چكيده انگليسي :
A Study on the Coherent Systems with Shared Components Abdur rahim Sotoudeh abdorrahim sotoudeh@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sareh Goliforushani s goli@cc iut ac ir Advisor Dr Maryam Kelkinnama m kelkinnama@cc iut ac ir 2010 MSC 05C15 53C42 Keywords Coherent System Shared Matrix Signature AbstractIn the study of the reliability of technical systems in reliability enginerig coherent systems play akey role Today in the context of a coherent system reliability are examined from di erent per spectives One of the points of view of integrated systems under di erent assumptions on lifetimeof its components such as being independent and identically distributed exchangeable or assumenot exchangeable component lifetime distributions We derive with use concept of signature mixturerepresentations for reliability residual life functions and new representation for inactivity time of acoherent system under conditions on the states of components or systems according to reliabilityresidual life functions or inactivity times of coherent systems Another view investigated integratedsystems based on di erent states of its components A frequently encountered example of systemswith shared components occurs in networked computing in which a server say a le server or Webserver is used in tandem with several individual computers It is typical that departments withina company or university will store almost all of the les for the department s individual PCs on onecentral server If the central server goes down the PCs with local disks may retain certain limited ca pabilities while other PCs may not work at all The performance of any given pair of PCs will dependon the performance of the shared components those in the central server and the performance of itsown individual components An appropriate abstraction of the situation above is the case of two slave computers linked to a server The former computers have components with lifetimes U1 U2 Un and V1 V2 Vn respectively while the server has components with lifetimes W1 W2 Wn The
