Bayesian Reliablity Analyses For Complex Systems

Reliability is one property of a production. It's the probability that the production completes the prescribed functions under the set condition within the fixed time. Recentaly, reliability has been regarded as one important index of many products. As to the reliability of complex systems, the number of experiment is often small for the reasons of money , time and maintaining secrecy, the classical statistical ways are not suitable. But the Bayes statistical ways is been widely used , because it can synthesize the relevant data such as the worker's knowledge about the product, the information of the similar product. So the Bayes statistical ways are widely used in many fields of national economy.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 parallel system, the series-parallel system and parallel-series system. Moreover, the above systems are discussed from the two sides: one is that the components are dependent each other; the other is that the components are independent each other. First, Bayesian Reliability estimation for component with exponential distribution is studied in various prior pdf: The failure rate function X is assumed as follows: Gamma prior conjugate distribution, Bayes hypothesis and Jeffrey norm. And I calculate the posterior pdf of reliability function R in Bayes theorem. Second, The information of components is integrated using maximum entropy principle, and prior pdf P(R_s) of system reliability R_s is obtained. In this paper, the following systems are studied: the series system, the parallel system, the series-parallel system and parallel-series system. Moreover, the above systems are discussed from the two sides: one is that the components are dependent each other; the other is that the components are independent each other. Finally, if there is no information about the system, then we may use the prior pdf P(Rs) of system reliability directly to estimate the system reliability, and obtain the point estimation and the confidence interval estimation of the system reliability; If...