• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• International Journal of Highway Engineering
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• v.14 no.3
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• pp.77-85
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• 2012

Most of Automatic Accident Detection Algorithm has a problem of detecting an accident as traffic congestion. Actually, center's managers deal with accidents depend on watching CCTV or accident report by drivers even though they run the Automatic Accident Detection system. It is because of the system's detecting errors such as detecting non-accidents as accidents, and it makes decreasing in the system's overall reliability. It means that Automatic Accident Detection Algorithm should not only have high detection probability but also have low false alarm probability, and it has to detect accurate accident spot. The study tries to verify and evaluate the effectiveness of using Gaussian Mixture Model and individual vehicle tracking to adapt Accident Detection Algorithm to Center Management System by measuring accident detection probability and false alarm probability's frequency in the real accident.

• Asia-Pacific Journal of Atmospheric Sciences
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• v.54 no.4
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• pp.623-637
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• 2018

This study investigates the effects of horizontal resolution, cumulus parameterization scheme (CPS), and probability forecasting on precipitation forecasts over the Korean Peninsula from 00 UTC 15 August to 12 UTC 14 September 2013, using the limited-area ensemble prediction system (LEPS) of the Korea Meteorological Administration. To investigate the effect of resolution, the control members of the LEPS with 1.5- and 3-km resolution were compared. Two 3-km experiments with and without the CPS were conducted for the control member, because a 3-km resolution lies within the gray zone. For probability forecasting, 12 ensemble members with 3-km resolution were run using the LEPS. The forecast performance was evaluated for both the whole study period and precipitation cases categorized by synoptic forcing. The performance of precipitation forecasts using the 1.5-km resolution was better than that using the 3-km resolution for both the total period and individual cases. The result of the 3-km resolution experiment with the CPS did not differ significantly from that without it. The 3-km ensemble mean and probability matching (PM) performed better than the 3-km control member, regardless of the use of the CPS. The PM complemented the defect of the ensemble mean, which better predicts precipitation regions but underestimates precipitation amount by averaging ensembles, compared to the control member. Further, both the 3-km ensemble mean and PM outperformed the 1.5-km control member, which implies that the lower performance of the 3-km control member compared to the 1.5-km control member was complemented by probability forecasting.

• Proceedings of the KSRS Conference
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• 1999.11a
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• pp.117-121
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• 1999

Relations between GMS-5 infrared brightness temperature with SSM/I retrieved rain rate are determined by a probability matching method similar to Atlas et al. and Crosson et al. For this study, coincident data sets of the GMS-5 infrared measurements and SSM/I data during two summer seasons of 1997 and 1998 are constructed. The cumulative density functions (CDFs) of infrared brightness temperature and rain rate are matched at pairs of two variables which give the same percentile contribution. The method was applied for estimating rain rate on 31 July 1998, examining heavy rainfall estimation of a flash flood event over Mt. Jiri. Results were compared with surface gauge observations run by Korean Meteorological Administration. It was noted that the method produced reasonably good quality of rain estimate, however, there was large area giving false rain due to the anvil type clouds surrounding deep convective clouds. Extensive validation against surface rain observation is currently under investigation.

• Proceedings of the Korean Reliability Society Conference
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• 2000.04a
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• pp.63-70
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• 2000

Brown and Proschan(1983) introduced a model for imperfect repair. At each feilure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1 - p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about ${\mu}$$\_$k/, the expected time between the k-th and the (k + 1)-st repair under the assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimizes the long-run average cost for a fixed p under the condition that distribution F of the device is DMRL.

• Journal of Integrative Natural Science
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• v.13 no.4
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• pp.152-157
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• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

• Journal of Korean Society for Quality Management
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• v.26 no.3
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• pp.31-45
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• 1998

This paper proposes a method of designing one-sided cumulative scored control charts to control the process mean with a normally distributed quality characteristic. The average run length(ARL) is obtained from the average sample number of sequential probability ratio test(SPRT) on trinomial distribution. Using the analogy between cumulative scored control chart and SPRT for trinomial observations, a procedure is presented to determine three control chart parameters; lower and u, pp.r scoring boundaries and action limit. The parameters are determined by minimizing the ARL when the process is out of control with prespecified ARL when the process is in control.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.8
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• pp.1128-1136
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• 1989

The power spectral densities of run-length-limited(RLL) minimum-bandwidth(MB) line codes are obtained for some values of the zero probability of input data. They can be obtianed by implementing a computer program for the G.L. Cariolaro's algorithm. Using the program we calculate the power spectra of the known RLL MB line codes, such as VDB5, TIB5, VMDB5, RMD35, DRMD35, RMD45, and RMD33, and compare the characteristics of them. Specially, the relationship between eye widths and power spectra is analyzed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.11 no.17
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• pp.9-14
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• 1988

A (s, S) inventory policy is studied for a continuous inventory model in which lead times are dependent on the ordering quantity. The model assumes that at most one order is outstanding and demands occur in a compound poison process. The steady-state probability distributions of the inventory levels are derived so as to determine the long-run expected average cost. And the computational procedure is presented.