Estimating Complex System Reliability Based On Bayes Methods

Reliability, which is one of the most important indexes to measure the qualityof products, has been developing rapidly and applied to many fields, since the WorldWar Ⅱ. With the development of industrial technology, the product structure is moreand more complex; a complex system is the system which consists of severalsubsystems arranged in a certain way.In fact, when we evaluate the reliability of complex systems through the trials,some reasons lead to a small sample, such as time, the cost of restricting, etc., andby using the classic method, it is difficult to get the accurate estimation of reliability.Bayes method can evaluate the reliability of the system synthetically, by combiningrelevant data of the system with the experience of people. The Bayes method is morescientific than the classical method especially when information of the test isinadequate. Most studies for complex system reliability are just for series, parallel,k-out-of-n, or a specific system. This paper mainly studies on general complexsystems described by minimum path, and it is more general. It is just based on thesefacts that studying reliability of complex systems described by minimum path, usingBayes Method, not only has theoretical significance but also has application value.In this paper, assuming that the component life obeys exponential distribution,for general complex systems that are constituted by independence componentsdescribed by minimal path, Bayes Method is used to study reliability of complexsystems. We get the results as follows:Firstly, the complex system is described by k minimum paths and constitutedby N independent exponential-type components, the minimum path matrix isknown. When the life of each component obeys exponential distribution with thesame or different parameters, combining with the analytical expression of complexsystem reliability, the paper gets the expression of reliability for general complex system under exponential distribution.Secondly, in the condition of doubly censored samples, when the life of eachcomponent obeys exponential distribution with the same or different parameters,combining with the reliability expression of general complex system, this paper getsthe Bayes estimate and EB estimate of reliability for the system, under squared errorloss, by Bayes Method and the Maximum Likelihood Estimation Method.Finally, in a given time, when the estimation of the reliability of the system isconsidered as multi-sources prior information, this paper gets the Bayes estimationof component failure rate and complex system reliability.