Research On Reliability Importance Of Two Special Types Of K-out-of-n:G System

A system normally consists of multiple components,which are not necessarily equally important for the performance of the system.Such a system often needs to be maintained efficiently using limited resources,in this situation,resources are allocated according to how important the components are to the system and concentrated on the small subset of components that are most important to the system,which are very important to the Optimization of the system performance.Marginal reliability importance?MRI?and joint reliability importance?JRI?are defined as the rate at which the system reliability changes as the reliability of one or two components reliability changes.But,sometimes we may improve system reliability through improving reliabilities of three or more components.This paper discusses the above problems of two special types of k-out-of-n:G systems.First of all,Wu and Chen^[31]come up with a binary weighted k-out-of-n:G system which is composed by n components.We use the UGF?Universal generating function?method to propose a simpler general formula for calculating MRI and JRI from the perspective of the set,and generalizing it to multiple components.Secondly,based on the concepts of MRI and JRI of binary components,we also uses the UGF method to calculate MRI and JRI of two types of multi-state weighted k-out-of-n:G system models proposed by Li and Zuo^[17].Thirdly,in the binary k-out-of-n:G system with random weights for components,we directly use the probabilistic approach to extend the WI?Weighted Importance?and the component reliability importance to multiple components.Finally,the relationship between JRI and JFI?Joint Failure Importance?in the binary system is proved.