• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.

• Journal of Information Technology Applications and Management
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• v.28 no.4
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• pp.13-20
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• 2021

In this paper, I was applied the life distribution following linear failure rate distribution, Lindley distribution and Burr-Hatke exponential distribution extensively used in the arena of software reliability and were associated the reliability possessions of the software using the nonhomogeneous Poisson process with finite failure. Furthermore, the average value functions of the life distribution are non-increasing form. Case of the linear failure rate distribution (exponential distribution) than other models, the smaller the estimated value estimation error in comparison with the true value. In terms of accuracy, since Burr-Hatke exponential distribution and exponential distribution model in the linear failure rate distribution have small mean square error values, Burr-Hatke exponential distribution and exponential distribution models were stared as the well-organized model. Also, the linear failure rate distribution (exponential distribution) and Burr-Hatke exponential distribution model, which can be viewed as an effectual model in terms of goodness-of-fit because the larger assessed value of the coefficient of determination than other models. Through this study, software workers can use the design of mean square error, mean value function as a elementary recommendation for discovering software failures.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.4
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• pp.25-34
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• 2012

In this study, in the process of testing before the release of the software products designed, software testing manager in advance should be aware of the testing-information. Therefore, the effective learning effects perspective has been studied using the NHPP software. The finite failure nonhomogeneous Poisson process models presented and applied property of learning effect based on truncated time and delayed S-shaped software reliability. Software error detection techniques known in advance, but influencing factors for considering the errors found automatically and learning factors, by prior experience, to find precisely the error factor setting up the testing manager are presented comparing the problem. As a result, the learning factor is greater than autonomous errors-detected factor that is generally efficient model can be confirmed. This paper, a failure data analysis was performed, using time between failures, according to the small sample and large sample sizes. The parameter estimation was carried out using maximum likelihood estimation method. Model selection was performed using the mean square error and coefficient of determination, after the data efficiency from the data through trend analysis was performed.

• Convergence Security Journal
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• v.6 no.3
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• pp.145-153
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• 2006

Infinite failure NHPP models for a record value satisfies mode proposed in the literature exhibit either monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, propose comparative study of software reliability model using Erlang distribution, Rayleigh and Gumbel distribution. Equations to estimate the parameters using maximum likelihood estimation of infinite failure NHPP model based on failure data collected in the form of interfailure times are developed. For the sake of proposing distribution, we used to the special pattern. Analysis of failure data set using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

• Structural Engineering and Mechanics
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• v.75 no.5
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• pp.633-642
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• 2020

Artificial neural networks (ANNs) are known as intelligent methods for modeling the behavior of physical phenomena because of it is a soft computing technique and takes data samples rather than entire data sets to arrive at solutions, which saves both time and money. ANN is successfully used in the civil engineering applications which are suitable examining the complicated relations between variables. Functionally graded materials (FGMs) are advanced composites that successfully used in various engineering design. The FGMs are nonhomogeneous materials and made of two different type of materials. In the present study, the bending analysis of functionally graded material (FGM) beams presents on theoretical based on combination of mixed-finite element method, Gâteaux differential and Timoshenko beam theory. The main idea in this study is to build a model using ANN with four parameters that are: Young's modulus ratio (E_t/E_b), a shear correction factor (k_s), power-law exponent (n) and length to thickness ratio (L/h). The output data is the maximum displacement (w). In the experiments: 252 different data are used. The proposed ANN model is evaluated by the correlation of the coefficient (R), MAE and MSE statistical methods. The ANN model is very good and the maximum displacement can be predicted in ANN without attempting any experiments.

• Journal of Information Technology Applications and Management
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• v.12 no.2
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• pp.1-13
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• 2005

This paper proposes a software-reliability growth model incoporating the amount of testing effort expended during the software testing phase after developing it. The time-dependent behavior of testing effort expenditures is described by a Logistic curve. Assuming that the error detection rate to the amount of testing effort spent during the testing phase is proportional to the current error content, a software-reliability growth model is formulated by a nonhomogeneous Poisson process. Using this model the method of data analysis for software reliability measurement is developed. After defining a software reliability, This paper discusses the relations between testing time and reliability and between duration following failure fixing and reliability are studied. SRGM in several literatures has used the exponential curve, Railleigh curve or Weibull curve as an amount of testing effort during software testing phase. However, it might not be appropriate to represent the consumption curve for testing effort by one of already proposed curves in some software development environments. Therefore, this paper shows that a logistic testing-effort function can be adequately expressed as a software development/testing effort curve and that it gives a good predictive capability based on real failure data.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.818-822
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• 2003

We propose a software-reliability growth model incoporating the amount of uniform and Weibull testing efforts during the software testing phase in this paper. The time-dependent behavior of testing effort is described by uniform and Weibull curves. Assuming that the error detection rate to the amount of testing effort spent during the testing phase is proportional to the current error content, the model is formulated by a nonhomogeneous Poisson process. Using this model the method of data analysis for software reliability measurement is developed. The optimum release time is determined by considering how the initial reliability R(x|0) would be. The conditions are $R(x|0)>R_o$, $R_o>R(x|0)>R_o^d$ and $R(x|0)<R_o^d$ for uniform testing efforts. Ideal case is $R_o>R(x|0)>R_o^d$. Likewise, it is $R(x|0){\geq}R_o$, $R_o>R(x|0)>R_o^{\frac{1}{g}$ and $R(x\mid0)<R_o^{\frac{1}{g}}$ for Weibull testing efforts. Ideal case is $R_o>R(x|0)>R_o^{\frac{1}{g}}$.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.133-145
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• 1995

This paper is concerned with the method of estimating lifetime distribution from field data for repairable products with multiple modes of failure, and is an extension of Bai et al.(1995). The log linear function is considered as a model for describing the relation between failure time of a product and covariates. Using the nonhomogeneous poisson process, general methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and specific formulas for Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extension to case-cohort design is also considered.

• Management Science and Financial Engineering
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• v.5 no.2
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• pp.43-53
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• 1999

In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonho-mogeneous process with/without a cyclic component in the failure rate function. The analytical re-sults for various situations are presented along with numerical examples using simulated data.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.155-166
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• 2006

Many software reliability growth models (SRGMs) based on nonhomogeneous Poisson process (NHPP) have been developed and applied in practice. NHPP SRGMs are characterized by their mean value functions. Mean value functions are usually derived from differential equations representing the fault detection/removal process during testing. In this paper such differential equations are regarded as frameworks for generating mean value functions. Currently available frameworks are theoretically discussed with respect to capability of representing the fault detection/removal process. Then two general frameworks are proposed.