. At the same time, this paper gives the yardstick of verdicting the Bayesian estimation of quadratic loss function that is conservative estimation or not. In the end, The Bayesian estimation of the parameter when it is in the complexion of weighted quadratic loss function is given in this paper.