• 제어로봇시스템학회논문지
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• 제5권4호
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• pp.394-402
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• 1999

In this paper, we present an effective RLS algorithm with forgetting factor of Erlang function for the system identification. In the proposed algorithm, the forgetting factor decreases monotonically in the first stage, and then it increases monotonically in the second stage in contrary to the conventional forgetting factor RLS algorithms. In addition, annealing effect and an asymptotically stability of the proposed algorithm is discussed based on the analysis of convergency property on. Simulation results for the system identification problem indicate the superiority of the proposed algorithm in comparison to the RLS algorithm such as NLMS and Kalman filter based algorithm.

• 산업융합연구
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• 제18권3호
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• pp.19-25
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• 2020

소프트웨어 개발과정에서 소프트웨어 신뢰도 평가는 매우 중요한 문제이다. 특히, 소프트웨어 개발자에게 높은 신뢰도을 만족시키는 최적의 개발모형을 찾아내는 일은 더욱 중요한 과제이다. 이를 위해, 본 연구에서는 파레토 및 어랑 수명분포을 유한고장 NHPP 모형에 적용하여, 신뢰도 속성을 평가하였다. 이를 위하여 모수추정은 최우추정법을 적용하였고, 비선형 방정식의 풀이는 이분법을 사용하였다. 그 결과, 강도함수와 평균값함수에서 Erlang 모형이 Pareto 모형보다 우수한 성능을 보였고, 평균제곱오차도 작아서 효율적인 모형임을 확인하였다. 또한, 미래의 임무시간을 투입하고 신뢰도를 평가한 결과, Erlang 모형이 Pareto모형과 함께 효율적으로 높게 나타났으나, 반면에 Goel-Okumoto 기본모형은 감소하는 추세를 보였다. 결론적으로, Erlang 모형이 제안된 모형중 가장 우수한 성능을 가진 모형임을 알 수 있었다. 본 연구를 통하여 소프트웨어 개발자들이 최적의 소프트웨어 신뢰성 모형을 탐색하고, 평가하는데 필요한 기본지침으로 활용할 수 있을 것으로 기대한다.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• Journal of Information Technology Applications and Management
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• 제25권4호
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• pp.115-122
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• 2018

Software reliability has the greatest impact on computer system reliability and software quality. For this software reliability analysis, In this study, we compare and analyze the trends of the properties affecting the reliability according to the shape parameters of Erlang distribution based on the finite fault NHPP. Software failure time data were used to analyze software failure phenomena, the maximum likelihood estimation method was used for parameter estimation. As a result, it can be seen that the intensity function is effective because it shows a tendency to decrease with time when the shape parameters a = 1 and a = 3. However, the pattern of the mean value function showed an underestimation pattern for the true values when the shape parameters a = 1 and a = 2, but it was found to be more efficient when a = 3 because the error width from the true value was small. Also, in the reliability evaluation of the future mission time, the stable and high trend was shown when the shape parameters a = 1 and a = 3, but on the contrary, when a = 2, the reliability decreased with the failure time. Through this study, the property of finite fault NHPP Erlang model according to the change of shape parameter without existing research case was newly analyzed, and new research information that software developers can use as basic guideline was presented.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.449-468
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• 2023

This paper deals in the study of the estimation of the parameters of Erlang distribution based on rank set sampling and some of its modifications. Here we considered Maximum Likelihood (ML) and the Bayesian technique to estimate the shape and scale parameter of Erlang distribution based on RSS and its some modifications such as ERSS, MRSS, and MRSSu. The derivation for unknown parameters of Erlang distribution is well presented using normal approximation to the asymptotic distribution of ML estimators. But due to the complexity involves in the integral, the Bayes estimator of unknown parameters is obtained using MCMC method. Further, we compared the MSE of estimation in different sampling schemes with different set sizes and cycle size. A real-life data application is also given to illustrate the efficiency of the proposed scheme.

• Journal of Information Technology Applications and Management
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• 제24권2호
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• pp.71-80
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• 2017

Software reliability is one of the most elementary and important problems in software development In order to find the software failure occurrence, the instantaneous failure rate function in the Poisson process can have a constant, incremental or decreasing tendency independently of the failure time. In this study, we compared the reliability performance of the software reliability model using the parameters of Pareto life distribution with the intensity decreasing pattern and the shape parameter of Erlang life distribution with the intensity increasing and decreasing pattern in the software product testing. In order to identify the software failure environment, the parametric estimation was applied to the maximum likelihood estimation method. Therefore, in this paper, we compare and evaluate software reliability by applying software failure time data. The reliability of the Erlang and Pareto life models is shown to be higher than that of the Pareto lifetime distribution model when the shape parameter is higher and the Erlang model is more reliable when the shape parameter is higher. Through this study, the software design department will be able to help the software design by applying various life distribution and shape parameters, and providing basic knowledge using software failure analysis.

• 응용통계연구
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• 제11권2호
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• pp.377-387
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• 1998

컴퓨터의 발전에 따른 마코브체인 몬테카를로방법을 소프트웨어 신뢰확률모형에 이용하였다. 베이지안 추론에서 조건부분포를 가지고 사후분포를 결정하는데 있어서의 계산문제와 이론적인 정당성을 고려, 마코프연쇄와 메트로폴리스방법의 관계를 고찰하였으며, 특히 Mus-Okumoto와 Erlang(2)의 중첩모형에 대하여 깁스샘플링 알고리즘과 메트로폴리스 알고리즘을 활용하며 베이지안 계산과 예측 우도기준에 의 한 모형선택을 제안하고 Cox-Lewis에 의해 계시된 Thing method를 이용한 모의실험자료를 이용하여 수치적인 계산을 시행하고 그 결과가 제시되었다.

• 품질경영학회지
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• 제33권3호
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 춘계학술대회
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• 한국정보전자통신기술학회논문지
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• 제10권5호
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• pp.469-475
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• 2017

소프트웨어 개발시행 과정에서 소프트웨어 신뢰성은 매우 기본적이고 필수적인 문제 중에 하나이다. 소프트웨어 고장현상을 파악하기 위하여 비동질적인 포아송 과정에서 순간 고장률인 강도함수가 고장시간에 독립적으로 일정하거나, 증가형 혹은, 감소형 추세를 가질 수 있다. 본 논문에서는 소프트웨어 설계 과정에서 강도형태가 감소패턴을 따르는 랜들리 수명분포와 증가하다가 감소하는 어랑수명 분포를 활용한 소프트웨어 신뢰속성 모형에 대하여 신뢰도 장단점에 관한 연구를 하였다. 소프트웨어 고장현상을 파악하기 위하여 모수추정은 최우추정법을 적용하였다. 따라서, 본 논문에서는 소프트웨어 고장시간 자료를 적용하여 소프트웨어 신뢰도를 비교하고, 평가하였다. 그 결과, 랜들리 모형이 어랑분포 모형보다 신뢰도가 상승하는 것으로 나타났으나, 어랑분포 모형에서는 형상모수가 높을수록 높은 신뢰도를 나타내는 추세를 보였다. 본 논문를 통하여 소프트웨어 기획 부서에서는 특정한 수명분포와 형상모수를 활용함으로서 소프트웨어 고장분석을 활용한 소프트웨어 신뢰성 모형에 대한 신뢰성 속성을 적용한 데이터 및 기본 지식을 제공함으로서 소프트웨어 설계에 실질적인 도움을 줄 수 있다.