• 대한산업공학회지
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• 제39권2호
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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.

• 대한기계학회논문집A
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• 제35권2호
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• pp.125-130
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• 2011

확정론적 최적설계 방법은 설계 혹은 공정과정에서 발생하는 설계변수의 불확실성을 고려하지 않아 최적점이 제한조건의 경계점에 위치한다. 신뢰성기반 최적설계는 설계자가 요구하는 신뢰도를 만족하는 범위에서 목적함수가 최소가 되는 최적점을 찾는 방법이다. 이 과정은 최적설계 과정과 설계변수의 불확실성을 고려하는 신뢰성해석 과정으로 나눌 수 있다. 모멘트기반 신뢰성해석은 시스템의 통계적 모멘트를 이용하여 신뢰도를 구하는 방법이다. 일반적으로 신뢰성해석은 통계적 모멘트의 값에 따라 피어슨 시스템을 통해 시스템의 확률밀도함수를 7 가지 형태로 분류하여 신뢰도를 구한다. 하지만 피어슨 시스템에서 타입 IV 분포의 경우에는 수식이 복잡하여 다루기 어려운 문제점이 있었다. 본 논문에서는 크리깅모델을 이용하여 피어슨 시스템의 단점을 개선한 신뢰성 해석기법을 크리깅모델을 이용하여 개발하고 이를 적용하여 신뢰성기반최적설계 방법을 제안하다. 피어슨 타입 IV 의 수학 및 공학예제에 대하여 신뢰성기반최적설계를 수행하고 이를 몬테카를로 시뮬레이션을 이용하여 정확성을 검증한다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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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.

• 산업경영시스템학회지
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• 제22권52호
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• pp.69-79
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• 1999

The main objective of this study are to propose two methods that would be a comprehensive measure of evaluation for non-normal process capability with Beta distributions. First method is introduced using process capability index $C_{psk}$ by the Pearson system and Johnson system. The Pearson system and the Johnson System selected for process capability index calculation have a equivalent result of this study that the ranking of the seven indices in terms of sensitivity to departure of the process median from the target value from the most sensitive one up to the least sensitive are $C^{*}_{pm}$ , $C_{psk}$ , $C_{s}$ , $C_{pmk}$ , $C_{pm}$ , $C_{pk}$ , $C_{p}$ . Second method show using the percentage nonconforming by the Pearson, Johnson and Burr functions. In thus study, we find that the Pearson system and the Burr system are a reasonable method to estimate percentage nonconforming. But, the exact procedure for deriving this estimate will be based on Beta distribution. Accordingly, if a process is not normally distributed , but normal-based techniques are used serious errors can result.

• 한국경영과학회지
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• 제17권2호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.690-693
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• 2005

In this paper, probabilistic distribution of fatigue life of chassis component is determined statistically by applying the design of experiments and the Pearson system. To construct $p-\varepsilon-N$ curve, the case that fatigue data are random variables is attempted. Probabilistic density function(p.d.f) for fatigue life is obtained by design of experiment and using this p.d.f fatigue reliability about any aimed fatigue life can be calculated. Lower control arm and rear torsion bar of chassis component are selected as examples for analysis. Component load histories, which are obtained by multi-body dynamic simulation for Belsian load history, are used. Finite element analysis are performed using commercial software MSC Nastran and fatigue analysis are performed using FE Fatigue. When strain-life curve itself is random variable, probability density function of fatigue life has very little difference from log-normal distribution. And the case of fatigue data are random variables, probability density functions are approximated to Beta distribution. Each p.d.f is verified by Monte-Carlo simulation.

• 한국정밀공학회지
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• 제24권2호
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• pp.110-117
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• 2007

In this paper, probabilistic distribution of chassis component fatigue life is determined statistically by applying the design of experiments and the Pearson system. To construct p - ${\varepsilon}$ - N curve, the case that fatigue data are random variables is attempted. Probabilistic density function (p.d.f) for fatigue life is obtained by the design of experiment and using this p.d.f fatigue reliability, any aimed fatigue life can be calculated. Lower control arm and rear torsion bar of chassis components are selected as examples for analysis. Component load histories which are obtained by multi-body dynamic simulation for Belsian load history are used. Finite element analysis is performed by using commercial software MSC Nastran and fatigue analysis is performed by using FE Fatigue. When strain-life curve itself is random variable, the probability density function of fatigue life has very little difference from log-normal distribution. And the cases of fatigue data are random variables, probability density functions are approximated to Beta distribution. Each p.d.f is verified by Monte-Carlo simulation.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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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.

• 대한안전경영과학회지
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• 제3권3호
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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.