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|Written by RENKUAN GUO, DANNI GUO, and CHRISTIEN THIART|
Hybrid Poisson Processes with Fuzzy Rate
Volume 7, Number 1, January 2011 - Paper 8 - pp. 97-106
RENKUAN GUO1, DANNI GUO2, and CHRISTIEN THIART11 Department of Statistical Sciences, University of Cape Town, Private Bag, Rondebosch 7701, Cape Town, South Africa
2 Climate Change and BioAdaptation Division, Kirstenbosch Research Center, South African National Biodiversity Institute, Private Bag X7, Claremont 7735, Cape Town, South Africa
(Received on November 18, 2009, revised August 23, 2010)
Poisson processes, particularly the time-dependent extension, play important roles in reliability and risk analysis. It should be fully aware that the Poisson modeling in the current reliability engineering and risk analysis literature is merely an ideology under which the random uncertainty governs the phenomena. In other words, current Poisson Models generate meaningful results if randomness assumptions hold. However, the real world phenomena are often facing the co-existence reality and thus the probabilistic Poisson modeling practices may be very doubtful. In this paper, we define the random fuzzy Poisson process, explore the related average chance distributions, and propose a scheme for the parameter estimation and a simulation scheme as well. It is expecting that a foundational work can be established for Poisson random fuzzy reliability and risk analysis.
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