• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.271-282
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• 2004

We discuss complete convergence of weighted sums for arrays of ø-mixing random variables. As application, we obtain the complete convergence of moving average processes for ø-mixing random variables. The result of Baum and Katz (1965) as well as the result of Li et al. (1992) on iid case are extended to ø-mixing setting.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.401-408
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• 2009

Let {$Y_i,-{\infty}<i<{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables and {$a_i,-{\infty}<i<{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of $\{\sum\limits_{k=1}^n\;\sum\limits_{n=-\infty}^\infty\;a_{i+k}Y_i/n^{1/t};\;n{\geq}1\}$ under suitable conditions.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.223-229
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• 2010

We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.

• 대한수학회논문집
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• 제12권3호
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• pp.743-754
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• 1997

We introduce a class of finite and infinite moving average (MA) sequences of multivariate random vectors exponential marginals. The theory of dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain some probability bounds for the multivariate processes.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.677-686
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• 1999

In this paper we introduce a class of moving-average(MA) sequences of multivariate random vectors with geometric marginals. The theory of positive dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain weakly probability inequality of the multivariate processes.

• 산업경영시스템학회지
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• 제34권4호
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• pp.57-65
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• 2011

Monitoring auto correlated processes is prevalent in recent manufacturing environments. As a proactive control for manufacturing processes is emphasized especially in the semiconductor industry, it is natural to monitor real-time status of equipment through sensor rather than resultant output status of the processes. Equipment's sensor data show various forms of correlation features. Among them, considerable amount of sensor data, statistically autocorrelated, is well represented by Box-Jenkins autoregressive moving average (ARMA) model. In this paper, we present a design method of statistical process control (SPC) used for monitoring processes represented by the ARMA model. The proposed method shows benefits in the power of detecting process changes, and considers robustness to ARMA modeling errors simultaneously. We prove benefits through Monte carlo simulation-based investigations.

• 대한수학회논문집
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• 제23권4호
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• pp.597-606
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• 2008

Let {$Y_{ij}-{\infty}\;<\;i\;<\;{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables with zero means and finite variances and {$a_{ij}-{\infty}\;<\;i\;<\;{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}$; $n\;{\geq}\;1$} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the ${\rho}^*$-mixing case.

• 한국경영과학회지
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• 제34권4호
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• pp.91-112
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• 2009

The bullwhip effect means the phenomenon of increasing demand variation as moving UP to the upstream in the supply chain. Therefore, it is recognized that the bullwhip effect is problematic for effective supply chain operations. In this paper, we exactly quantifies the bullwhip effect for the case of stochastic lead time and seasonal demand in two-echelon supply chain where retailer employs a base-stock policy considering SARMA demand processes and stochastic lead time. We also investigate the behavior of the proposed measurement for the bullwhip effect with autoregressive and moving average coefficient, stochastic lead time, and seasonal factor.

• Industrial Engineering and Management Systems
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• 제4권1호
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• pp.75-81
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• 2005

Borror et al. discussed the EWMA(Exponentially Weighted Moving Average) chart to monitor the count of defects which follows the Poisson distribution, referred to the $EWMA_c$ chart, as an alternative Shewhart c chart. In the $EWMA_c$ chart, the Markov chain approach is used to calculate the ARL (Average Run Length). On the other hand, in order to monitor the process fraction defectives P in high-yield processes, Xie et al. presented the CCC(Cumulative Count of Conforming)-r chart of which quality characteristic is the cumulative count of conforming item inspected until observing $r({\geq}2)$ nonconforming items. Furthermore, Ohta and Kusukawa presented the $CS(Confirmation Sample)_{CCC-r}$ chart as an alternative of the CCC-r chart. As a more superior chart in high-yield processes, in this paper we present an $EWMA_{CCC-r}$ chart to detect more sensitively small or moderate shifts in P than the $CS_{CCC-r}$ chart. The proposed $EWMA_{CCC-r}$ chart can be constructed by applying the designing method of the $EWMA_C$ chart to the CCC-r chart. ANOS(Average Number of Observations to Signal) of the proposed chart is compared with that of the $CS_{CCC-r}$ chart through computer simulation. It is demonstrated from numerical examples that the performance of proposed chart is more superior to the $CS_{CCC-r}$ chart.

• 품질경영학회지
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• 제34권4호
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• pp.125-132
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• 2006

An adjusted control limit of the $\overline{X}$ chart is proposed for monitoring the continually improving processes. The continual improvement of the process implies the decrease of the process variance, which is represented by a logistic curve. The process standard deviation is estimated by the exponentially weighted moving average of the sample standard deviations from the past to the current times. The control limits are adjusted by the estimated standard deviation at every sampling time. The performance of the adjusted control limit is compared with that of the standard control limits for various cases of the decreasing speed and size of the variance. The results show that the $\overline{X}$ chart with the adjusted control limits provides better performances for monitoring the small and moderate shifts in continually improving processes.