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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.

DEAR theory and applicability in system dynamics analysis

Guo R., Guo D.

Journal of Polish Safety and Reliability Association

2008

Vol. 1

149--158

In this paper, we introduce our newly created DEAR (an abbreviation of Differential Equation Associated Regression) theory, which merges differential equation theory, regression theory and random fuzzy variable theory into a new rigorous small sample based inferential theoretical foundation. We first explain the underlying idea of DEAR modelling, its classification, and then the M-estimation of DEAR model. Furthermore, we explore the applicability of DEAR theory in the analysis in system dynamics, for example, repairable system analysis, quality dynamics analysis, stock market analysis, and ecosystem analysis, etc.

An univariate DEMR modelling on repair effects

Guo R.

Journal of Polish Safety and Reliability Association

2007

Vol. 1

157--165

Repairable system analysis is in nature an evaluation of repair effects. Recent tendency in reliability engineering literature was estimating system repair effects or linking repair to certain covariate to extract repair impacts by imposing repair regimes during system reliability analysis. In this paper, we develop a differential equation motivated regression (abbreviated as DEMR) model with a random fuzzy error term based on the axiomatic framework of self-dual fuzzy credibility measure theory proposed by Liu [5] and grey differential equation models. The fuzzy variable indexes the random fuzzy error term will be used to facilitate the evaluation of repair effects. We further propose a parameter estimation approach for the fuzzy variable (repair effect) under the maximum entropy principle.