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...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-dimensional survival distribution functions of the processes {δ and γ, and their Lebesgue decompositions are derived.展开更多
An advanced reliability growth model, i. e. exponential model, was presented to estimate the model parameters for multi-systems, which was synchronously tested, synchronously censored, and synchronously improved. In t...An advanced reliability growth model, i. e. exponential model, was presented to estimate the model parameters for multi-systems, which was synchronously tested, synchronously censored, and synchronously improved. In the presented method, the data during the reliability growth process were taken into consideration sufficiently, including the failure numbers, safety numbers and failure time at each censored time. If the multi-systems were synchronously improved for many times, and the reliability growth of each system fitted AMSAA （Army Material Systems Analysis Activity） model, the failure time of each system could be considered rationally as an exponential distribution between two adjoining censored times. The nonparametric method was employed to obtain the reliability at each censored time of the synchronous multisystems. The point estimations of the model parameters, a and b, were given by the least square method. The confidence interval for the parameter b was given as well. An engineering illustration was used to compare the result of the presented method with those of the available models. The result shows that the presented exponential growth model fits AMSAA-BISE （ Army Material Systems Analysis Activity-Beijing Institute of Structure and Environment） model rather well, and two models are suitable to estimate the reliability growth for the synchronously developed multi-systems.展开更多
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 process.In thispaper,the GP is used to ana...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 process.In 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 GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.展开更多
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...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 that BSDE has a unique adapted solution.展开更多
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...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）.展开更多
基金Supported partly by Aeronautical Science Foundation of China
文摘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-dimensional survival distribution functions of the processes {δ and γ, and their Lebesgue decompositions are derived.
文摘An advanced reliability growth model, i. e. exponential model, was presented to estimate the model parameters for multi-systems, which was synchronously tested, synchronously censored, and synchronously improved. In the presented method, the data during the reliability growth process were taken into consideration sufficiently, including the failure numbers, safety numbers and failure time at each censored time. If the multi-systems were synchronously improved for many times, and the reliability growth of each system fitted AMSAA （Army Material Systems Analysis Activity） model, the failure time of each system could be considered rationally as an exponential distribution between two adjoining censored times. The nonparametric method was employed to obtain the reliability at each censored time of the synchronous multisystems. The point estimations of the model parameters, a and b, were given by the least square method. The confidence interval for the parameter b was given as well. An engineering illustration was used to compare the result of the presented method with those of the available models. The result shows that the presented exponential growth model fits AMSAA-BISE （ Army Material Systems Analysis Activity-Beijing Institute of Structure and Environment） model rather well, and two models are suitable to estimate the reliability growth for the synchronously developed multi-systems.
文摘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 process.In 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 GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.
文摘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 that BSDE has a unique adapted solution.
文摘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）.
