| Based on the k-out-of-n system, this thesis studies the allocation problem of the redundant components at the levels of component and system and the closure problems that the property of IFR of signature in interacted system.First, the redundancy allocation of k-out-of-n system and the basic theory and research status of the signature are introduced.Second, the redundancy allocation in k-out-of-n system is discussed in this thesis. Analyzing a basic principle that redundancy allocation at component level is more efficient than that at system level, a conception of system assembly at the levels of component and system is carried out and the advantages and disadvantages of these two systems are revealed. Based on the likelihood ratio ordering, it is proved that assembly system at component level is superior to that at system level under the case of components complete matching. In the case of partial matching, based on the failure rate and anti-failure rate, the thesis compares assembly system at component and system level.Finally, the Sealing ability of some correlation system under k-out-of-n system is discussed. The signature is a very effective way to measure correlation system structure. The thesis proposes a new research idea which provides effective information for inferring the structure of the related system by studying the properties of the associated system and fully understanding its shape. By using mode decomposition, this thesis studies Signature’s FIR under the k-out-of-n system from three aspects: 1) Sealing ability under the correlation system with a single element in series; 2) Sealing ability under some correlation system in series; 3) Sealing ability of some correlation system under k-out-ofn system. For 1), we proved Signature’s FIR is entirely closed; for 2), we designed an algorithm and did an analog computation which written by C# to verify the sealing ability of FIR; for 3), we give a counterexample that IFR under parallel structure is not closed. |
