As one of the most important indexes to evaluate the quality of software, software reliability experiences an increasing development in recent years. We investigate a software reliability growth model(SRGM). The appli...As one of the most important indexes to evaluate the quality of software, software reliability experiences an increasing development in recent years. We investigate a software reliability growth model(SRGM). The application of this model is to predict the occurrence of the software faults based on the non-homogeneous Poisson process(NHPP). Unlike the independent assumptions in other models, we consider fault dependency. The testing faults are divided into three classes in this model: leading faults, first-step dependent faults and second-step dependent faults. The leading faults occurring independently follow an NHPP, while the first-step dependent faults only become detectable after the related leading faults are detected. The second-step dependent faults can only be detected after the related first-step dependent faults are detected. Then, the combined model is built on the basis of the three sub-processes. Finally, an illustration based on real dataset is presented to verify the proposed model.展开更多
Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test run...Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test runs, the number of executed test cases. This paper discusses discrete software reliability measurement based on a discretized nonhomogeneous Poisson process (NHPP) model. Especially, we use a bootstrapping method in our discrete software reliability measurement for discussing the statistical inference on parameters and software reliability assessment measures of our model. Finally we show numerical examples of interval estimations based on our bootstrapping method for the several software reliability assessment measures by using actual data.展开更多
In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function...In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function is established to fit the fault removal process. By using two sets of practical data, the descriptive and predictive abilities of the improved NHPP model are compared with those of the NHPP model, G-O model, and delayed S-shape model. The results show that the improved model can fit and predict the data better.展开更多
Statistical predictions are useful to predict events based on statistical models.The data is useful to determine outcomes based on inputs and calculations.The Crow-AMSAA method will be explored to predict new cases of...Statistical predictions are useful to predict events based on statistical models.The data is useful to determine outcomes based on inputs and calculations.The Crow-AMSAA method will be explored to predict new cases of Coronavirus 19(COVID19).This method is currently used within engineering reliability design to predict failures and evaluate the reliability growth.The author intents to use this model to predict the COVID19 cases by using daily reported data from Michigan,New York City,U.S.A and other countries.The piece wise Crow-AMSAA(CA)model fits the data very well for the infected cases and deaths at different phases during the start of the COVID19 outbreak.The slope b of the Crow-AMSAA line indicates the speed of the transmission or death rate.The traditional epidemiological model is based on the exponential distribution,but the Crow-AMSAA is the Non Homogeneous Poisson Process(NHPP)which can be used to modeling the complex problem like COVID19,especially when the various mitigation strategies such as social distance,isolation and locking down were implemented by the government at different places.展开更多
In this paper, the authors will study the estimation of maintenance efficiency in Arithmetic Reduction of Intensity （ARI） and Arithmetic Reduction of Age （ARA） models with a memory m. These models have been propos...In this paper, the authors will study the estimation of maintenance efficiency in Arithmetic Reduction of Intensity （ARI） and Arithmetic Reduction of Age （ARA） models with a memory m. These models have been proposed by Doyen （2005）, the failure process is simply Non Homogeneous Poisson Process （NHPP）. Our models are defined by reformulation of ARI and ARA ones using bathtub failure intensity. This form is presented like a superposition of two NHPP and Homogeneous Poisson Process （HPP）. Moreover, the particularity of this model allows taking account of system state improvement in time course. The maintenance effect is characterized by the change induced on the failure intensity before and after failure during degradation period. To simplify study, the asymptotic properties of failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied.展开更多
基金the National Natural Science Foundation of China(No.71671016)the School Fund of Beijing Information Science&Technology University(No.1935004)
文摘As one of the most important indexes to evaluate the quality of software, software reliability experiences an increasing development in recent years. We investigate a software reliability growth model(SRGM). The application of this model is to predict the occurrence of the software faults based on the non-homogeneous Poisson process(NHPP). Unlike the independent assumptions in other models, we consider fault dependency. The testing faults are divided into three classes in this model: leading faults, first-step dependent faults and second-step dependent faults. The leading faults occurring independently follow an NHPP, while the first-step dependent faults only become detectable after the related leading faults are detected. The second-step dependent faults can only be detected after the related first-step dependent faults are detected. Then, the combined model is built on the basis of the three sub-processes. Finally, an illustration based on real dataset is presented to verify the proposed model.
文摘Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test runs, the number of executed test cases. This paper discusses discrete software reliability measurement based on a discretized nonhomogeneous Poisson process (NHPP) model. Especially, we use a bootstrapping method in our discrete software reliability measurement for discussing the statistical inference on parameters and software reliability assessment measures of our model. Finally we show numerical examples of interval estimations based on our bootstrapping method for the several software reliability assessment measures by using actual data.
基金the National High Technology Research and Development Program of China (863 Program) under Grant No. 2006AA01Z173.
文摘In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function is established to fit the fault removal process. By using two sets of practical data, the descriptive and predictive abilities of the improved NHPP model are compared with those of the NHPP model, G-O model, and delayed S-shape model. The results show that the improved model can fit and predict the data better.
基金The author appreciates the data which provided by website in reference(WorldOMeters).(Click On Detroit News,2020)and(New York City Gov)The author thanks my friend KevinWeiss who is working as principal quality engineer at ZF to edit this paper,and also thanks the Fulton Findings company to provide the SuperSmith package.
文摘Statistical predictions are useful to predict events based on statistical models.The data is useful to determine outcomes based on inputs and calculations.The Crow-AMSAA method will be explored to predict new cases of Coronavirus 19(COVID19).This method is currently used within engineering reliability design to predict failures and evaluate the reliability growth.The author intents to use this model to predict the COVID19 cases by using daily reported data from Michigan,New York City,U.S.A and other countries.The piece wise Crow-AMSAA(CA)model fits the data very well for the infected cases and deaths at different phases during the start of the COVID19 outbreak.The slope b of the Crow-AMSAA line indicates the speed of the transmission or death rate.The traditional epidemiological model is based on the exponential distribution,but the Crow-AMSAA is the Non Homogeneous Poisson Process(NHPP)which can be used to modeling the complex problem like COVID19,especially when the various mitigation strategies such as social distance,isolation and locking down were implemented by the government at different places.
文摘In this paper, the authors will study the estimation of maintenance efficiency in Arithmetic Reduction of Intensity （ARI） and Arithmetic Reduction of Age （ARA） models with a memory m. These models have been proposed by Doyen （2005）, the failure process is simply Non Homogeneous Poisson Process （NHPP）. Our models are defined by reformulation of ARI and ARA ones using bathtub failure intensity. This form is presented like a superposition of two NHPP and Homogeneous Poisson Process （HPP）. Moreover, the particularity of this model allows taking account of system state improvement in time course. The maintenance effect is characterized by the change induced on the failure intensity before and after failure during degradation period. To simplify study, the asymptotic properties of failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied.
