Replacement Policies with a Random Threshold Number of Faults
Most systems fail when a certain amount of reliability quantities have exceeded their threshold levels. The typical example is cumulative damage model in which a system is subjected to shocks and suffers some damage due to shocks, and fails when the total damage has exceeded a failure level K. This paper proposes the following reliability model: Faults occur at a nonhomogeneous Poisson process and the system fails when N faults have occurred, which could be applied to optimization problems in computer systems with fault tolerance, and we suppose that the system is replaced before failure at a planned time T. Two cases where the threshold fault number N is constantly given and is a random variable are considered, we obtain the expected cost rates and discuss their optimal policies.
KeywordsReplacement Constant threshold Random threshold Faults
This work is partially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science under Grant No. 22500897 and No. 24530371; National Science Council of Taiwan NSC 100-2628-E-0330-002.
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