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Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage

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3 Author(s)
S. V. Amari ; Relex Software Corp., Greensburg, PA, USA ; Hoang Pham ; G. Dill

Systems subjected to imperfect fault-coverage may fail even prior to the exhaustion of spares due to uncovered component failures. This paper presents optimal cost-effective design policies for k-out-of-n:G subsystems subjected to imperfect fault-coverage. It is assumed that there exists a k-out-of-n:G subsystem in a nonseries-parallel system and, except for this subsystem, the redundancy configurations of all other subsystems are fixed. This paper also presents optimal design polices which maximize overall system reliability. As a special case, results are presented for k-out-of-n:G systems subjected to imperfect fault-coverage. Examples then demonstrate how to apply the main results of this paper to find the optimal configurations of all subsystems simultaneously. In this paper, we show that the optimal n which maximizes system reliability is always less than or equal to the n which maximizes the reliability of the subsystem itself. Similarly, if the failure cost is the same, then the optimal n which minimizes the average system cost is always less than or equal to the n which minimizes the average cost of the subsystem. It is also shown that if the subsystem being analyzed is in series with the rest of the system, then the optimal n which maximizes subsystem reliability can also maximize the system reliability. The computational procedure of the proposed algorithms is illustrated through the examples.

Published in:

IEEE Transactions on Reliability  (Volume:53 ,  Issue: 4 )