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Bayesian Reliability——Growth Analysis for Statistical of Diverse Population Based on non-homogeneous poisson process

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Chinese Journal of Mechanical Engineering 2009年第4期22卷 535-541页

作者： MING Zhimao TAO Junyong ZHANG Yunan YI Xiaoshan CHEN Xun College of Mechatronics Engineering and Automation National University of Defense Technology Changsha 410073 China Center for Risk and Reliability Department of Mechanical Engineering University of Maryland MD 20742 USA

New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.

关键词： diverse population statistic order relations reliability growth Bayesian approach non-homogeneous poisson process Gamma-Beta distribution

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A transient process observation method based on the non-homogeneous poisson process model

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Chinese Physics C 2021年第4期45卷 394-403页

作者： Kuo Zhao Xiao-Ping Ouyang Hui-Ping Guo Liang Chen Lei-Dang Zhou Jin-Lu Ruan Han Wang Ning Lv Run-Long Gao Xi'an Research Institute of Hi-Tech Xi'an 710025China Northwest Institute of Nuclear Technology Xi'an 710024China Department of Engineering Physics Tsinghua UniversityBejing 100084China Xi'an Jiaotong University Xi'an 710049China

The current-mode-counting method is a new approach to observing transient processes,especially in transient nuclear fusion,based on the non-homogeneous poisson process(NHPP)*** this paper,a new measurement process model of the pulsed radiation field produced by transient nuclear fusion is built based on the NHPP.A simulated measurement is performed using the model,and the current signal from the detector is obtained by simulation based on poisson process *** neutron time spectrum is reconstructed and is in good agreement with the theoretical value,with its maximum error of a characteristic parameter less than 2.3%.Verification experiments were carried out on a CPNG-6 device at the China Institute of Atomic Energy,with a detection system with a nanosecond response *** experimental charge amplitude spectra are in good agreement with those obtained by the traditional counting mode,and the characteristic parameters of the time spectrum are in good agreement with the theoretical *** shows that the current-mode-counting method is effective for the observation of transient nuclear fusion processes.

关键词： non-homogeneous poisson process pulsed radiation field current-mode-counting method

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Grey-based approach for estimating software reliability under nonhomogeneous poisson process

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Journal of Systems Engineering and Electronics 2022年第2期33卷 360-369页

作者： LIU Xiaomei XIE Naiming College of Economics and Management Nanjing University of Aeronautics and AstronauticsNanjing 211106China College of Science Jiujiang UniversityJiujiang 332005China

Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous poisson process(NHPP) is the most used ***, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.

关键词： software reliability model stochastic process uncertainty system non-homogeneous poisson process grey system theory

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One-Sample Bayesian Predictive Analyses for a nonhomogeneous poisson process with Delayed S-Shaped Intensity Function Using non-Informative Priors

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Open Journal of Statistics 2023年第5期13卷 717-733页

作者： Otieno Collins Orawo Luke Akong’o Matiri George Munene Department of Mathematics Egerton University Egerton Kenya

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.

关键词： Failure Intensity non-Informative Priors Software Reliability Model Bayesian Approach non-homogeneous poisson process

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Considering the Fault Dependency Concept with Debugging Time Lag in Software Reliability Growth Modeling Using a Power Function of Testing Time

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International Journal of Automation and computing 2007年第4期4卷 359-368页

作者： V.B.Singh Kalpana Yadav Reecha Kapur V.S.S.Yadavalli Delhi College of Arts and Commerce University of DelhiDelhi 110023India Indira Gandhi Institute of Technology Guru Gobind Singh Indraprastha UniversityDelhi 110006India Department of Mathematics and Computer Application Bundelkhand UniversityJhansi 284128India Department of Industrial and Systems Engineering University of PretoriaPretoria 0002South Africa

Since the early 1970s tremendous growth has been seen in the research of software reliability growth modeling. In general, software reliability growth models （SRGMs） are applicable to the late stages of testing in software development and they can provide useful information about how to improve the reliability of software products. A number of SRGMs have been proposed in the literature to represent time-dependent fault identification / removal phenomenon; still new models are being proposed that could fit a greater number of reliability growth curves. Often, it is assumed that detected faults are immediately corrected when mathematical models are developed. This assumption may not be realistic in practice because the time to remove a detected fault depends on the complexity of the fault, the skill and experience of the personnel, the size of the debugging team, the technique, and so on. Thus, the detected fault need not be immediately removed, and it may lag the fault detection process by a delay effect factor. In this paper, we first review how different software reliability growth models have been developed, where fault detection process is dependent not only on the number of residual fault content but also on the testing time, and see how these models can be reinterpreted as the delayed fault detection model by using a delay effect factor. Based on the power function of the testing time concept, we propose four new SRGMs that assume the presence of two types of faults in the software： leading and dependent faults. Leading faults are those that can be removed upon a failure being observed. However, dependent faults are masked by leading faults and can only be removed after the corresponding leading fault has been removed with a debugging time lag. These models have been tested on real software error data to show its goodness of fit, predictive validity and applicability.

关键词： non-homogeneous poisson process fault dependency leading fault dependent fault delay effect.

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Analysis on testing and operational reliability of software

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Journal of Harbin Institute of Technology(New Series) 2008年第3期15卷 345-350页

作者：赵靖刘宏伟崔刚王慧强 Dept. of Computer Harbin Engineering University School of Computer Science and Technology Harbin Institute of Technology

Software reliability was estimated based on NHPP software reliability growth models. Testing reliability and operational reliability may be essentially different. On the basis of analyzing similarities and differences of the testing phase and the operational phase, using the concept of operational reliability and the testing reliability, different forms of the comparison between the operational failure ratio and the predicted testing failure ratio were conducted, and the mathematical discussion and analysis were performed in detail. Finally, software optimal release was studied using software failure data. The results show that two kinds of conclusions can be derived by applying this method, one conclusion is to continue testing to meet the required reliability level of users, and the other is that testing stops when the required operational reliability is met, thus the testing cost can be reduced.

关键词： software reliability non-homogeneous poisson process testing reliability operational reliability

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Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

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International Journal of Automation and computing 2007年第4期4卷 396-405页

作者： D.N.Goswami Sunil K.Khatri Reecha Kapur School of Studies in Computer Science and Applications Jiwaji UniversityGwalior 474011India Mother Teresa Institute of Management Guru Gobind Singh Indraprastha UniversityDelhi110092India Department of Mathematics and Computer Applications Bundelkhand UniversityJhansi 284128India

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

关键词： Discrete software reliability growth model non-homogeneous poisson process fault severity change point probability generating function.

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An Imperfect-debugging Fault-detection Dependent-parameter Software

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International Journal of Automation and computing 2007年第4期4卷 325-328页

作者： Hoang Pham Department of Industrial and Systems Engineering Rutgers UniversityNew JerseyNJ 08855-8018USA

Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.

关键词： non-homogeneous poisson process software reliability growth least squares estimate predictive power predictive-ratio risk.

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Experiment and validation system forX-ray pulsar-based navigation

Experiment and validation system forX-ray pulsar-based navig...

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第四届中国卫星导航学术年会

作者： Su Zhe Meng Yansong Xu Qibing Wang Xiaoliang Feng Xingang Academy of Space Information System

Due to the huge costs, space flight experiment cannot be realized in the preliminary step of X-ray pulsar based navigation （XPNAV） research. So, a kind of XPNAV experiment and 1 validation system is designed in this paper. This system is composed of two parts: the simulation of the pulsar signals and the calculation of navigation parameters. In the first part, the time at which X-ray photon arrive the solar system barycentre is modelled by non-homogeneous poisson process, then the output pulse of X-ray detector while the observation of pulsars can be simulated by time transformation. In the second part, navigation information included in the pulsar signals which are simulated in the first part can be reached using the Delta-Correction method. This system can simulate four pulsar signals and the process of XPNAV at photo level. This system has the advantage of low costs and high simulation accuracy, and provides a reference for the design of prototype for space flight experiments.

关键词： pulsar navigation experiment and validation system non-homogeneous poisson process time transfer

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