• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.6
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• pp.67-72
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• 2020

Life tests are essential in reducing the catastrophic damage caused by the accidents of large machinery such as aircraft and ships. However, life tests are challenging to implement due to the high costs and time required to test the life of large machinery parts. Therefore, it is advantageous and convenient to apply accelerated life test techniques for key components to reduce costs and time. In fact, extensive research has already been conducted on these techniques. However, recently, there have been cases in which an experimental value was applied to the shape parameter of the Weibull distribution used in the reliability test, but the test time was not significantly reduced. Therefore, in this paper, the shape parameters are estimated from the probability density function of the Weibull distribution for the analysis of an accelerated life test for bladder accumulators, which are core components of military helicopters. The test time was derived based on the number of samples and confidence level by substituting it into the test time equation. Next, the accelerated life test time was calculated using the steady-state test time with an acceleration factor obtained from the Arrhenius model. The steady-state life test required approximately 15,000 H, whereas the accelerated life test time for one sample at 100 ℃ was 34% shorter than that of the steady-state life test.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.425-445
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• 2021

A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley's approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an efficient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.

• 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.

• Journal of the Korea Institute of Military Science and Technology
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• v.17 no.2
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• pp.204-212
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• 2014

The purpose of this paper is to investigate the effects of calibration rounds on the statistical distribution of the muzzle velocity in acceptance test of propelling charge. It is shown that the normal distribution fits best among statistical distributions from goodness-of fit test. The 3p-Weibull distribution is also acceptable because the shape of the probability density function curve is similar to that of normal distribution and it also has near zero skewness value. Muzzle velocities of test rounds uncompensated by calibration rounds showed high variation and had comparatively higher skewness. Because the skewness of normal distribution is defined to be zero, calibration rounds make the normality of data higher.

• 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.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.265-279
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• 1999

In this study, one of the techniques on the extension of low flow series has been developed, in which the daily streamflows were simulated by the Tank model with the input of extended daily rainfall series which were stochastically generated by the Markov chain model. The annual lowest flow serried for each of the given durations were formulated form the simulated daily streamflow sequences. The frequency of the estimated annual lowest flow series was analyzed. The distribution types to be used for the frequency analysis were two-parameter and three-parameter log-normal distribution, two-parameter and three-parameter Gamma distribution, three-parameter log-Gamma distribution, Gumbel distribution, and Weibull distribution, of which parameters were estimated by the moment method and the maximum likelihood method. The goodness-of-fit test for probability distribution is evaluated by the Kolmogorov-Sminrov test. The fitted distribution function for each duration series is applied to frequency analysis for developing duration-low flow-frequency curves at Yongdam Dam station. It was shown that the purposed technique in this study is available to generate the daily streamflow series with fair accuracy and useful to determine the probabilistic low flow in the watersheds having the poor historic records of low flow series.

• Journal of Energy Engineering
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• v.23 no.3
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• pp.36-41
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• 2014

The world's overall need for natural gas (NG) has been growing up fast, especially in the residential sector. The better the estimation of residential NG consumption (RNGC) distribution, the better decision-making for a residential NG policy such as pricing, demand estimation, management options and so on. Approximating the distribution of RNGC is complicated by zero observations in the sample. To deal with the zero observations by allowing a point mass at zero, a mixture model of RNGC distributions is proposed and applied. The RNGC distribution is specified as a mixture of two distributions, one with a point mass at zero and the other with full support on the positive half of the real line. The model is empirically verified for household RNGC survey data collected in Korea. The mixture model can easily capture the common bimodality feature of the RNGC distribution. In addition, when covariates were added to the model, it was found that the probability that a household has non-expenditure significantly varies with some variables. Finally, the goodness-of-fit test suggests that the data are well represented by the mixture model.

• KIEE International Transactions on Electrophysics and Applications
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• v.3C no.1
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• pp.1-4
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• 2003

This paper presents an attempt to develop probabilistic multistress life models to evaluate the lifetime characteristics of epoxy-encapsulated magnet wire with heavy build polyurethane enamel. A set of accelerated life tests were conducted over a wide range of pulsating voltages, temperatures, and frequencies. Samples of fine gauge twisted pairs of the encapsulated magnet wire were tested us-ing a pulse endurance dielectric test system. An electrical-thermal lifetime function was combined with the Weibull distribution of lifetimes. The parameters of the combined Weibull-electrical-thermal model were estimated using maximum likelihood estimation. Likewise, a generalized electrical-thermal-frequency life model was also developed. The parameters of this new model were estimated using multiple linear regression technique. It was found in this paper that lifetime estimates of the two proposed probabilistic multistress life models are good enough. This suggests the suitability of using the general electrical-thermal-frequency model to estimate the lifetime of the encapsulated magnet wire over a wide range of voltages, temperatures and pulsating frequencies.

• Journal of the Korean Data and Information Science Society
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• v.2
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• pp.23-39
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• 1991

The maximum likelihood estimators and Bayes estimators of the parameters and reliability function for the two-parameter Weibull distribution under the type-II progressively censoring schemes are derived when a shape parameter is known and unknown, respectively. Efficiencies for above estimators are also compared each other in terms of the mean square errors, and Bayes risk sensitivities of the Bayes estimators are investigated.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.643-652
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• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.