• Journal of Applied Reliability
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• v.18 no.2
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• pp.130-142
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• 2018

Purpose: The purpose of this study is to introduce regression method in the presence of competing risks and to show how you can use the method with hypothetical data. Methods: Survival analysis has been widely used in biostatistics division. But the same method has not been utilized in reliability division. Especially competing risks, where more than a couple of 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 utilized in the area of reliability or they are analysed in the wrong way. Specifically Kaplan-Meier method 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. In addition, sample competing risks data are analysed using cumulative incidence function along with some graphs. Lastly we compare cumulative incidence functions with regression type analysis briefly. Results: We used cumulative incidence function to calculate the survival probability or failure probability in the presence of competing risks. We also drew some useful graphs depicting the failure trend over the lifetime. Conclusion: This research shows that Kaplan-Meier method is not appropriate for the evaluation of survival or failure over the course of lifetime in the presence of competing risks. Cumulative incidence function is shown to be useful in stead. Some graphs using the cumulative incidence functions are also shown to be informative.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.865-869
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• 2008

Juryeonggu is a Cuboctahedral die that had used in ancient Korea. This Cuboctahedral is consisted of different two penal servitudes of 14 facepieces, but the probability distribution can appear equally so it can be usable as a die. In this paper, achieved research study about probability of a Cuboctahedral die that have quadrilateral and triangle preferentially to search Juryeonggu's probability calculation method. First, confirmed probability distribution through Multibody-dynamics analysis and verified probability distribution through several experiments. Finally, with this simulation data, achieved theoretical analysis about Cuboctahedral die occurrence probability by using the residual momentum energy.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• The Journal of Engineering Geology
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• v.17 no.3
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• pp.411-418
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• 2007

It is a very difficult thing to estimate an occurrence possibility location and hazard expectation area by landslide. The prediction difficulty of landslide occurrence has relativity in factor of various geological physical factors and contributions. However, estimation of landslide occurrence possibility and classification of hazard area became available correlation mechanism through analysis of landslide occurrence through landslide data analysis and statistical analysis. This study analyzed a damage possibility of a cultual heritage area due to landslide occurrence by a heavy rainfall. We make a landslide prediction map and tried to analysis of landslide occurrence possibility for the cultural heritage site. The study area chooses a temple of Silsang-Sa Baekjang-Am site and made a landslide prediction map. In landslide prediction map, landslide hazard possibility area expressed by occurrence probability and divided by each of probability degrees. This degree used to evaluate occurrence possibility for existence and nonexistence of landslide in the study site. For the prediction and evaluation of landslide hazard for the cultural heritage site, investigation and analysis technique which is introduced in this study may contribute an efficient management and investigation in the cultural heritage site, Korea.

• Journal of Environmental Science International
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• v.6 no.2
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• pp.95-106
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• 1997

The characteristics on the transtion probabilities and periodicity for the daily precipitation occurrence in Korean peninsula are investigated by applying the Markov chain properties to daily precipitation occurrence. In order to examine the responses of Markov Chain properties to the applied period and their magnitudes, three cases (Case A: 1956~ 1985 at 14 stations, Case B: 1965~ 1994 at 14 stations, and Case C: 1985~ 1994 at 63 stations) are considered In this study. The transition probabilities from wet day to wet day for all cases are about 0.50 and in summer, especially July, are higher. In addition, considering them in each station we can find that they are the highest at Ullung-do and lowest at Inchon for all cases. The annual equilibrium probabilities of a wet day appear 0.31 In Case A, 0.30 Case B, and 0. 29 Case C, respectively. This may explain that as the data-period used becomes shorter, the higher the equilibrium probability is. The seasonal distributions of equilibrium probabilities are appeared the lowest(0.23~0.28) in winter and the highest(more than 0.39) in spring and monthly in .truly and in October, repectively. The annual mean wet duration for all cases is 2.04 days in Case A, 1.99 Case B, and 1.89 Case C, repectively. The weather cycle obtained from the annual mean wet and dry duration is 6.54~6.59 days, which are closely associated with the movement of synoptic systems. And the statistical tests show that the transitions of daily precipitation occurrence for all cases may have two-state first Markov chain property, being the stationarity in time and heterogeneity in space.

• Ocean Systems Engineering
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• v.8 no.1
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• pp.41-55
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• 2018

Accidental oil and gas leak is a critical concern for the offshore industry because it can lead to severe consequences and as a result, it is imperative to evaluate the probabilities of occurrence of the consequences of the leakage in order to assess the risk. Event Tree Analysis (ETA) is a technique to identify the consequences that can result from the occurrence of a hazardous event. The probability of occurrence of the consequences is evaluated by the ETA, based on the failure probabilities of the sequential events. Conventional ETA deals with events with crisp failure probabilities. In offshore applications, it is often difficult to arrive at a single probability measure due to lack of data or imprecision in data. In such a scenario, fuzzy set theory can be applied to handle imprecision and data uncertainty. This paper presents fuzzy ETA (FETA) methodology to compute the probability of the outcomes initiated due to oil/gas leak in an actual offshore-onshore installation. Post FETA, sensitivity analysis by Fuzzy Weighted Index (FWI) method is performed to find the event that has the maximum contribution to the severe sequences. It is found that events of 'ignition', spreading of fire to 'equipment' and 'other areas' are the highest contributors to the severe consequences, followed by failure of 'leak detection' and 'fire detection' and 'fire water not being effective'. It is also found that the frequency of severe consequences that are catastrophic in nature obtained by ETA is one order less than that obtained by FETA, thereby implying that in ETA, the uncertainty does not propagate through the event tree. The ranking of severe sequences based on their probability, however, are identical in both ETA and FETA.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• Journal of Korean Society for Atmospheric Environment
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• v.21 no.3
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• pp.303-313
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• 2005

In this study, meteorological characteristics concerning the occurrence of fog are analyzed using 4-years $(2000\~2003)$ data at Chuncheon and the probability of prediction is investigated. From the analysis of meteorological characteristics, the fog at Chuncheon occurred before sunrise time and disappeared after that time and lasted for $2\~4$ hours. When fog occurred, on the whole, wind direction was blew the northerly and wind speed was below 2.1m/s. Especially, about $42\%$ of foggy day fell on the calm $(0\~0.2\;ms^{-1})$ conditions. The difference between air temperature and dew point temperature near the surface were mainly less than $2^{\circ}C$. For the lack of water surface temperature, the water surface temperature was calculated by using Water Quality River Reservoir System (WQRRS) and then it was used as the surface boundary condition of MM5. The numerical experiment was carried out for 2 days from 1300 LST on 14 October 2003 to 1300 LST on 16 October 2003 and fog was simulated at dawn on 15 and 16 October 2003. Simulated air temperature and dew point temperature indicate the similar tendency to observation and the simulated difference between air temperature and dew point temperature has also the similar tendency within $2^{\circ}C$. Thus, the occurrence of fog is well simulated in the terms of the difference between air temperature and dew point temperature. Horizontal distribution of the difference between air temperature and dew point temperature from the numerical experiment indicates occurrence, dissipation and lasting time of fog at Chuncheon. In Chuncheon, there is close correlation between the frequency of fog day and outflow from Soyang reservoir and high frequency of occurrence due to the difference between air and cold outlet water temperature.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.123.2-123.2
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• 2012

We investigate the solar flare occurrence rate and daily flare probability in terms of the sunspot classification supplemented with sunspot area and its changes. For this we use the NOAA active region data and GOES solar flare data for 15 years (from January 1996 to December 2010). We consider the most flare-productive eleven sunspot classes in the McIntosh sunspot group classification. Sunspot area and its changes can be a proxy of magnetic flux and its emergence/cancellation, respectively. We classify each sunspot group into two sub-groups by its area: "Large" and "Small". In addition, for each group, we classify it into three sub-groups according to sunspot area changes: "Decrease", "Steady", and "Increase". As a result, in the case of compact groups, their flare occurrence rates and daily flare probabilities noticeably increase with sunspot group area. We also find that the flare occurrence rates and daily flare probabilities for the "Increase" sub-groups are noticeably higher than those for the other sub-groups. In case of the (M+X)-class flares in the 'Dkc' group, the flare occurrence rate of the "Increase" sub-group is three times higher than that of the "Steady" sub-group. Our results statistically demonstrate that magnetic flux and its emergence enhance the occurrence of major solar flares.