• Journal of Korean Society for Quality Management
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• v.47 no.1
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• pp.87-96
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• 2019

Purpose: The purpose of this paper is to determine an optimal production time for economic production quantity model with preventive maintenance and random defective rate as the function of a machinery deteriorates. Methods: If a machinery shifts from "in-control" state to "out-of-control" state, a proportion of defective items being produced increases. It is assumed that time to state shift is a random variable and follows an arbitrary distribution. The elapsed time until process shift decreases stochastically as a production cycle repeats and quasi-renewal process is used to implement for production facilities to deteriorate. Results: When the exponential parameter for exponential distribution increases, the optimal production time increases. When Weibull distribution is considered, the optimal production time is closely affected by the shape parameter of Weibull distribution. Conclusion: A mathematical model is suggested to find optimal production time and optimal number of production cycles and numerical examples are implemented to validate the patterns for changes of optimal times under different parameters assumptions. The real application is implemented using the proposed approach.

• The Journal of Information Technology
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• v.10 no.2
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• pp.47-64
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• 2007

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. Accurate predictions of software release times, and estimation of the reliability and availability of a software product require quantification of a critical element of the software testing process : test coverage. This model called enhanced non-homogeneous poission process(ENHPP). In this paper, exponential coverage and S-coverage model was reviewed, proposes the exponentiated exponential coverage reliability model, which maked out efficiency substituted for gamma and Weibull model(2 parameter shape illustrated by Gupta and Kundu(2001). In this analysis of software failure data, algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE statistics for the sake of efficient model, was employed.

• Journal of Food Hygiene and Safety
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• v.19 no.1
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• pp.19-24
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• 2004

Dose-response models in microbial risk assessment can be divided into biologically plausible models and empirical models. Biologically plausible models are formed by the assumptions in dose distribution of microbes, host sensitivity to microbes, and minimal infectious dose of microbes : there are Exponential model and $\beta$-Poisson model, representatively. Empirical models are mainly used to express the toxicity of chemicals : there are Weibull-Gamma model etc. Deviance function (Y) is used to fit available data to dose-response models, and some dose-response models for food-borne pathogens are developed in humans and experimental animals.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.441-451
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• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.11
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• pp.476-484
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• 2006

The failure prediction and preventive maintenance for the equipment of nuclear power plant area using reliability-centered maintenance have been grown. On the other hand, the maintenance for power distribution system consists of time-based maintenance mainly. In this paper, the new maintenance algorithms for power distribution system are developed considering reliability indices. First of all, Time-varying failure rates are extracted from data accumulated at KEPCO using exponential distribution function and weibull distribution function. Next, based on the extracted failure rate, reliability for real power distribution system is evaluated for applying the effective maintenance algorithm which is the analytic method deciding the maintenance point of time and searching the feeder affecting the specific customer. Also the algorithm deciding the maintenance priority order are presented based on sensitivity analysis and equipment investment plan are analyzed through the presented algorithm at real power distribution system.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.59 no.2
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• pp.154-157
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• 2010

In this paper, the Time-varying Failure Rates(TFR) of power distribution system components are extracted from the recorded failure data of KEPCO(Korea Electric Power Corporation) and the reliability of power distribution system is evaluated using Mean Failure Rate(MFR) and TFR. The TFR is approximated to bathtub curve using the exponential and Weibull distribution function. In addition, Kaplan-Meier estimation is applied to TFR extraction because of incomplete failure data of KEPCO. Also the reliability of the real power distribution system of Korea is evaluated using the MFR and TFR extracted from real failure data, respectively and the results of each case are compared with each other. As a result, it is proved that the reliability evaluation using the TFR is more realistic than MFR. In addition, it is presented that the application method at power distribution system maintenance and repair using the result of TFR.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1677-1683
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• 2006

Color image segmentation is useful for fast retrieval in large image database. For that purpose, new image segmentation technique based on the probability of pixel distribution in the image is proposed. Color image is first divided into R, G, and B channel images. Then, pixel distribution from each of channel image is extracted to select to which it is similar among the well known probabilistic distribution function-Weibull, Exponential, Beta, Gamma, Normal, and Uniform. We use sum of least square error to measure of the quality how well an image is fitted to distribution. That P.d.f has minimum score in relation to sum of square error is chosen. Next, each image is quantized into 4 gray levels by applying thresholds to the c.d.f of the selected distribution of each channel. Finally, three quantized images are combined into one color image to obtain final segmentation result. To show the validity of the proposed method, experiments on some images are performed.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.445-461
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• 2019

It is possible that data are not always fitted with sufficient precision by the existing distributions; therefore this article presents a methodology that enables the use of families of asymmetric distributions as alternative probabilistic models for survival analysis, with censorship on the right, different from those usually studied (the Exponential, Gamma, Weibull, and Lognormal distributions). We use a more flexible parametric model in terms of density behavior, assuming that data can be fit by a distribution of stable distribution families considered unconventional in the analyses of survival data that are appropriate when extreme values occur, with small probabilities that should not be ignored. In the methodology, the determination of the analytical expression of the risk function h(t) of the $L{\acute{e}}vy$ distribution is included, as it is not usually reported in the literature. A simulation was conducted to evaluate the performance of the candidate distribution when modeling survival times, including the estimation of parameters via the maximum likelihood method, survival function ${\hat{S}}$(t) and Kaplan-Meier estimator. The obtained estimates did not exhibit significant changes for different sample sizes and censorship fractions in the sample. To illustrate the usefulness of the proposed methodology, an application with real data, regarding the survival times of patients with colon cancer, was considered.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2007.05a
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• pp.366-368
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• 2007

In this paper, the Time-varying Failure Rate (TFR) of power distribution system equipment is extracted from the recorded failure data of Korea Electric Power Corporation (KEPCO). For TFR extraction, it is used that the fault data accumulated by KEPCO during 10 years. The TFR is approximated to bathtub curve using the exponential (random failure) and Weibull (aging failure) distribution function. In addition, Kaplan-Meier estimation is applied to TFR extraction because of incomplete failure data of KEPCO. Finally, Probability plot and regression analysis is applied. It is presented that the extracted TFR is more effective and useful than Mean Failure Rate (MFR) through the comparison between TFR and MFR.