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3 Journal of Polish Safety and Reliability Association

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Random fuzzy Poisson processes

Guo R., Nyirenda J., Guo D.

Journal of Polish Safety and Reliability Association

2009

Vol. 1

113--122

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.

Random fuzzy continuous-time Markov chains

Guo R., Nyirenda J., Dunne T., Guo D.

Journal of Polish Safety and Reliability Association

2009

Vol. 1

123--132

Continuous-time Markov chains is an important subclass in stochastic processes, which have facilitated many applications in business decisions, investment risk analysis, insurance policy making and reliability modeling. It should be fully aware that the existing continuous-time Markov chains theory is merely an ideology under which the random uncertainty governs the phenomena. However, the real world phenomena are often revealing the randomness and vagueness co-existence reality and thus the probabilistic continuous-time Markov chains modeling practices may be not adequate. In this paper, we define the random fuzzy continuous-time Markov chains, 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 reliability modeling and risk analysis, particularly, repairable system modeling.

Fuzzy regression : a scalar variable formation

Guo R., Guo D.

Journal of Polish Safety and Reliability Association

2008

Vol. 1

159--167

In reliability, quality control and risk analysis, fuzzy methodologies are more and more involved and inevitably introduced difficulties in seeking fuzzy functional relationship between factors. In this paper, we propose a scalar variable formation of fuzzy regression model based on the credibility measure theoretical foundation. It is expecting our scalar variable treatments on fuzzy regression models will greatly simplify the efforts to seeking fuzzy functional relationship between fuzzy factors. An M-estimator for the regression coefficients is obtained and accordingly the properties and the variance-covariance for the coefficient M-estimators are also investigated in terms of weighted least-squares arguments. Finally, we explore the asymptotic membership function for the coefficient M-estimators.