• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.70-75
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• 2007

This paper discusses condition based preventive replacement for deteriorating systems. The system continuouslydeteriorates in time and fails at any deterioration level which is always monitored, It is replaced at failure or atsome deteriorated level preventively before failure. The deterioration process is represented by a Weibulldistribution with a time-linear scale parameter. The cost rate function is formed considering replacement costand opportunity loss cost and deterioration dependent failure distribution, If the system has an increasingdeterioration dependent failure rate, the optimal deterioration level for preventive replacement can be determinedfrom minimizing the cost rate. An illustrative example is given for a Weibull deterioration dependent failuredistribution.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.141-150
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• 1993

For the three parameter Weibull distribution, the parameter estimation techniques are applied and the asymptotic variances of the quantile to obtain the confidence limits for a given return period are derived. Three estimation techniques are used for these purposes: the methods of moments, maximum likelihood and probability weighted moments. The three parameter Weibull distribution as a flood frequency model is applied to actual flood data.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.3
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• pp.193-200
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• 2022

In this study, the finite-failure NHPP software reliability model was applied to the software development model based on the Weibull lifetime distribution (Goel-Okumoto, Rayleigh, Type-2 Gumbe), which is widely used in the software reliability field, and then the cost attributes were compared and evaluated. For this study, failure time data detected during normal operation of the software system were collected and used, the most-likelihood estimation (MLE) method was applied to the parameter estimation of the proposed model, and the calculation of the nonlinear equation was solved using the binary method. As a result, first, in the software development model, when the cost of testing per unit time and the cost of removing a single defect increased, the cost increased but the release time did not change, and when the cost of repairing failures detected during normal system operation increased, the cost increased and the release time was also delayed. Second, as a result of comprehensive comparative analysis of the proposed models, it was found that the Type-2 Gumble model was the most efficient model because the development cost was lower and the release time point was relatively faster than the Rayleigh model and the Goel-Okumoto basic model. Third, through this study, the development cost properties of the Weibull distribution model were newly evaluated, and the analyzed data is expected to be utilized as design data that enables software developers to explore the attributes of development cost and release time.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.6
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• pp.67-74
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• 1995

This paper proposes the step-stress type-I censoring model for analyzing the data of accelerated life test and reducing the time of accelerated life test. In order to obtain the data of accelerated life test, the step-stress accelerated life test was run with voltage stress to CMOS Hex Buffer. The Weibull distribution, the Inverse-power-law model and Maximum likelihood method were used. The iterative procedure using modified-quasi-linearization method is applied to solve the nonlinear equation. The proposed Weibull step-stress type-I censoring model exactly estimases the life time of units, while reducting the time of accelerated life test and the equipments of test.

• Journal of the Korea Safety Management & Science
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• v.1 no.1
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• pp.135-143
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• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected bum-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.

• Journal of the Korean Wood Science and Technology
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• v.31 no.3
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• pp.61-69
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• 2003

This study investigated the effect of moisture content and loading direction on dowel bearing strength of two types of SCL. Dowel bearing tests of LVL and PSL were conducted with two different MC level, 7.5% and 19%, and two different oriention, L-direction(loading parallel to grain) and X-direction(loading perpendicular to grain). Most of specimens showed typical load-deformation curves and intersected 5% offset line. Failure modes were classified into two categories; spliting(for L-direction specimens) and peeling(for X-direction specimens). Dowel bearing strength generally decreased with increasing MC. The decreasing rate was more significant in X-directon. ESG also decreased with increasing MC, and the ratio of ESG of 7.5% versus 19% was about 1.47. Dowel bearing strength of LVL and PSL in L-direction was higher than that of X-direction. This results indicated that MC and loading orientation had a significant effect on dowel bearing strength of SCL. The average dowel bearing strength of LVL were higher than that of PSL in each loading direction. Two types of probability distribution model were chosen to quantify strength distribution, normal and 2-parameter weibull distribution. The two models showed good agreement with the data, especially in lower tail of the cumulative distribution. Normal and 2-parameter weibull distribution seemed to proper model of the dowel bearing strength for each MC levels.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.263-272
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• 1996

In this parer, under random censorship model, an estimation of scale and shape parameters in Weibull lifetime model is considered. Based on nonparametric estimator of survival function, the least square method is proposed. The proposed estimation method is simple and the performance of the proposed estimator is as efficient as maximum likelihood estimators. An example is presented, using field winding data. Simulation studies are performed to compare the performaces of the proposed estimator and maximum likelihood estimator.

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.3-11
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• 1981

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased (MVU) estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distirubtions are Weibull with unknown scale parameters and same known shape parameter. The asymptotic distribution of MVU estimate of system reliability in the model is obtained by using the standard asymptotic properties of the maximum likelihood estimate of system reliability and establishing their equivalence. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability. Empirical comparison of the two estimates for small samples is studies by Monte Carlo simulation.

• Journal of Korean Society for Quality Management
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• v.34 no.3
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• pp.19-30
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• 2006

For highly reliable products, it is difficult to assess the lifetime of the products with traditional life tests. Accordingly, a recent approach is to observe the performance degradation of product during the test rather than regular failure time. This study compares performances of three methods(i.e. the approximation, analytical and numerical methods) to estimate the parameters and quantiles of the lifetime when the time-to-failure distribution follows Weibull and lognormal distributions under a random coefficient degradation rate model. Numerical experiments are also conducted to investigate the effects of model error such as measurements in a random coefficient model.

• 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.