• Journal of the Korean Mathematical Society
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• 제50권1호
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• Journal of the Korean Data and Information Science Society
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• 제21권4호
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• pp.747-756
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• 2010

With the recent recession, studies on the economy are actively being conducted throughout the industry. Based on the Small Business data registered in the Credit Guarantee Fund, we estimated the survival probability in the context of the survival analysis. We also analyzed the survival time for the construction and the other industries which are distinguished depending on the types of business and assets in the Small Business. The survival probability was estimated by using the life-table and the difference between the survival probabilities for the different types of business was described via the method of the Log-rank test and the Wilcoxon test. We found that the small business with over one billion asset has the highest survival probability and that with less than 1000 million asset showed the similar survival probability. In terms of types of business Wholesale and Retail trade industry and Services were relatively high in the survival probability than Light, Heavy, and the construction industries. Especially the construction industry showed the lowest survival probability. Most of the Small Business tend to increase in the hazard rate over time.

• The Journal of Korean Medicine
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• 제23권4호
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• pp.91-97
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• 2002

Objective: This study was conducted to know the survival probability of the patients with cerebrovascular disease. Method: 1,341 patients who were suspected of having cerebrovascular disease clinically were investigated by telephone and NHIC (National Health Insurance Corporation) data. Conclusion: 1. The study population was grouped as 'Negative Brain CT findings' (11.8%), 'Hemorrhage' (12.4%) and 'Infarction' (75.7%). 2. The survival probabilities calculated by the Life Table method were statistically significant among brain CT finding groups (P<0.01). 3. The mean survival time calculated by the Kaplan-Meier method were also statistically significant among brain CT finding groups (P<0.01). 4. The result of Cox regression model was that sex (OR=0.7), age (OR=1.07), diabetes mellitus (OR=1.38), and heart disease (OR=1.69) affected the survival of the patients with cerebrovascular disease.

• Journal of the military operations research society of Korea
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• 제22권2호
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• pp.200-214
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• 1996

In this paper, the problem of determining the probability of kill(or survival) of a vulnerable target by one or more missiles is considered. The general formulas are obtained for the kill or survival probability the target is killed or survival. Several well-known concepts such as those of vulnerability, lethality, multi-component target, and a general combinatorial theorem of probability are introduced and used. For the convenience in this paper, the word missile is used in a very general sense and the target is generally taken to be a point target. And, this paper, is concentrated primarily with the probabilistic aspects of the problem, also a general numerical procedures are also described. Two examples are shown to illustrate the use of some of the formulas in this study, but also illustrate a few points which may not have been sufficiently emphasized. The extension study to complete a software package will be followed.

• Journal of Applied Reliability
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• 제16권1호
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• pp.56-63
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• 2016

Purpose: The purpose of this study is to point out that the Kaplan-Meier method is not valid to calculate the survival probability or failure probability (risk) in the presence of competing risks and to introduce more valid method of cumulative incidence function. Methods: Survival analysis methods have been widely used in biostatistics division. However the same methods have not been utilized in reliability division. Especially competing risks cases, where several causes of failure occur and the occurrence of one event precludes the occurrence of the other events, are scattered in reliability field. But they are not noticed in the realm of reliability expertism or they are analysed in the wrong way. Specifically Kaplan-Meier method which assumes that the censoring times and failure times are independent is used to calculate the probability of failure in the presence of competing risks, thereby overestimating the real probability of failure. Hence, cumulative incidence function is introduced and sample competing risks data are analysed using cumulative incidence function and some graphs. Finally comparison of cumulative incidence functions and regression type analysis are mentioned briefly. Results: Cumulative incidence function is used to calculate the survival probability or failure probability (risk) in the presence of competing risks and some useful graphs depicting the failure trend over the lifetime are introduced. Conclusion: This paper shows that Kaplan-Meier method is not appropriate for the evaluation of survival or failure over the course of lifetime. In stead, cumulative incidence function is shown to be useful. Some graphs using the cumulative incidence functions are also shown to be informative.

• Asian Pacific Journal of Cancer Prevention
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• 제17권12호
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• pp.5287-5294
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• 2016

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer.

• Health Policy and Management
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• 제11권1호
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• pp.1-18
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• 2001

The purpose of the present study was to assess the agreement of survival probability estimated by International Classification of Diseases l0th Edition(ICD-10) based International Classification of Diseases based Injury Severity Score(ICISS) with professional panel's judgment on preventable death. ICISS has a promise as an alternative to Trauma and Injury Severity Score(TRISS) which have served as a standard measure of trauma severity, but requires more validation studies. Furthermore as original version of ICISS was based ICD-9CM, it is necessary to test its performance employing ICD-10 which has been used in Korea and is expected to replace ICD-9 in many countries sooner or later. Methods : For 1997 and 1998 131 trauma deaths and 1,785 blunt trauma inpatients from 6 emergency medical centers were randomly sampled and reviewed. Trauma deaths were reviewed by professional panels with hospital records and survival probability of trauma inpatients was assessed using ICD-10 based ICISS. For trauma mortality degree of agreement between ICISS survival probability with judgment of professional panel on preventable death was assessed and correlation between W-score and preventable death rate by each emergency medical center was assessed. Results : Overall agreement rate of ICISS survival probability with preventable death judged by professional panel was 66.4%(kappa statistic 0.36). Spearman's correlation coefficient between W-score and preventable death rate by each emergency medical center was -0.77(p=0.07) and Pearson's correlation coefficient between them was -0.90(p=0.01). Conclusions : The agreement rate of ICD-10 based ICISS survival probability with of professional panel's judgment on preventable death was similar to TRISS. The W-scores of emergency medical centers derived from ICD-10 based ICISS were highly correlated with preventable death rates of them with marginal statistical significance.

• The KSFM Journal of Fluid Machinery
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• 제16권2호
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• pp.42-47
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• 2013

Ship stability prediction is very complex in reality. In this paper, risk based approach is applied to predict the probability of a certified ship, which is effected by the forces of sea especially the wave loading. Safety assessment and risk analysis process are also applied for the probabilistic prediction of ship stability. The survival probability of ships encountering with different waves at sea is calculated by the existed statistics data and risk based models. Finally, ship capsizing probability is calculated according to single degree of freedom(SDF) rolling differential equation and basin erosion theory of nonlinear dynamics. Calculation results show that the survival probabilities of ship excited by the forces of the seas, especially in the beam seas status, can be predicted by the risk based method.

• Asian Pacific Journal of Cancer Prevention
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• 제15권14호
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• pp.5571-5575
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• 2014

Background: The ability to predict the survival time of breast cancer patients is important because of the potential high morbidity and mortality associated with the disease. To develop a predictive inference for determining the survival of breast cancer patients, we applied a novel Bayesian method. In this paper, we propose the development of a databased statistical probability model and application of the Bayesian method to predict future survival times for White Hispanic female breast cancer patients, diagnosed in the US during 1973-2009. Materials and Methods: A stratified random sample of White Hispanic female patient survival data was selected from the Surveillance Epidemiology and End Results (SEER) database to derive statistical probability models. Four were considered to identify the best-fit model. We used three standard model-building criteria, which included Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) to measure the goodness of fit. Furthermore, the Bayesian method was used to derive future survival inferences for survival times. Results: The highest number of White Hispanic female breast cancer patients in this sample was from New Mexico and the lowest from Hawaii. The mean (SD) age at diagnosis (years) was 58.2 (14.2). The mean (SD) of survival time (months) for White Hispanic females was 72.7 (32.2). We found that the exponentiated Weibull model best fit the survival times compared to other widely known statistical probability models. The predictive inference for future survival times is presented using the Bayesian method. Conclusions: The findings are significant for treatment planning and health-care cost allocation. They should also contribute to further research on breast cancer survival issues.

• International Journal of Fluid Machinery and Systems
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• 제5권4호
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• pp.143-151
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• 2012

Predicting the future condition of machine and assessing the remaining useful life are the center of prognostics. This paper contributes a new prognostic method based on grey model and survival probability. The first step of the method is building a normal condition model then determining the error indicator. In the second step, the survival probability value is obtained based on the error indicator. Finally, grey model coupled with one-step-ahead forecasting technique are employed in the last step. This work has developed a modified grey model in order to improve the accuracy of prediction. For evaluating the proposed method, real trending data of low methane compressor acquired from condition monitoring routine were employed.