• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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• pp.311-319
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• 2001

All indices that are now in use assume normally distributed data, and any use of the indices on non-normal data results in inaccurate capability measurements. Therefore, $C_{s}$ is proposed which extends the most useful index to date, the Pearn-Kotz-Johnson $C_{pmk}$, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness. Therefore we propose, a new process capability index $C_{psk}$( WV) applying the weighted variance control charting method for non-normally distributed. The main idea of the weighted variance method(WVM) is to divide a skewed or asymmetric distribution into two normal distribution from its mean to create two new distributions which have the same mean but different standard distributions. In this paper we propose an example, a distribution generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and the Wright methods. This example shows that the weighted valiance-based indices are more consistent than the other two methods In terms of sensitivity to departure to the process mean/median from the target value for non-normal process.s.s.s.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.29-35
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• 2011

In statistical process control, the primary method used to monitor the number of nonconformities is the c-chart. The conventional c-chart is based on the assumption that the occurrence of nonconformities in samples is well modeled by a Poisson distribution. When the Poisson assumption is not met, the X-chart is often used as an alternative charting scheme in practice. And CUSUM-chart is used when it is desirable to detect out of control situations very quickly because of sensitive to a small or gradual drift in the process. In this paper, I compare CUSUM-chart to X-chart for the Katz family covering equi-, under-, and over-dispersed distributions relative to the Poisson distribution.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.30 no.2
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• pp.83-91
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• 2018

A datacenter is a high energy consuming facility whose cooling energy consumption rate is 10~20 times larger than general office buildings. The higher the temperature of supply air from a CRAC (computer room air-conditioner) is supplied, the more energy efficient cooling is possible because of improving the COP of a chiller and advanced range of outdoor air temperature available for the economizer cycles. However, because the temperature of cold air flowing into server computers varies depending on air mixing configurations in a computer room, the proper supply air temperature must be considered based on the investigation of air mixing and heat dissipation. By these, this study aims to understand the effects of variation of the supply air temperature on the air flow distributions, temperature distributions and rack cooling efficiencies. Computational fluid dynamics (CFD) aided in conducting the investigation. As a result, the variation of the supply air temperature does not affect the air flow distributions. However, it mainly affects the temperature distribution. From the results of CFD simulations, Rack cooling indices (RCIHI and RCILO) were evaluated and showed the ideal state set at $19^{\circ}C$ of the supply air temperature.

• Smart Structures and Systems
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• v.25 no.5
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• pp.593-604
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• 2020

Temperature may have more significant influences on structural responses than operational loads or structural damage. Therefore, a comprehensive understanding of temperature distributions has great significance for proper design and maintenance of bridges. In this study, the temperature distribution of the steel box girder is systematically investigated based on the structural health monitoring system (SHMS) of the Sutong Cable-stayed Bridge. Specifically, the characteristics of the temperature and temperature difference between different measurement points are studied based on field temperature measurements. Accordingly, the probability density distributions of the temperature and temperature difference are calculated statistically, which are further described by the general formulas. The results indicate that: (1) the temperature and temperature difference exhibit distinct seasonal characteristics and strong periodicity, and the temperature and temperature difference among different measurement points are strongly correlated, respectively; (2) the probability density of the temperature difference distribution presents strong non-Gaussian characteristics; (3) the probability density function of temperature can be described by the weighted sum of four Normal distributions. Meanwhile, the temperature difference can be described by the weighted sum of Weibull distribution and Normal distribution.

• Journal of radiological science and technology
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• v.23 no.2
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• pp.75-79
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• 2000

This study was performed for the clinical applications applying the Monte Carlo methods. In this study we calculated the absorbed dose distributions for the 6 MeV electron beam in water phantom and compared the results with measured values. The energy data of electron beam used in Monte Carlo calculation is the energy distribution for 6 MeV electron beam which is assumed as a Gaussian form. We calculated percent depth doses and beam profiles for three field sizes of $10{\times}10,\;15{\times}15$, and $20{\times}20\;cm^2$ in water phantom using Monte Carlo methods and measured those data using a semiconductor detector and other devices. We found that the calculated percent depth doses and beam profiles agree with the measured values approximately. However, the calculated beam profiles at the edge of the fields were estimated to be lower than the measured values. The reason for that result is that we did not consider the angular distributions of the electrons in phantom surface and contamination of X-rays in our calculations. In conclusion, in order to apply the Monte Carlo methods to the clinical calculations we are to study the source models for electron beam of the linear accelerator beforehand.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.7
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• pp.822-830
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• 2012

Clutters are all unwanted radar returns to affect on detection of targets. Radar clutter is characterized by amplitude distributions, spectrum, etc. Clutter is modelled with considering these kinds of characteristics. In this paper, a Weibull distribution function approximated by uniform distribution function is suggested. Weibull distribution function is used to model the various clutters. This paper shows that the data generated by the approximated solution of Weibull distribution function satisfy the Weibull probability density function. This paper shows that the data generation time of approximated Weibull distribution function solution is reduced by 20 % compared with the generation time of original Weibull probability density function.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Journal of Forest and Environmental Science
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• v.34 no.6
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• pp.451-456
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• 2018

The use of single component distribution to describe the irregular stand structure of degraded forest often lead to bias. Such biasness can be overcome by the application of finite mixture distribution. Therefore, in this study, finite mixture distribution was used to characterise the irregular stand structure of the Gmelina arborea plantation in Omo forest reserve. Thirty plots, ten each from the three stands established in 1984, 1990 and 2005 were used. The data were pooled per stand and fitted. Four finite mixture distributions including normal mixture, lognormal mixture, gamma mixture and Weibull mixture were considered. The method of maximum likelihood was used to fit the finite mixture distributions to the data. Model assessment was based on negative loglikelihood value ($-{\Lambda}{\Lambda}$), Akaike information criterion (AIC), Bayesian information criterion (BIC) and root mean square error (RMSE). The results showed that the mixture distributions provide accurate and precise characterisation of the irregular diameter distribution of the degraded Gmelina arborea stands. The $-{\Lambda}{\Lambda}$, AIC, BIC and RMSE values ranged from -715.233 to -348.375, 703.926 to 1433.588, 718.598 to 1451.334 and 3.003 to 7.492, respectively. Their performances were relatively the same. This approach can be used to describe other irregular forest stand structures, especially the multi-species forest.

• Nuclear Engineering and Technology
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• v.54 no.9
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• pp.3225-3234
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• 2022

Alloy 690 tubing has been shown to be highly resistant to primary water stress corrosion cracking (PWSCC). Nevertheless, predicting the failure by PWSCC in Alloy 690 SG tubes is indispensable. In this work, a Bayesian-based statistical approach is proposed to predict the occurrence of failure by PWSCC in Alloy 690 SG tubing. The prior distributions of the model parameters are developed based on the prior knowledge or information regarding the parameters. Since Alloy 690 is a replacement for Alloy 600, the parameter distributions of Alloy 600 tubing are used to gain prior information about the parameters of Alloy 690 tubing. In addition to estimating the model parameters, analysis of tubing reliability is also performed. Since no PWSCC has been observed in Alloy 690 tubing, only right-censored free-failure life of the tubing are available. Apparently the inference is sensitive to the choice of prior distribution when only right-censored data exist. Thus, one must be careful in choosing the prior distributions for the model parameters. It is found that the use of non-informative prior distribution yields unsatisfactory results, and strongly informative prior distribution will greatly influence the inference, especially when it is considerably optimistic relative to the observed data.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.427-436
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• 2000

In this paper, we consider a Bayesian model selection problem of lifetime distributions using fractional Bayes factor with noninformative prior when type II censored data are given. For a given type II censored data, we calculate the posterior probability of exponential, Weibull and lognormal distributions and select the model which gives the highest posterior probability. Our proposed methodology is explained and applied to real data and simulated data.