Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.     

分布未知情形下基于Burr近似的VSSI EWMA图多目标优化设计

为了提高过程质量监控效率和降低过程质量控制成本，针对过程质量特性分布未知情形，利用Burr分布近似未知分布，研究可变样本容量和抽样间隔(VSSI)的指数加权移动平均(EWMA)控制图的统计经济多目标优化设计问题。首先，建立基于Burr近似的未知分布VSSI EWMA图，采用平均产品长度、单位产品质量成本分别作为统计和经济指标，构造该图的统计经济多目标优化设计模型 。之后，采用NSGA-Ⅱ算法对模型进行算例求解和灵敏度分析。最后，将该方案与已有几种EWMA图设计方案比较。结果表明，在总体分布未知时，该方案在统计监控效率和过程监控成本两方面都要优于VSSI EWMA图的单一性设计，以及EWMA图多目标优化设计。     

A less sensitive linear detector for the change point based on kernel smoothing method

In this paper, a new detecting procedure for the change point in the mean is proposed based on a linear kernel smoother. It uses a discontinuous kernel function and has a relative high constant efficiency in an interval of shift value and thus is less sensitive than the simple CUSUM, EWMA, FMA and Shiryayev-Roberts procedures. It also generalizes the FMA procedure.     

Statistical process adjustment: a brief retrospective, current status, and some opportunities for further work

Industrial statisticians frequently face problems in their practice where adjustment of a manufacturing process is necessary. In this paper, a view of the origins and recent work in the area of statistical process adjustment (SPA) is provided. A discussion of some topics open for further research is also given including new problems in semiconductor manufacturing process control. The goal of the paper is to help display the SPA field as a research area with its own identity and content, and promote further interest in its development and application in the industry.     

EWMA-GARCH模型与GARCH模型在估计收益率波动上的差异的实证及理论分析

VaR作为衡量风险的指标,其核心则在于对波动,亦即方差的估计。基于时间序列,关于条件方差的经典模型是GARCH模型,尽管后来又衍生出了EGARCH,PARCH等复杂模型,但在实务中GARCH模型仍占有重要的地位。文章分析了一种比较新的结合了EWMA模型的GARCH模型(以下称为EWMA-GARCH模型)计算VaR的参数估计方法,以检验其在估计波动上的实用性,并对实证检验结果做了理论分析。分析结果表明,尽管该结合模型缺乏完整的理论支持,但是其计算效果仍比较良好,当然这样良好的结果是建立在因缺乏理论依据而导致的对模型的其他要求之上的.至于是采用受理论支持的模型还是并不输实践价值的模型,文章也给出了一定的建议。     

有偏型EWMA的股指期货保证金设定的实证研究

本文是对建立在正态分布假设的EWMA期货保证金模型的改进.文中引入基于非对称Laplace分布发展起来的有偏型EWMA方法,建立了新的期货交易保证金模型,较好地反映了期货合约价格序列有偏、厚尾的现象.同时采用comish-Fisher(CF)方法确定出期货价格波动系数,降低了预测误差.将此模型应用到股指期货合约保证金水平的测定中,结果表明本研究所建立模型能够节省保证金的收取总量,预测结果较好.     

Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis

The potential for stock market growth in Asian Pacific countries has attracted foreign investors. However, higher growth rates come with higher risk. We apply value at risk (VaR) analysis to measure and analyze stock market index risks in Asian Pacific countries, exposing and detailing both the unique risks and system risks embedded in those markets. To implement the VaR measure, it is necessary to perform "volatility modeling" by mixture switch, exponentially weighted moving average (EWMA), or generalized autoregressive conditional heteroskedasticity (GARCH) models. After estimating the volatility parameters, we can calibrate the VaR values of individual and system risks. Empirically, we find that, on average, Indonesia and Korea exhibit the highest VaRs and VaR sensitivity, and currently, Australia exhibits relatively low values. Taiwan is liable to be in high-state volatility. In addition, the Kupiec test indicates that the mixture switch VaR is superior to delta normal VaR; the quadratic probability score (QPS) shows that the EWMA is inclined to underestimate the VaR for a single series, and GARCH shows no difference from GARCH t and GARCH generalized error distribution (GED) for a multivariate VaR estimate with more assets.     

Comparisons of control schemes for monitoring the means of processes subject to drifts

Although statistical process control (SPC) techniques have been focused mostly on detecting step (constant) mean shift, drift which is a time-varying change frequently occurs in industrial applications. In this research, for monitoring drift change, the following five control schemes are compared: the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) charts which are recommended detecting drift change in the literature; the generalized EWMA (GEWMA) chart proposed by Han and Tsung (2004) and two generalized likelihood ratio based schemes, GLR-S and GLR-L charts which are respectively under the assumption of step and linear trend shifts. Both the asymptotic estimation and the numerical simulation of the average run length (ARL) are presented. We show that when the in-control (IC) ARL is large (goes to infinity), the GLR-L chart has the best overall performance among the considered charts in detecting linear trend shift. From the viewpoint of practical IC ARL, based on the simulation results, we show that besides the GLR-L chart, the GEWMA chart offers a good balanced protection against drifts of different size. Some computational issues are also addressed.     

Design and investigation of EWMA and double EWMA with quadratic process model in R2R controllers

In the last few years, “Run-to-Run” (R2R) control techniques have been developed and used to control various processes in industries. These techniques combine control engineering and statistical process control techniques. The R2R controller is basically consists of a linear regression model that relates the input variables to the output variables using Exponentially Weighted Moving Average (EWMA) or double EWMA (dEWMA) scheme. In this paper, we have developed a quadratic R2R controller model as an extension of Box, Luceno and Del Castillo models. The validity and performance of the developed models were tested in the magnetic ceramic process. By this study we have found that the quadratic model improves capability of process and applying dEWMA procedure decreases variance of the response variables. The results of the study shows that the quadratic R2R control models outperform linear R2R controls in the certain manufacturing process.