Abstract
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time-dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi-group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.
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Project supported by the National Natural Science Foundation of China(Grant No. 70171059)
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Shi, DH., Xu, H., Xiong, Y. et al. Operator semi-group of density evolution equation for a repairable redundant system with two same components. J. of Shanghai Univ. 6, 278–281 (2002). https://doi.org/10.1007/s11741-002-0050-z
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DOI: https://doi.org/10.1007/s11741-002-0050-z