• Proceedings of the KSME Conference
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• 2004.11a
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• pp.840-845
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• 2004

The reliability analysis for nonnormal distributions using the three level DOE(design of experiments) method was developed by Seo and Kwak in 2002. Although this method estimates only up to the first four moments(mean, standard deviation, skewness, and kurtosis) of the system response function, the result and the type of probability distribution determined by using the Pearson system are shown very good. However the accuracy is low in case of nonlinear performance function and sometimes, the level calculated is outside of the region in which the random variable is defined. In this article we suggest a modified three level DOE method to overcome these weaknesses and to obtain optimum choice for 3 levels and weights to handle nonnormal distributions. Furthermore we extend it to finding the optimum choice for 5 levels and weights to increase the accuracy in case of nonlinear performance function. A systematic procedure for reliability analysis is then proposed by using the Pearson system.

• 한국경영정보학회:학술대회논문집
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• 2007.06a
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• pp.576-581
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• 2007

The purpose of this paper is to strengthen trust on the automated collaborative filtering system. Automated collaborative filtering system is quickly becoming a popular technique for recommendation system. This elaborative methodology contributes for reducing information overload and the result becomes index of users' preference. In addition, it can be applied to various industries in various fields. After it collaborative filtering system was developed, many researches are executed to enhance credibility and to apply in various fields. Among these diverse systems, collaborative filtering system which uses Pearson correlation coefficient is most common in many researches. In this paper, we proposed new process diagram of collaborative filtering algorithm and new factors which should improve the credibility of system. In addition, the effects and relationships are also tested.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.327-332
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• 2001

An experimental design technique is developed for estimating the moments of system response functions. It is easy to implement and provides accurate results compared with other traditional methods. It is based on the work of Taguchi, later improved by D'Errico and Zaino. The existing experimental techniques, however, is applicable only for normally distributed cases. In this article the three-level Taguchi method is extended to obtain optimum choice for levels and weights to handle nonnormal distributions. A systematic procedure for reliability analysis is then proposed by using the Pearson system and the narrow system reliability bounds. Illustrative examples including a tolerance optimization problem are shown very accurate comparing with those by Monte-Carlo simulations and the first-order reliability method.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.2
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• pp.109-118
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• 2013

We propose a method for estimating coefficients of AR (autoregressive) model which named MLPAR (Maximum Likelihood of Pearson system for Auto-Regressive model). In the present method for estimating coefficients of AR model, there is an assumption that residual or error term of the model follows the normal distribution. In common cases, we can observe that the error of AR model does not follow the normal distribution. So the normal assumption will cause decreasing prediction accuracy of AR model. In the paper, we propose the MLPAR which does not assume the normal distribution of error term. The MLPAR estimates coefficients of auto-regressive model and distribution moments of residual by using pearson distribution system and maximum likelihood estimation. Comparing proposed method to auto-regressive model, results are shown to verify improved performance of the MLPAR in terms of prediction accuracy.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.3
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• pp.183-189
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• 2013

In this paper, uncertainties and failure criteria of structure are mathematically expressed by random variables and a limit state equation. A limit state equation is approximated by Fleishman's 3rd order polynomials and the theoretical moments of an approximated limit state equation are calculated. Fleishman introduced a 3rd order polynomial in terms of only standard normal distiribution random variables. But, in this paper, Fleishman's polynomial is extended to various random variables including beta, gamma, uniform distributions. Cumulants and a normalized limit state equation are used to calculate a theoretical moments of a limit state equation. A cumulative distribution function of a normalized limit state equation is approximated by a Pearson system.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.852-857
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• 2004

A new and efficient method for estimating the statistical moments of a system performance function has been developed. The method consists of two steps: (1) An approximate response surface is generated by a quadratic regression model, and (2) the statistical moments of the regression model are then calculated by experimental design techniques proposed by Seo and $Kwak^{(4)}$. In this approach, the size of experimental region affects the accuracy of the statistical moments. Therefore, the region size should be selected suitably. The D-optimal design and the central composite design are adopted over the selected experimental region for the regression model. Finally, the Pearson system is adopted to decide the distribution type of the system performance function and to analyze structural reliability.

• Journal of the Korea Safety Management & Science
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• v.3 no.3
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• pp.175-190
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• 2001

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 distributions from its mean to create two new distributions which have the same mean but different standard deviations. In this paper we propose an example, a distributions 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 processes. Second method show using the percentage nonconforming by the Pearson, Johnson and Burr systems. This example shows a little difference between the Pearson system and Burr system, but Johnson system underestimated than the two systems for process capability.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.6
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• pp.48-53
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• 2002

품질보증 부분에서 대부분 통계적 수법들은 기지분포를 가정하여 데이터를 분석하고 있다. 예를 들면 공정능력에서는 정규분포를 가정하고 있고, 신뢰성 분석에서는 지수분포, 대수정규분포 또는 와이블분포 등을 가정하고 있다. 만약 이러한 것들이 가정하는 확률분포와 크게 편의될 때 도출된 결론은 그 유효성을 상실하게 된다. 따라서 공정이 정규분포를 하지 않는다면 정규분포에 기초한 공정능력지수의 사용은 부정확한 공정의 정보를 제시하게 된다. 이러한 문제를 해결하기 위하여 그 사례로 소표본일 경우 정규성의 유무를 Lilliefors 검정통계량으로 검정하였다. 그리고 최우추정량(MLE), 수정적률추정량(MME), 및 적률추정량(ME)을 사용하여 모수추정을 하여 그 각각의 경우에 공정능력지수로 평가하였다. 공정능력지수의 평가는 공정이 지수분포를 하는 경우에 적합한 공정능력지수($C_{pe}$)를 제안하고, 이것의 대안으로써 Pearson 시스템, Johnson 시스템 및 Burr 시스템과도 비교평가 하였다.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1694-1700
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• 2004

In this paper, we propose the AWLS/MFT (Adaptive Weighed Least Squares/ Modulation Function Technique) devised by A. E. Pearson et al. for the transfer function estimation of a modal system and investigate the performance of several algorithms, the Gram matrix method, a Luenberger Observer (LO), Least Squares (LS), and Recursive Least Squares (RLS), for the estimation of initial conditions. With the benefit of the Modulation Function Technique (MFT), we can separate the estimation problem into two phases: the transfer function parameters are estimated in the first phase, and the initial conditions are estimated in the second phase. The LO method produces excellent IC estimates in the noise free case, but the other three methods show better performance in the noisy case. Finally, we compared our result with the Prony based method. In the noisy case, the AWLS and one of the three methods - Gram matrix, LS, and RLS- show better performance in the output Signal to Error Ratio (SER) aspect than the Prony based method under the same simulation conditions.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.2
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• pp.91-106
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• 1992

It an inventory control system, the demand over time are often assumed to be independently identically distributed (i. i. d.). However, the demands may well be correlated over time in many situations. The estimation of reorder points is not simple for correlated demands with variable lead time. In this paper, a general class of autoregressive and moving average processes is considered for modeling the demands of an inventory item. The first four moments of the lead-time demand (L) are derived and used to approximate the distribution of L. The reorder points at given service level are then estimated by the three approximation methods : normal approximation, Charlier series and Pearson system. Numerical investigation shows that the Pearson system and the Charlier series performs extremely well for various situations whereas the normal approximation show consistent underestimation and sensitive to the distribution of lead time. The same conclusion can be reached when the parameters are estimated from the sample based on the simulation study.