• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.651-657
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• 2017

A sequence {$X_n,\;n{\geq}1$} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. We obtain two characterizations of a family of continuous probability distribution by independence property of record values.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.561-570
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• 2003

We propose a nonparametric test procedure for checking the proportionality assumption between hazard functions using a functional equation. Because of the involvement of censoring distribution function, we consider the large sample case only and obtain the asymptotic normality of the proposeed test statistic. Then we discuss the rationale of the use of the functional equation, give some examples and compare the performances with Andersen's procedure by computing powers through simulations.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.237-244
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• 2014

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

• The Korean Journal of Ecology
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• v.23 no.6
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• pp.435-438
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• 2000

Diameter distributions describe forest stand structure information. Prediction equations for percentiles of diameter distribution and parameter recovery procedures for the Weibull distribution function based on four percentile equations were applied to develop prediction system of even-aged slash pine stand structure development in terms of the number of stems per diameter class changes. Four percentiles of the cumulative diameter distribution were predicted as a function of stand characteristics. The predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level. Statistically, no significant differences were detected based on the data from 236 evaluation data sets. This stand level diameter distribution prediction system will be useful in slash pine stand structure modeling and in updating forest inventories for the long-term forest management planning.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1908-1918
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• 1991

Fatigue tests have been carried out to measure the degradation of the residual strength and the fatigue life in carbon/epoxy (0/45/90/-45)$_{2s}$ composite materials. Theoretical predictions of residual strength and fatigue life were compared with experimental results. Distribution characteristics were studied using the probability of failure based on the cumulative distribution function and median rand. The static ultimate strength of carbon/epoxy composites used herein is observed to be relatively higher than that of existing similar composites ; while fatigue life is shorter due to the brittleness of matrix. The fatigue life obtained in these experiments is shorter than that estimated by residual strength degradation model when the stress level above 0.6 For the stress level of 0.6, the experimental value was abruptly increased. The cumulative distribution function for the static ultimate strength is well correlated to that for the strength converted from the measured fatigue life. Also, the predicted distribution of residual strength shows good agreement with the experimental results. Therefore, it is proven that the residual strength degradation model is reasonable.e.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.629-638
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• 2012

We propose some methods to obtain optimal thresholds and classification functions by using various cutoff criterion based on the bivariate ROC curve that represents bivariate cumulative distribution functions. The false positive rate and false negative rate are calculated with these classification functions for bivariate normal distributions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.4
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• pp.274-279
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• 2015

Wave data acquired over eleven years near Sokcho Harbor located in the central area of the east coast were analyzed using spectral method and wave-by-wave analysis method and its major wave characteristics were examined. Significant wave heights were found to be high in winter and low in summer, and peak periods were also found to be long in winter and short in summer. The maximum significant wave height observed was 8.95 m caused by the East Sea twister. The distributional pattern of the significant wave heights and peak periods were both fitted better by Kernel distribution function than by Generalized Gamma distribution function and Generalized Extreme Value distribution function. The wave data were compiled to subdivide the wave height into intervals for each month, and the cumulative occurrence rates of wave heights were calculated to be utilized for the design and construction works in nearby construction works.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.2
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• pp.142-147
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• 2015

Wave data acquired over seven years near Daejin Harbor located in the north central area of the east coast was analyzed using spectral method and wave-by-wave analysis method and its major wave characteristics were examined. Significant wave heights were found to be high in winter and low in summer, and peak periods were also found to be long in winter and short in summer. The maximum significant wave height observed was 6.59 m and was caused by Typhoon No. 1216, SANBA. The distributional pattern of the significant wave heights and peak periods were both reproduced better by Kernel distribution function than by Generalized Gamma distribution function and Generalized Extreme Value distribution function. Meanwhile, the wave data was subdivided by month and wave height level and the cumulative appearance rate was proposed to aid designing and constructing works in nearby coastal areas.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3892-3898
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• 1996

In this study, the prediction of the fatigue life as well as the extimation of the characteristics of fatigue cumulative damage on GFRP under random loading were performed. The constant amplitude tests and the ramdom loading test were carried on notched GFRP specimens with a circular hole. Random waves were generated with a micro-computer and had wide band spectra. Since it is useful that the prediction of fatigue life ot the given load sequences is based on S-N curves under constant amplitude loading, the estimation of equivalent stress is done on every random waves. The equivalent stress wasat first estimated by Miner's rule and then by the proposed model which was based on Hashin-Rotem's comulative damage theory regarding nonlinear fatigue cumulative damage behavior. The fatigue lives were predicted from each equivalent stress evaluated. And each predicted fatigue llife was compared with experimental results. The number of cycles of random loads were counted by mean-cross counting method. The reuslts showed that the fatigue life predicted by proposed model was correlated well with the experimental results in comparison with Miner's model.