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
The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of ...The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.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
Risk modeling for recurrent cervical cancer requires the development of new concepts and methodologies. Unlike most daily decisions, many medical decision making have substantial consequences, and involve important un...Risk modeling for recurrent cervical cancer requires the development of new concepts and methodologies. Unlike most daily decisions, many medical decision making have substantial consequences, and involve important uncertainties and trade-offs. The uncertainties may be about the accuracy of available diagnostic tests, the natural history of the cervical cancer, the effects of treatment in a patient or the effects of an intervention in a group or population as a whole. With such complex decisions, it can be difficult to comprehend all options “in our heads”. This study applied Bayesian decision analysis to an inferential problem of recurrent cervical cancer in survival analysis. A formulation is considered where individual was expected to experience repeated events, along with concomitant variables. In addition, the sampling distribution of the observations is modelled through a proportional intensity Nonhomogeneous Poisson process. The proposed decision models can provide decision support techniques not only for taking action in the light of all available relevant information, but also for minimizing expected loss. The decision process is useful in selecting the best alternative when a patient with recurrent cervical cancer, in particular, the proposed decision process can provide more realistic solutions.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
The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHP...The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHPP model as it describes exponential software failure curve. Parameter estimation, model fit and predictive analyses based on one sample have been conducted on the Goel-Okumoto software reliability model. However, predictive analyses based on two samples have not been conducted on the model. In two-sample prediction, the parameters and characteristics of the first sample are used to analyze and to make predictions for the second sample. This helps in saving time and resources during the software development process. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model based on two samples. We have addressed three issues in two-sample prediction associated closely with software development testing process. Bayesian methods based on non-informative priors have been adopted to develop solutions to these issues. The developed methodologies have been illustrated by two sets of software failure data simulated from the Goel-Okumoto software reliability model.展开更多
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
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）.
文摘The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.
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.
基金Foundation item:supported by Science and Technology Foundation of Shanghai Higher Education(01D01-2)and the Foundation of Ministry of Education for Core Teachers of Higher Education.
文摘Risk modeling for recurrent cervical cancer requires the development of new concepts and methodologies. Unlike most daily decisions, many medical decision making have substantial consequences, and involve important uncertainties and trade-offs. The uncertainties may be about the accuracy of available diagnostic tests, the natural history of the cervical cancer, the effects of treatment in a patient or the effects of an intervention in a group or population as a whole. With such complex decisions, it can be difficult to comprehend all options “in our heads”. This study applied Bayesian decision analysis to an inferential problem of recurrent cervical cancer in survival analysis. A formulation is considered where individual was expected to experience repeated events, along with concomitant variables. In addition, the sampling distribution of the observations is modelled through a proportional intensity Nonhomogeneous Poisson process. The proposed decision models can provide decision support techniques not only for taking action in the light of all available relevant information, but also for minimizing expected loss. The decision process is useful in selecting the best alternative when a patient with recurrent cervical cancer, in particular, the proposed decision process can provide more realistic solutions.
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The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHPP model as it describes exponential software failure curve. Parameter estimation, model fit and predictive analyses based on one sample have been conducted on the Goel-Okumoto software reliability model. However, predictive analyses based on two samples have not been conducted on the model. In two-sample prediction, the parameters and characteristics of the first sample are used to analyze and to make predictions for the second sample. This helps in saving time and resources during the software development process. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model based on two samples. We have addressed three issues in two-sample prediction associated closely with software development testing process. Bayesian methods based on non-informative priors have been adopted to develop solutions to these issues. The developed methodologies have been illustrated by two sets of software failure data simulated from the Goel-Okumoto software reliability model.
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.
