The Journal of Korea Institute of Information, Electronics, and Communication Technology (한국정보전자통신기술학회논문지)

Korea Information Electronic Communication Technology (한국정보전자통신기술학회)
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A Study on Comparative Evaluation of Application of Software Reliability Model Dependent on Various Hazard Functions

다양한 위험함수에 의존한 소프트웨어 신뢰모형의 적용에 대한 비교 평가에 관한 연구

  • Yang, Tae-Jin (Department of Electronic Engineering, Namseoul University)
  • Received : 2018.11.29
  • Accepted : 2018.12.17
  • Published : 2018.12.29
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Abstract

Software efficiency is the probability of failure free use in operating environments, and is the most fundamental factor affecting software system stability. The malfunction of the computer system used in the information technology field may cause a significant loss in the related industry. Therefore, in this study, we analyze the attributes of software reliability models that depend on various hazard functions based on finite fault NHPP model with software failure time data. The hazard function pattern of proposed model is constant for the Goel-Okumoto model, and the Minimax and Rayleigh models follow the incremental pattern, but the hazard function increase value of the Minimax model is smaller than that of the Rayleigh model and the Goel-Okumoto model. Also, the Minimax model was relatively efficient because the true value error of the mean value function m(t) and the mean square error (MSE) of the Minimax model were smaller than those of the Rayleigh and Goel-Okumoto models. The results of this study are expected to be useful for software developers as basic information about the hazard function.

소프트웨어 효율성은 운용 환경에서 사용시간에 따라 고장없이 사용할 수 있는 확률이며, 소프트웨어 시스템 안정성에 영향을 미치는 가장 근본적인 요인이다. 정보기술 분야에서 활용되고 있는 컴퓨터 시스템의 오작동은 관련 산업분야에 중요한 손실을 야기할 수도 있다. 따라서, 본 연구에서는 소프트웨어 고장시간 자료를 가지고 유한고장 NHPP 모형에 기반하여 다양한 위험함수에 의존한 소프트웨어 신뢰성 모형의 속성을 분석 하였다. 제안한 모형의 위험함수 패턴은 Goel-Okumoto모형은 상수가 되고, Minimax 모형과 Rayleigh모형은 증가패턴을 따르지만, 위험함수의 증가폭은 Minimax 모형이 Rayleigh모형과 Goel-Okumoto모형 보다 작은 것으로 나타났다. 또한, 평균값 함수m(t)의 참값 오차와 평균제곱오차(MSE)는 Minimax 모형이 모두 Rayleigh 모형과 Goel-Okumoto모형 보다 작아서 상대적으로 효율적이였다. 본 연구의 결과는 소프트웨어 개발자에게 위험함수에 관한 기본정보로 활용될 수 있을 것으로 기대한다.

Keywords

JBJTBH_2018_v11n6_800_f0001.png 이미지

그림 1. 박스플롯의 결과 Fig. 1. Result of Box-plot

JBJTBH_2018_v11n6_800_f0002.png 이미지

그림 2. 각 시점에 대한에 평균제곱오차 추이 Fig. 2. Transition of mean square error for each failure number

JBJTBH_2018_v11n6_800_f0003.png 이미지

그림 3 강도함수의 추세 Fig. 3. Transition of Intensity function

JBJTBH_2018_v11n6_800_f0004.png 이미지

그림 4. 각 모형에 대한 평균값 함수 추이 Fig. 4. Mean value function trend for each model

JBJTBH_2018_v11n6_800_f0005.png 이미지

그림 4 신뢰도의 추세 Fig. 4. Transition of reliability

표 1. 확률밀도함수와 위험함수 Table 1. Probability density function and hazard function

JBJTBH_2018_v11n6_800_t0001.png 이미지

표 2. 고장시간자료 Table 2. Failure time data

JBJTBH_2018_v11n6_800_t0002.png 이미지

표 3. 모수추정 및 MSE , R2 Table 3. Parameter estimation and MSE , R2

JBJTBH_2018_v11n6_800_t0003.png 이미지

표 4. 강도함수의 추정 Table 4. Eestimation of the intensiry function

JBJTBH_2018_v11n6_800_t0004.png 이미지

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