The estimation of parameters of the hypergeometric distribution and its application to the software reliability growth model

Tohma, Y.; Yamano, Hitoshi; Ohba, Mitsuru; Jacoby, R.

doi:10.1109/32.90450

Cited by 57 publications

(19 citation statements)

References 6 publications

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“…Here we demonstrate the data fitting ability of our PH-SRM by compared with these latest SRMs under the same data set used in [30,40]. The data was originally reported by Tohma et al [83], which consists of 111 observations of the number of detected faults (grouped data) in actual software testing. The tested programs were for the monitoring and real-time control system with about 200 modules, where each module has around 1000 lines of code.…”

Section: Numerical Experimentsmentioning

confidence: 94%

Ph Fitting Algorithm and Its Application to Reliability Engineering

Okamura

2016

JORSJ

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This article presents parameter estimation of phase-type (PH) distribution. PH distribution is widely used in model-based performance evaluation such as reliability and queueing system, and is defied by an absorbing continuous-time Markov chain (CTMC). Since non-Markovian model can be approximated by a CTMC by replacing general distributions with PH distributions, the parameter estimation is a challenging issue in stochastic modeling. We focus on the statistical inference algorithms to estimate not only the parameters of PH distribution with grouped, truncated and missing data but also the probability density function, and give two examples of PH fitting in reliability engineering.

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Section: Numerical Experimentsmentioning

confidence: 94%

Ph Fitting Algorithm and Its Application to Reliability Engineering

Okamura

2016

JORSJ

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“…The EM algorithm is applied to obtain the maximum likelihood estimates of the parameters to characterize the proposed model. In addition, we also compare the proposed model with several existing NHPP models by testing data set reported by Pham and Zhang (1997) and Tohma, Yamano, Obha, and Jacoby (1991) and by a simulation study.…”

Section: Introductionmentioning

confidence: 96%

Mean functions based on meta-mixtures in nonhomogeneous Poisson processes

Kim

Park

Yeo

2010

Journal of the Korean Statistical Society

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a b s t r a c tThis paper deals with the software reliability model based on a nonhomogeneous Poisson process. We introduce new types of mean functions which can be either NHPP-I or NHPP-II according to the choice of the distribution function. The proposed mean function is motivated by the fact that a strictly monotone increasing function can be modeled by a distribution function and an unknown distribution function approximated by a mixture of beta distributions. Some existing mean functions can be regarded as special cases of the proposed mean functions. The EM algorithm is used to obtain maximum likelihood estimates of the parameters in the proposed model. Crown

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“…In the earlier papers, Jacoby and Tohma $[10, 12]$ and Tohma et al $ [35,36]$ derived arecursive formula on the mean cumulative number of software faults detected up to the $i$ -th $(>0)$ test instance in testing phase. The derivation of the recursive formula is rather heuristic but is correct.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, their effort should be encouraged to apply the HGDSRM to the real software testing process. However, every method proposed in [11,35,36,37] is not always acceptable, since some of their methods are based on intuitive approximation schemes. The method with the genetic algorithm in [23] may be positioned as aheuristic estimation method.…”

Section: Introductionmentioning

confidence: 99%

“…Tohma et al [11,35,36,37] focused on both the maximum likelihood method and the least square method to estimate the model parameters from the software fault data, and compared the methods on some real data sets. In fact, the problem to estimate the model parameters has not been solved consistently in the statistical theory even for asimple two parameter hypergeometric distribution function [15].…”

Section: Introductionmentioning

confidence: 99%

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