Bayesian Estimation Of Reliability For A Complex System Under Zero-failure Data

The characteristics like reliability, average life and failure rate are importantindexes to evaluate the quality of the products, which are collectively called thereliability indexes of the product. However one product doesn’t only have oneseparate component. A system accords to certain rule have more than one element,we called it complex system. Complex system is composed by one or moresubsystems according to certain way. There aren’t any reliability samples ofcomplex system itself, relatively speaking, the reliability information of componentsor the subsystem are more, so on the basis of experimental data of each subsystem orcomponent to estimate complex system reliability is feasible. The most commoncomplex system is based on the minimum path or minimum cut sets, so moreattention has been paid to the research of this kind system.Different censored data tend to be obtained from the reliability test. Research offailure data, which the failure number is greater than zero, have been relativelymature. Today, all kinds of long life and high reliability products are rapidlydeveloped, in fixed time censoring reliability test, if the test samples are from allkinds of high reliability and long life products, within the prescribed period of timewithout failure data, we call this kind data zero-failure data. Different from thefailure data of various estimation methods, when there is no failure data, how do wedraw the reliability index of long life and high reliability products? This is theproblems this paper to study: zero-failure data.The papers about zero-failure data are a lot, which mainly focused on the Bayesestimations. Most of such researches are the study of individual components of avariety of life indexes, or just a specific known simple system. For a complexsystem described by minimum paths or minimal cut sets, the Bayesian estimation ofits reliability is relatively rare.In reliability studies, exponential distribution is the most basic life distribution.For exponential distribution, when the test data is zero-failure data, the complexsystem research is particularly important. Finding the complex system science and effective estimation method under zero-failure data has become a new and importantfield of reliability research, which has important theoretical significance andpractical application value.In this paper, using the method of Bayes theorem, assuming the component lifeobey exponential distribution and the data are zero-failure data, we do a study on thecomplex systems described by minimum path. The paper got the following results:Firstly, in the condition of zero-failure data, combined with general complexsystem reliability expression under the exponential distribution, when eachcomponent life obey the same parameter exponential distribution, we used Bayestheorem and Hierarchical Bayesian estimation method to get the complex systemreliability estimation under quadratic loss function.Secondly, in the condition of zero-failure data, combined with general complexsystem reliability expression under the exponential distribution, when eachcomponent life obey different parameter exponential distribution, we used Bayestheorem and Hierarchical Bayesian estimation method to get the complex systemreliability estimation under quadratic loss function.