• 정보처리학회논문지D
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• 제11D권7호
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• pp.1451-1458
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• 2004

Gompertz 성장곡선에 기반한 기존의 소프트웨어 신뢰성 성장모델들은 모두 대수형이다. 대수형 Gompertz 성장 곡선에 기반한 소프트웨어 신뢰성 성장 모델들은 모수 추정에 어려움을 갖고 있다. 그러므로 본 논문은 로지스틱형 Gompertz 성장곡선에 기반한 신뢰성 성장 모델을 제안한다. 13개의 다른 소프트웨어 프로젝트로부터 얻은 고장 데이터를 분석하여 그 유용성을 검토하였다. 모델의 모수들은 변수변환을 통한 선형희귀분석과 Virence의 방법으로 추정되었다. 제안된 모델은 평균 상대 예측 오차에 기반하여 성능을 비교하였다. 실험 결과 제안된 모델은 대수형 Gompertz 성장 곡선에 기반한 모델보다 좋은 성능을 보였다.

• Asian-Australasian Journal of Animal Sciences
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• 제11권1호
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• pp.84-88
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• 1998

The aim of this study was to describe growth patterns of mice using Gompertz model. Two distinct types of mice, laboratory mouse $CF_{\sharp1}$ (Mus musculus domesticus) and Yonakuni wild mouse (Yk, Mus musculus molossinus yonakuni) were used. From all possible crosses, there were two parental types and two reciprocal $F_1$ crosses obtained. Individual body weights were measured weekly from birth to ten weeks of age on 321 mice. Standardization to six mice was conducted and only first litters were used. Growth curve parameters were estimated to fit growth data. The results showed that growth among genetic groups were significantly different (p < 0.05) for both sexes, in which parental type of $CF_{\sharp1}$ and Yk had the highest and the smallest values, respectively. Meanwhile, reciprocal $F_1$ crosses were intermediate between parental types. It was concluded that Gompertz model provided and excellent fit for the growth data with a high coefficient determination $(R^2 = 0.999)$.

• 정보처리학회논문지D
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• 제15D권2호
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• pp.207-212
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• 2008

본 논문은 소프트웨어 비용추정 모델의 적합성을 평가하고, 가장 적합한 모델을 제시하였다. 먼저, 해당 모델의 함수를 변수변환시켜 선형식으로 만든다. 다음으로 실제 개발 소프트웨어의 비용 데이터가 모델의 선형식에 얼마나 적합한지로 모델의 성능을 평가한다. 모델 성능평가에는 절대오차 대신 상대오차 개념인 MMRE를 적용하였다. 기존의 소프트웨어 비용추정 모델은 Weibull, Gamma와 Rayleigh 함수를 따르고 있다. 본 논문에서는 성장곡선의 일종인 Gompertz 곡선 모델을 제안하였다. 추가로 다른 성장곡선들도 적합성을 검증하였다. 모델 성능평가 결과 Gompertz 성장곡선이 소프트웨어 비용추정 모델로 가장 적합한 성능을 보였다.

• Communications for Statistical Applications and Methods
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• 제21권6호
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• pp.521-528
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• 2014

A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

• 디지털산업정보학회논문지
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• 제10권2호
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• pp.29-36
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• 2014

Finite failure NHPP software reliability models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, proposes the Gompertz distribution reliability model, which made out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on mean square error (MSE) and coefficient of determination$(R^2)$, for the sake of efficient model, was employed. Analysis of failure using real data set for the sake of proposing fixed shape parameter of the Gompertz distribution was employed. This analysis of failure data compared with the Gompertz distribution model of shape parameter. In order to insurance for the reliability of data, Laplace trend test was employed. In this study, the proposed Gompertz model is more efficient in terms of reliability in this area. Thus, Gompertz model can also be used as an alternative model. From this paper, software developers have to consider the growth model by prior knowledge of the software to identify failure modes which can was helped.

• 한국산업융합학회 논문집
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• 제20권5호
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• pp.395-404
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• 2017

Cultivating soybeans in rice paddy field reduces labor costs and increases the yield. Soybeans, however, are highly susceptible to excessive soil water in paddy field. Controlled drainage system can adjust groundwater level (GWL) and control soil moisture content, resulting in improvement soil environments for optimum crop growth. The objective of this study was to fit the soybean growth data (canopy height and stem diameter) using Gompertz model and Logistic model at different GWL and validate those models. The soybean, Daewon cultivar, was grown on the lysimeters controlled GWL (20cm and 40cm). The soil textures were silt loam and sandy loam. The canopy height and stem diameter were measured from the 20th days after seeding until harvest. The Gompertz and Logistic models were fitted with the growth data and each growth rate and maximum growth value was estimated. At the canopy height, the $R_2$ and RMSE were 0.99 and 1.58 in Gompertz model and 0.99 and 1.33 in Logistic model, respectively. The large discrepancy was shown in full maturity stage (R8), where plants have shed substantial amount of leaves. Regardless of soil texture, the maximum growth values at 40cm GWL were greater than the value at 20cm GWL. The growth rates were larger at silt loam. At the stem diameter, the $R_2$ and RMSE were 0.96 and 0.27 in Gompertz model and 0.96 and 0.26 in Logistic model, respectively. Unlike the canopy height, the stem diameter in R8 stage didn't decrease significantly. At both GWLs, the maximum growth values and the growth rates at silt loam were all larger than the values at sandy loam. In conclusion, Gompertz model and Logistic model both well fit the canopy heights and stem diameters of soybeans. These growth models can provide invaluable information for the development of precision water management system.

• 한국농공학회논문집
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• 제52권6호
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• pp.19-26
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• 2010

Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

• 한국식품위생안전성학회지
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• 제26권1호
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• pp.25-30
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• 2011

본 연구에서는 식중독 예방과 식품의 안전성 확보 및 정량적 미생물 위해평가에 활용하기위하여, Gompertz model과 Baranyi model을 이용하여 샐러드용 신선채소에서 L. monocytogenes의 SGR에 관한 성징예측모델(SGR by Gompertz equation=-0.1606+$0.0574^*Temp$+$0.0009^*Temp^*Temp$, SGR by Baranyi equation=0.3502-$0.0496^*Temp$+$0.0022^*Temp^*Temp$)을 개발하였다. 개발된 모델의 적합성 평가를 위해 MSE, Bf, 및 Af factor를 산출하였다. 샐러드용 신선 채소의 MSE, Bf, Af는 Gompertz model식을 적용한 경우 0.002718, 1.050084, 1.160767, Baranyi model 식을 적용한 경우 0.055186, 1.931472, 2.137181으로 나타나 Gompertz model식을 적용하여 개발한 예측모델이 Baranyi model 식을 이용하여 개발한 예측모델에 비해 적합성이 높은 것으로 나타났다. Gompertz model식을 활용하여 본 연구에서 개발된 샐러드용 신선 채소에서의 L. monocytogenes 성장 예측모델은 신선 채소류를 생산, 가공, 보관 및 판매하는 산업체에서 널리 활용 가능할 것으로 판단되며, 더욱 정확한 예측모델 개발을 위해서는 pH 및 수분활성도 등 다양한 변수에 따른 미생물의 성장패턴 변화 등에 관한 연구가 추가적으로 시행되어야 할 것으로 생각되어 진다.

• 한국식품과학회지
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• 제37권5호
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• pp.850-855
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• 2005

본 연구는 냉장돈육에서의 식중독 원인균이면서 냉장온도에서 성장이 가능한 병원성균인 L. monocytogenes에 대한 적절한 위생관리를 제시하기 위하여 포장돈육 작업장 원료돈육에서 분리된 야생균주 L. monocytogenes 이용하여 돈육포장공정 및 유통조건에서의 L. mnocytogenes에 대한 성장예측모델을 제시하고자 실시하였다. 성장실험은 온도 5, 10, 15, $20^{\circ}C$ 시간은 0, 1, 2, 3, 18, 48, 120시간에서 실시하였으며, 이를 바탕으로 온도별 Gompertz value인 A, C, B, M의 값과 Growth kinetic인 exponential growth rate(EGR), generation time(GT), lag phase duration(LPD), maximum population density(MPD)를 산출하였다. GT, LPD는 온도가 상승할수록 그 값이 점점 낮아지는 경향을 나타났으며, EGR의 경우는 반대로 온도가 높아질수록 점점 높아지는 경향을 나타냈다. Gompertz value중 B와 M 값을 이용하여 온도를 주요 control factor로 선정한 반응표면분석(Response surface analysis)을 실시하여 온도에 따른 다항식을 산출하였고 이 식을 Gompertz 식에 적용하여 온도와 시간에 따른 냉장돈육에서의 L. monocytogenes에 대한 성장정도를 예측할 수 있는 성장예측모델을 제시하였다. 개발된 성장예측모델에 대한 검증은 GT, LPD, EGR에 대한 실험값과 예측값의 비교를 통하여 실시하였으며, 그 결과 GT, LPD, EGR 모두 통계적으로 유의하게 나타났다(p<0.01). 따라서 이 모델은 risk assessment 중 exposure assessment를 위한 성장예측모델로 충분히 이용가능 한 것으로 보이며, 추후 냉장돈육 위성관리기준에 대한 과학적 근거자료로 활용될 수 있을 것으로 보인다.

• 농업과학연구
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• 제43권4호
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• pp.623-633
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• 2016

A total of 6,973 steer growth records of Hanwoo breeding bull's progeny test data collected from 1989 to 2015 were analyzed to identify the most appropriate growth curve among three growth curve models (Gompertz, Logistic and von Bertalanffy). The Gompertz growth curve model equation was $W_t=990.5e^{{-2.7479e}^{-0.00241t}}$, the Logistic growth curve model equation was $W_t=772(1+8.3314e^{-0.00475t})^{-1}$, and the von Bertalanffy growth curve model equation was $W_t=1,196.4(1-0.646e^{-0.00162t})^3$. The Gompertz model parameters A, b, and k were estimated to be $990.5{\pm}10.27$, $2.7479{\pm}0.0068$, and $0.00241{\pm}0.000028$, respectively. The inflection point age was estimated to be 421 days and the weight of inflection point was 365.3 kg. The Logistic model parameters A, b, and k were estimated to be $772.0{\pm}4.12$, $8.3314{\pm}0.0453$, and $0.00475{\pm}0.000033$, respectively. The inflection point age was estimated to be 445 days and the weight of inflection point was 385.0 kg. The von Bertalanffy model parameters A, b, and k were estimated to be $1196.4{\pm}18.39$, $0.646{\pm}0.0010$, and $0.00162{\pm}0.000027$, respectively. The inflection point age was estimated to be 405 days and the weight of inflection point was 352.0 kg. Mature body weight of the von Bertalanffy model was 1196.4 kg, the Gompertz model was 990.5 kg, and the Logistic model was 772.0 kg. The difference between actual and estimated weights was similar in the Logistic model and the von Bertalanffy model. The difference between market weight and estimated market weight was the lowest in the Gompertz model. The growth curve using the von Bertalanffy model showed the lowest mean square error.