• Journal of Korean Society for Quality Management
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• v.27 no.4
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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.

• Journal of Korean Society for Atmospheric Environment
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• v.28 no.6
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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.

• Earthquakes and Structures
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• v.22 no.1
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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.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.4
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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'.

• Journal of Korea Water Resources Association
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• v.54 no.11
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• pp.915-924
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• 2021

In this study, the probability of exceeding capacity for 4 check dams in Muju mountain region have been estimated. From the results, optimum design of check dam and safety according to wild fire have been discussed. Reliability model has been established by using MSDPM for calculating debris yield to estimate the probability of exceeding capacity of check dam. Probability of exceeding capacity for 4 check dams has been estimated according to maximum rainfall intensity of return periods (10year, 50year, 100year, and 200year). It was found that 1 check dam of Samga-ri basin and 1 check dam of Jeungsan-ri basin were designed by overestimation and 61% and 47% of capacity should be reduced, respectively. Furthermore, probability of exceeding capacity according to burned area has been estimated and compared. It was found that check dam of Sanga-ri basin is the weakest for the wild fire effect in this study area.

• Journal of Korean Society of Water and Wastewater
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• v.34 no.4
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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.

• Journal of the Korean Geotechnical Society
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• v.22 no.10
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• pp.69-76
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• 2006

A reliability-groundwater flow analysis is performed and the influence of flow parameters on the probability of exceeding the threshold value is examined. For this study, the 3-D numerical groundwater flow program, DGU-FLOW, is developed by extending the 2-D flow program and is coupled to the first and second order reliability program. The 3-D flow program is verified by solving the examples of groundwater flow through the underground excavation and comparing the results from commercial MODFLOW program. Reliability routine of the program is also verified by comparing the probability of failure with that of Monte-Carlo Simulation. The reliability analysis of the groundwater flow showed that the probability of failure from the first and second order reliability method are quite close to that of Monte-Carlo Simulation. from the parametric study of hydraulic conductivity of soil layers, the increase of both mean and variance of hydraulic conductivity results in the increase of probability of exceeding the threshold flow quantity. The probability of failure was more sensitive to constant head located at the end of the flow domain than the other parameters.

• Fire Science and Engineering
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• v.30 no.5
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• pp.116-123
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• 2016

The quantitative risk assessment methods for thermal failure in targets were studied using fire modeling. To this end, Fire Dynamics Simulator (FDS), as a representative fire model, was used and the probabilities related to thermal damage to an electrical cable were evaluated according to the change in fire area inside a specific compartment. 'The maximum probability of exceeding the damage thresholds' adopted in a conservative point of view and 'the probability of failure' including the time to damage were compared. The probability of failure suggested in the present study could evaluate the quantitative fire risk more realistically, compared to the maximum probability of exceeding the damage thresholds with the assumption that thermal damage occurred the instant the target reached its minimum failure criteria in terms of the surface temperature and heat flux.

• Earthquakes and Structures
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• v.19 no.5
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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.

• Wind and Structures
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• v.14 no.2
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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.