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MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME processES IN nonhomogeneous poisson process

Applied Mathematics(A Journal of Chinese Universities) 1993年第2期8卷 198-210页

作者：叶尔骅华就昆 Nanjing University of Aeronautics and Astronautics Nanjing 210016

Let {V(t),t≤0} be the nonhomogeneous poisson process with cumulative intensituy parameter A(t). |δ,t≥0 the, age process, and y, t≥0} the residual lifetime process. In the present-paper the expressions of n-dimensi... 详细信息

关键词： nonhomogeneous poisson process Age process. Residual Lifetime process SurvivalDistribution Function. Lebesgue Decomposition.

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A THREE-PARAMETER FAULT-DETECTION SOFTWARE RELIABILITY MODEL WITH THE UNCERTAINTY OF OPERATING ENVIRONMENTS

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Journal of Systems Science and Systems Engineering 2017年第1期26卷 121-132页

作者： Kwang Yoon Song In Hong Chang Hoang Pham Department of Computer Science and Statistics Chosun University Gwangju 62022 Korea Department of Industrial and Systems Engineering Rutgers University NJ 08855-8018 USA

As requirements for system quality have increased, the need for high system reliability is also increasing. Soflnvare systems are extremely important, in terms of enhanced reliability and stability, for providing high quality services to customers. However, because of the complexity of software systems, soft-ware development can be time-consuming and expensive. Many statistical models have been developed in the past years to estimate soflnvare reliability. In this paper, we propose a new three-parameter fault-detection software reliability model with the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous poisson process （NHPP） models based on three sets of failure data collected from software applications. The results show that the proposed model fits significantly better than other existing NHPP models based on three criteria such as mean squared error （MSE）, predictive ratio risk （PRR）, and predictive power （PP）.

关键词： nonhomogeneous poisson process ratio risk predictive power fault detection software reliability mean squared error predictive

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Analysis of Data from a Series of Events by a Geometric process Model

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Acta Mathematicae Applicatae Sinica 2004年第2期20卷 263-282页

作者： YehLain Li-xingZhu JenniferS.K.Chan QunLiu NortheasternUniversityatQinhuangdao 066004China AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing

Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a^(i-1)X_i,i=1,2,...} forms a renewal *** thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the *** limiting distributions of the three estimators are *** the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous poisson *** seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.

关键词： nonhomogeneous poisson process hazard function renewal process geometric process limiting distribution the lindeberg-feller theorem

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SOLUTION TO BSDE WITH nonhomogeneous JUMPS UNDER LOCALLY LIPSCHITZIAN CONDITION

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Annals of Differential Equations 2008年第4期24卷 443-450页

作者： Xie Zhenyun, Xia Ningmao (Dept. of Math., East China University of Science and Technology, Shanghai 200237)

In this paper, we investigate the existence and uniqueness of the solution to a quasilinear backward stochastic differential equation with poisson jumps. By introducing a series of approximate equations, we can show t... 详细信息

关键词： backward stochastic differential equation nonhomogeneous poisson process existence and uniqueness

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