• Smart Structures and Systems
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• 제14권3호
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• pp.377-395
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• 2014

Vibration-based fault detection and condition monitoring of rotating machinery, using statistical process control (SPC) combined with statistical pattern recognition methodology, has been widely investigated by many researchers. In particular, the discrete wavelet transform (DWT) is considered as a powerful tool for feature extraction in detecting fault on rotating machinery. Although DWT significantly reduces the dimensionality of the data, the number of retained wavelet features can still be significantly large. Then, the use of standard multivariate SPC techniques is not advised, because the sample covariance matrix is likely to be singular, so that the common multivariate statistics cannot be calculated. Even though many feature-based SPC methods have been introduced to tackle this deficiency, most methods require a parametric distributional assumption that restricts their feasibility to specific problems of process control, and thus limit their application. This study proposes a nonparametric multivariate control chart method, based on multiscale wavelet scalogram (MWS) features, that overcomes the limitation posed by the parametric assumption in existing SPC methods. The presented approach takes advantage of multi-resolution analysis using DWT, and obtains MWS features with significantly low dimensionality. We calculate Hotelling's $T^2$-type monitoring statistic using MWS, which has enough damage-discrimination ability. A bootstrap approach is used to determine the upper control limit of the monitoring statistic, without any distributional assumption. Numerical simulations demonstrate the performance of the proposed control charting method, under various damage-level scenarios for a bearing system.

• 응용통계연구
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• 제35권3호
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• pp.347-356
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• 2022

본 논문에서는 금융 시계열 비대칭 변동성을 모형화하기 위해서 다중 임계점을 가진 비대칭-ARCH 점화식(A-ARCH(1))을 제안하고 있다. 특히 임계점이 두 개인 간단한 모형에 초점을 맞추어 설명하고 있으며 미국 S&P500 자료 분석을 통해 예시하였다. 다양한 A-ARCH(1) 모형의 예측력 비교를 위해 모수적-붓스트랩을 활용하여 예측오차의 평가 및 예측구간의 정확도를 설명하였다.

• 한국습지학회지
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• 제10권3호
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• pp.125-132
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• 2008

일반적으로 빈도해석을 진행할 경우 자료는 정상성을 가정하고 분석하게 된다. 그러나 최근 들어 기후변화 등의 원인으로 인하여 강우나 유출량이 변화하고 있어 변화하는 강우나 유출량을 고려해서 빈도해석을 해야 한다는 주장이 제기되고 있다. 이에 본 연구에서는 Bootstrap을 기반으로 개발된 SIR 알고리즘을 이용하여 홍수빈도해석을 수행하기위한 방안을 제시하였다. SIR 알고리즘은 우도함수를 고려하여 자료를 재추출하기 위해서 사용되어 왔으며, 본 연구에서도 최근에 변화하는 홍수량의 변화 양상을 고려하여 홍수량 자료를 재추출하기 위해서 적용되었다. 증가된 홍수 특성을 고려하여 재추출된 홍수량자료는 매개변수적 빈도해석을 함으로써 지속시간별 홍수량을 산정하였으며, 산정된 빈도별 홍수량들을 Bootstrap을 이용해서 재추출한 자료를 이용한 빈도해석결과와 원자료를 이용하여 분석한 빈도해석 결과를 비교하였다. 비교결과 SIR알고리즘을 이용해서 빈도해석을 진행한 경우의 빈도별 홍수량이 가장 크게 나타났다. 따라서 홍수빈도해석시 현재까지의 변화하는 홍수량 패턴을 고려할 경우, 확률홍수량이 증가하는 것을 확인하였다.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.93-110
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• 1992

A model selection approach is used to find out whether the mean and the variance of a unique sample are different from the pre-specified values. Normal distribution is selected as an approximating model. Kullback-Leibler discrepancy comes out as a natural measure of discrepancy between the operating model and the approximating model. Several estimates of selection criterion are computed including AIC, TIC, and a coupleof bootstrap estimator of the selection criterion are considered according to the way of resampling. It is shown that a closed form expression is available for the parametric bootstrap estimated cirterion. A Monte Carlo study is provided to give a formal comparison when the operating family itself is normally distributed.

• Communications for Statistical Applications and Methods
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• 제23권4호
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• pp.269-285
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• 2016

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

• Communications for Statistical Applications and Methods
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• 제16권4호
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• pp.697-705
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• 2009

The Pearson chi-squared statistic or the deviance statistic is widely used in assessing the goodness-of-fit of the generalized linear models. But these statistics are not proper in the situation of continuous explanatory variables which results in the sparseness of cell frequencies. We propose a goodness-of-fit test statistic for the cumulative logit models with ordinal responses. We consider the grouping of a dataset based on the ordinal scores obtained by fitting the assumed model. We propose the Pearson chi-squared type test statistic, which is obtained from the cross-classified table formed by the subgroups of ordinal scores and the response categories. Because the limiting distribution of the chi-squared type statistic is intractable we suggest the parametric bootstrap testing procedure to approximate the distribution of the proposed test statistic.

• 한국국방경영분석학회지
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• 제12권2호
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• pp.68-81
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• 1986

This thesis studies the estimation from interarrival and service time data of the mean number of customers in service at time t for an $M/G/{\infty}$ queue. The assumption is that the parametric form of the service time distribution is unknown and the empirical distribution of twe service time is used in the estimate the mean number of customers in service. In the case in which the customer arrival rate is known the distribution of the estimate is derived and an approximate normal confidence interval procedure is suggested. The use of the nonparametric methods, which are the jackknife and the bootstrap, to estimate variability and construct confidence intervals for the estimate is also studied both analytically and by simulation.

• 품질경영학회지
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• 제39권2호
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• pp.234-243
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• 2011

Multivariate control charts are widely used to monitor the performance of a multivariate process over time to maintain control of the process. Although existing multivariate control charts provide control limits to monitor the process and detect any extraordinary events, it is a challenge to identify the causes of an out-of-control alarm when the number of process variables is large. Several fault identification methods have been developed to address this issue. However, these methods require a normality assumption of the process data. In the present study, we propose a bootstrapped-based $T^2$ decomposition technique that does not require any distributional assumption. A simulation study was conducted to examine the properties of the proposed fault identification method under various scenarios and compare it with the existing parametric $T^2$ decomposition method. The simulation results showed that the proposed method produced better results than the existing one, especially in nonnormal situations.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.1-14
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• 2001

This paper discusses choosing the weight function of the Hardle and Mammen statistic in nonparametric goodness-of-fit test for regression curve. For this purpose, we modify the Hardle and Mammen statistic and derive its asymptotic distribution. Some results on the test statistic from the wild bootstrapped sample are also obtained. Through Monte Carlo experiment, we check the validity of these results. Finally, we study the powers of the test and compare with those of the Hardle and Mammen test through the simulation.

• 응용통계연구
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• 제6권2호
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• pp.401-408
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• 1993

본 논문에서는 회귀직선 기울기의 순서성에 대한 비모수적 검정법을 제안하였다. 자료의 정보를 최대한 활용하는 Potthoff 형태의 검정통계량을 붓스트랩 분산추정량으로 표준화하여 점근 분포무관 검정을 한다. 또한 제안된 검정법의 특성과 효율을 대표본과 소표본에서 비교연구하였다.