• Journal of Korean Society for Quality Management
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• v.31 no.1
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• pp.11-20
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• 2003

In the development of a complex systems, the early prototypes generally have reliability problems, and, consequently these systems are subjected to a reliability growth program to find problems and take corrective action. A variety of models have been proposed to account for the reliability growth phenomena. Clear guidelines need to be established to assist the reliability engineers for model selection. In this paper, some of more well-known growth models are surveyed and classified. These models are classified based upon distinguishing model features. A procedure for model selection is introduced which is based on this classification.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.5
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• pp.11-16
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• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• Journal of Forest and Environmental Science
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• v.30 no.2
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• pp.201-207
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• 2014

This study was conducted to estimate the best-fit nonlinear height-DBH growth models for Larix kaempferi in Gangwon and North Gyeongsang province in South Korea. Exponential, Modified Logistic, Chapman-Richards, and Weibull function were used for estimating height-DBH models. To evaluate the selected models, $R^2$, RMSE, MD, MAD, and residual plots were performed in each model. Also, the coefficients and patterns in models of the previous studies were compared with those in this study. The result showed that Weibull equation was found to be the best-fit model with $R^2$=0.9837, RMSE=2.6133, MD=0.0089, and MAD=2.0896. All model parameters in our study had similar values to those in the previous models except for asymptotic parameter a. Our research result showed that Gangwon and North Gyeongsang province were superior to other provinces with regard to height growth for Larix kaempferi.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.53 no.5
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• pp.699-706
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• 2020

Predictive models in food microbiology are used for predicting microbial growth or death rates using mathematical and statistical tools considering the intrinsic and extrinsic factors of food. This study developed predictive growth models for Bacillus cereus on dried laver Pyropia pseudolinearis stored at different temperatures (5, 10, 15, 20, and 25℃). Primary models developed for specific growth rate (SGR), lag time (LT), and maximum population density (MPD) indicated a good fit (R²≥0.98) with the Gompertz equation. The SGR values were 0.03, 0.08, and 0.12, and the LT values were 12.64, 4.01, and 2.17 h, at the storage temperatures of 15, 20, and 25℃, respectively. Secondary models for the same parameters were determined via nonlinear regression as follows: SGR=0.0228-0.0069*T₁+0.0005*T₁²; LT=113.0685-9.6256*T₁+0.2079*T₁²; MPD=1.6630+0.4284*T₁-0.0080*T₁² (where T₁ is the storage temperature). The appropriateness of the secondary models was validated using statistical indices, such as mean squared error (MSE<0.01), bias factor (0.99≤B_f≤1.07), and accuracy factor (1.01≤A_f≤1.14). External validation was performed at three random temperatures, and the results were consistent with each other. Thus, these models may be useful for predicting the growth of B. cereus on dried laver.

• Food Science of Animal Resources
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• v.30 no.1
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• pp.49-54
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• 2010

The aim of this research was to estimate the effect of temperature and develop predictive models for the growth of total viable cells (TVC) and Escherichia coli (EC) on chicken breast under aerobic and various temperature conditions. The primary models were determined by Baranyi model. The secondary models for the specific growth rate (SGR) and lag time (LT), as a function of storage temperature, were developed by the polynomial model. The initial contamination level of chicken breasts was around 4.3 Log CFU/g of TVC and 1.0 Log CFU/g of E. coli. During 216 h of storage, SGR of TVC showed 0.05, 0.15, and 0.54 Log CFU/g/h at 5, 15, and $25^{\circ}C$. Also, the growth tendency of EC was similar to those of TVC. As storage temperature increased, the values of SGR of microorganisms increased dramatically and the values of LT decreased inversely. The predicted growth models with experimental data were evaluated by $B_f$, $A_f$, RMSE, and $R^2$. These values indicated that these developed models were reliable to express the growth of TVC and EC on chicken breasts. The temperature changes of distribution and showcase in markets might affect the growth of microorganisms and spoilage of chicken breast mainly.

• Food Science of Animal Resources
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• v.29 no.3
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• pp.289-295
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• 2009

The aim of this research was to develop predictive models for the growth of spoilage bacteria (total viable cells, Pseudomonas spp., and lactic acid bacteria) on frankfurters and to estimate the shelf-life of frankfurters under aerobic conditions at various storage temperatures (5, 15, and $25^{\circ}C$). The primary models were determined using the Baranyi model equation. The secondary models for maximum specific growth rate and lag time as functions of temperature were developed by the polynomial model equation. During 21 d of storage under various temperature conditions, lactic acid bacteria showed the longest lag time and the slowest growth rate among spoilage bacteria. The growth patterns of total viable cells and Pseudomonas spp. were similar each other. These data suggest that Pseudomonas spp. might be the dominant spoilage bacteria on frankfurters. As storage temperature increased, the growth rate of spoilage bacteria also increased and the lag time decreased. Furthermore, the shelf-life of frankfurters decreased from 7.0 to 4.3 and 1.9 (d) under increased temperature conditions. These results indicate that the most significant factor for spoilage bacteria growth is storage temperature. The values of $B_f$, $A_f$, RMSE, and $R^2$ indicate that these models were reliable for identifying the point of microbiological hazard for spoilage bacteria in frankfurters.

• Korean Journal of Agricultural Science
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• v.43 no.4
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• pp.537-546
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• 2016

The development of models for agriculture systems, especially for crop production, has supported the prediction of crop yields under various environmental change scenarios and the selection of better crop species or cultivar. Crop models could be used as tools for supporting reasonable nutrient management approaches for agricultural land. This paper outlines the simplified structure of main crop models (crop growth model, crop-soil model, and crop-soil-environment model) frequently used in agricultural systems and shows diverse application of their simulated results. Crop growth models such as LINTUL, SUCROS, could provide simulated data for daily growth, potential production, and photosynthesis assimilate partitioning to various organs with different physiological stages, and for evaluating crop nutrient demand. Crop-Soil models (DSSAT, APSIM, WOFOST, QUEFTS) simulate growth, development, and yields of crops; soil processes describing nutrient uptake from root zone; and soil nutrient supply capability, e.g., mineralization/decomposition of soil organic matter. The crop model built for the DSSAT family software has limitations in spatial variability due to its simulation mechanism based on a single homogeneous field unit. To introduce well-performing crop models, the potential applications for crop-soil-environment models such as DSSAT, APSIM, or even a newly designed model, should first be compared. The parameterization of various crops under different cultivation conditions like those of intensive farming systems common in Korea, shortened crop growth period, should be considered as well as various resource inputs.

• Journal of Korean Society of Forest Science
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• v.96 no.2
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• pp.160-169
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• 2007

The data used to develop distance-independent individual models for natural mixed forests were collected from 712 remeasured permanent sample plots (25,526 trees) of 10-year periodic from 1990 to 2000 in Baihe Forest Bureau of Changbai Mountains, northeast China. Based on analyzing relationship between diameter increment of individual trees with tree size, competitive status, and site condition, the diameter growth models for individual trees of 15 species growing in mixed-species uneven-aged forest stands, that have simple form, good predicting precision, and easily applicable, were developed using stepwise regression method. The main variables influencing on diameter increment of individual trees were tree size and competition, however, the site conditions were not significantly related with diameter increment. The tree size variables (lnDBH and $DBH^2$) were the most significant and important predictors of diameter growth existing in all 15 growth models. The diameter increment was directly proportional to tree diameter for each species. For the competitive factors in growth model, the relative diameter (RD), canopy closure (P), and the ratio of diameter of subject tree with maximum diameter (DDM) were contributed to the diameter increment at a certain extent. Other measures of stand density, such as basal area of stand (G) and stand density index (SDI), were not significantly influenced on diameter increment. Site factors, such as site index, slope and aspect were not important to diameter increment and excluded in the final models. The total variance explained by the final models of squared diameter increment ($R^2$) for all 15 species ranged from 35% to 72% and these results compared quit closely with those of Wykoff (1990) for mixed conifer stands. Using independent data set, validation measures were evaluated for predicting models of diameter increment developed in this study. The result indicated that the estimated precision was all greater than 94% and the models were suitable to describe diameter increment.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1367-1375
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• 2015

Consider the linear growth models for longitudinal data analysis. Several kind of linear growth models are selected such as time-effect and random-effect models as well as a dummy variable included model. In this work, simulation data are generated with normality assumption, and both binormal ROC curve and AUC are obtained and compared for various linear growth models. It is found that ROC curves have different shapes and AUC increase slowly, as values of the covariance increase and the time passes for random-effect models. On the other hand, AUC increases very fast as values of covariance decrease. When the covariance has positive value, we explored that the variances of random-effect models increase and the increment of AUC is smaller than that of AUC for time-effect models. And the increment of AUC for time-effect models is larger than the increment for random-effect models.

• Journal of Korean Society of Forest Science
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• v.88 no.1
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• pp.47-54
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• 1999

To estimate optimal tree diameter and height growth function in Pinus thunbergii stands with site index of 12 class, quoted from two linear models of linear transformation(1) and linear transformation (2) and four non-linear models of exponential, Gompertz, Chapman-Richards, and Weibull etc.. Analyzed correlation among the estimated tree diameter and height by these function models, and observed diameter and height growth were compared. In the results of tree diameter and height growth estimation by stand age, non-linear models showed better appropriation than linear model and Chapman-Richards model was most fitted for tree height growth but few, if any, differences among their nonlinear models. Therefore, it is consider to be much more study about non-linear model to estimate tree diameter and height growth in the actual stands hereafter.