• 품질경영학회지
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• 제27권4호
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• pp.143-152
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• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.

• 한국대기환경학회지
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• 제28권6호
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• pp.697-705
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• 2012

Particulate matter (PM) data collected from the Urban Air Monitoring Network in Busan during the period from 2006 through 2010 were statistically examined and analyzed to estimate the probability of exceeding $PM_{2.5}$ 24 hour and annual standard to be implemented from January $1^{st}$, 2015. For Jangrimdong, Yeonsandong, Kijangeup, and Jwadong where simultaneous measurement of $PM_{10}$ and $PM_{2.5}$ was conducted, the probability of exceeding $PM_{2.5}$ standards was estimated using $PM_{2.5}$ data measured on site. For other areas where there were no measured $PM_{2.5}$ data available, the probability of exceeding $PM_{2.5}$ standards was statistically estimated using $PM_{10}$ measured on site and $PM_{2.5}/PM_{10}$ ratios obtained from the four stations where both $PM_{2.5}$ and $PM_{10}$ were monitored simultaneously. At Jangrimdong, Yeonsandong, Kijangeup, and Jwadong, mean value of annual 99 percentile of 24 hr average $PM_{2.5}$ for 5 years from 2006 through 2010 was 99.3, 74.5. 57.0, and $62.5{\mu}g/m^3$, respectively, and the probability of exceeding $PM_{2.5}$ 24 hr standard was estimated at 100%. For areas where there were no measured $PM_{2.5}$ data available, the estimated probability of exceeding $PM_{2.5}$ 24 hr standard was more than 0.82. Mean value of annual average $PM_{2.5}$ from 2008 through 2010 was 31.7 and $27.6{\mu}g/m^3$ for Jangrimdong and Yeonsandong, respectively, which exceeded $PM_{2.5}$ annual standard of $25{\mu}g/m^3$. Mean value of annual average $PM_{2.5}$ during the same period for Kijangeup and Jwadong was 19.2 and $20.7{\mu}g/m^3$, respectively, which satisfied $PM_{2.5}$ annual standard. For other areas where there were no measured $PM_{2.5}$ data available, the probability of exceeding $PM_{2.5}$ annual standard was more than 0.95 except Taejongdae and Kwangahndong. With $PM_{10}$ and $PM_{2.5}$ data measured at 17 Urban Air Monitoring Stations in Busan, the probability of exceeding $PM_{2.5}$ standards was estimated to be very high for almost all areas. This result indicates that proper measures to mitigate $PM_{2.5}$ in Busan should be investigated and established as soon as possible.

• 상하수도학회지
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• 제30권4호
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• pp.369-379
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• 2016

It was confirmed that the extreme value distribution model applies to probability of exceeding more than once a day monthly the facility capacities using data of daily maximum inflow rate for 7 wastewater treatment plant. The result of applying the extreme value model, A, D, E wastewater treatment plant has a problem compared to B, C, F, G wastewater treatment plant. but all the wastewater treatment plant has a problem except C, F wastewater treatment plant based 80% of facility capacity. In conclusion, if you make a standard in statistical aspects probability exceeding more than once a day monthly can be 'exceed day is less than a few times annually' or 'probability of exceeding more than once a day monthly is less than what percent'.

• Earthquakes and Structures
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• 제22권1호
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• pp.15-23
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• 2022

One of the key tools in assessing the seismic vulnerability of the structures is the use of fragile functions, which is the possibility of damage from a particular damage surface for several levels of risk from the seismic movements of the earth. The aim of this study is to investigate the effect of two categories of earthquake events on the fragile curve (FRC) of the steel construction system. In this study, the relative lateral displacement of the structures is considered as a damage criterion. The limits set for modifying the relative lateral position in the HAZUS instruction are used to determine the failure modes, which include: slight, moderate, extensive and complete. The results show, as time strong-motion increases, the probability of exceeding (PoE) increases (for Peak ground acceleration (PGA) less than 0.5). The increase in seismic demand increases the probability of exceeding. In other words, it increases the probability of exceeding, if the maximum earthquake acceleration increases. Also, 7-storey model in extensive mode has 20 and 26.5% PoE larger than 5- and 3-storey models, respectively.

• 한국수자원학회논문집
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• 제54권11호
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• pp.915-924
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• 2021

본 연구에서는 전라북도 무주군 산지 유역의 사방댐 4개소를 대상으로 용량초과확률을 산정하였으며, 이를 통해 국내 사방댐 설계의 적정성과 산불피해에 따른 안전성을 분석하였다. 용량초과확률을 산정하기 위한 신뢰성 모형을 구축하였고 토사유출량 산정에는 MSDPM을 사용하였다. 재현기간(10년, 50년, 100년, 200년)별 강우강도를 사용하여 사방댐의 용량초과확률을 산정하여 비교 분석하였다. 그 결과 무주군 삼가리 유역의 사방댐 1개소와 증산리 유역의 사방댐 1개소는 과대설계 되었다고 판단되며 각각 사방댐의 용량을 61%, 47% 축소해도 안전할 것으로 판단된다. 또한 산불피해면적에 대한 사방댐의 용량초과 확률을 산정해 비교분석 하였으며 연구대상 유역에서 산불로 인한 영향이 가장 큰 곳은 삼가리 유역의 사방댐인 것으로 확인되었다.

• 상하수도학회지
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• 제34권4호
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• pp.251-258
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• 2020

Sewer deterioration models are needed to forecast the remaining life expectancy of sewer networks by assessing their conditions. In this study, the serious defect (or condition state 3) occurrence probability, at which sewer rehabilitation program should be implemented, was evaluated using four probability distribution functions such as normal, lognormal, exponential, and Weibull distribution. A sample of 252 km of CCTV-inspected sewer pipe data in city Z was collected in the first place. Then the effective data (284 sewer sections of 8.15 km) with reliable information were extracted and classified into 3 groups considering the sub-catchment area, sewer material, and sewer pipe size. Anderson-Darling test was conducted to select the most fitted probability distribution of sewer defect occurrence as Weibull distribution. The shape parameters (β) and scale parameters (η) of Weibull distribution were estimated from the data set of 3 classified groups, including standard errors, 95% confidence intervals, and log-likelihood values. The plot of probability density function and cumulative distribution function were obtained using the estimated parameter values, which could be used to indicate the quantitative level of risk on occurrence of CS3. It was estimated that sewer data group 1, group 2, and group 3 has CS3 occurrence probability exceeding 50% at 13th-year, 11th-year, and 16th-year after the installation, respectively. For every data groups, the time exceeding the CS3 occurrence probability of 90% was also predicted to be 27th- to 30th-year after the installation.

• 한국지반공학회논문집
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• 제22권10호
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• pp.69-76
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• 2006

지하수흐름에 대한 신뢰성 해석을 실시하였으며, 흐름에 관여하는 매개변수들이 목표 값의 파괴확률을 초과하는데 미치는 영향을 알아보았다. 본 연구를 위하여 2차원 지하수흐름 프로그램을 3-D 프로그램 DGU-FLOW로 확장하여 제작하고, 이를 1계 및 2계 신뢰성 프로그램에 연계하였다. 3차원 흐름 프로그램의 검증은 지하굴착지반의 지하수 흐름 해석 문제를 풀고 이를 MODFLOW 프로그램과 비교하여 수행하였다. 신뢰성부분 또한 몬테칼로 해석을 수행하여 나타난 파괴확률을 비교함으로써 검증하였으며 지하수 흐름에 대한 1계 및 2계 신뢰성해석을 수행하여 산정된 파괴확률 값은 몬테칼로 해석을 통하여 나온 값과 매우 근접하였다. 토질층의 투수계수에 대한 매개변수 해석결과 투수계수의 평균과 분산의 증가는 목표 수량을 초과하는 파괴확률의 증가를 가져오는 것으로 나타났다. 또한 파괴확률의 민감도는 여러흐름 변수중에서 흐름영역 경계부의 일정 수두에 가장 민감한 것으로 나타났다.

• 한국화재소방학회논문지
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• 제30권5호
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• pp.116-123
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• 2016

화재모델링을 이용한 목표 대상물의 열적 손상에 대한 정량적 위험성 평가방법이 검토되었다. 이를 위해 대표적인 화재모델로서 FDS가 사용되었으며, 특정 구획 내에서 화원 면적 변화에 따른 전기 케이블의 열적 손상과 관련된 확률이 평가되었다. 보수적 관점에서 적용되고 있는 '최대 손상임계 초과확률'과 손상시간의 정보가 포함된 '손상확률'이 체계적으로 비교되었다. 목표 대상물이 표면온도 및 열유속에 대한 최소 손상기준에 도달하는 순간에 열적 손상이 발생된다는 가정이 적용된 최대 손상임계 초과확률에 비해 본 연구에서 제안된 손상확률은 정량적 화재 위험성을 보다 현실적으로 평가할 수 있음을 확인하였다.

• Wind and Structures
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• 제14권2호
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• pp.113-131
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• 2011

Excessive wind-induced motion in tall buildings can cause discomfort, affect health, and disrupt the daily activities of the occupants of a building. Dynamic vibration absorbers such as the tuned mass dampers (TMDs) can be used to reduce the wind-induced motion below a specified tolerable serviceability limit state (SLS) criterion. This study investigates whether the same probability of not exceeding specified wind-induced motion levels can be achieved by torsionally sensitive structures without/with linear/nonlinear TMDs subjected to partially correlated wind forces, if they are designed to just meet the same SLS criterion. For the analyses, different structures and the uncertainty in the response, wind load and perception of motion is considered. Numerical results indicate that for structures that are designed or retrofitted without or with optimum linear TMDs and satisfying the same SLS criterion, their probability of exceeding the considered criterion is very consistent, if the inherent correlation between the wind forces is considered in design. However, this consistency deteriorates if nonlinear TMDs are employed. Furthermore, if the correlation is ignored in the design, in many cases a slightly unconservative design, as compared to the designed by considering correlation, is achieved.

• Earthquakes and Structures
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• 제19권5호
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• pp.379-393
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• 2020

The purpose of this study is to first evaluate the seismic behavior of ageing arch bridges by using the Intensity Measure - based demand and DCFD format, which is referred to as the fragility-hazard format. Then, an investigation is performed for their seismic vulnerability. Analytical models are created for bridges concerning different features and these models are subjected to Incremental Dynamic Analysis (IDA) analysis using a set of 22 earthquake records. The hazard curve and results of IDA analysis are employed to evaluate the return period of exceeding the limit states in the IM-based probabilistic performance-based context. Subsequently, the fragility-hazard format is used to assess factored demand, factored capacity, and the ratio of the factored demand to the factored capacity of the models with respect to different performance objectives. Finally, the vulnerability curves are obtained for the investigated bridges in terms of the loss ratio. The results revealed that decreasing the span length of the unreinforced arch bridges leads to the increase in the return period of exceeding various limit states and factored capacity and decrease in the displacement demand, the probability of failure, the factored demand, as well as the factored demand to factored capacity ratios, loss ratio, and seismic vulnerability. Finally, it is derived that the probability of the need for rehabilitation increases by an increase in the span length of the models.