关于非自伴算子D~4+X~α+iX~β的极限点性质

本文解决了一般的非自伴问题：如果L＝（-1）kDkPkDk是极限点的，M是一个阶数不超过2n的微分算子，L＋iM如何能保持极限点的性质。     

On arcs with weighted points

In the present paper we start the study of arcs with weighted points in a finite projective plane, and we get some particular results about the existence or non-existence of these arcs.     

Dynamic sampling plans in on-line control charts

Three simple dynamic sampling plans for detecting the change point are investigated in the discrete-time case. The first is a two-rate sampling CUSUM procedure. The second is a two-rate sampling Shiryayev-Roberts procedure. The third is a periodic sequential testing procedure. Two problems are discussed. First, simple design methods are provided for practical use. Second, a comparison between the three plans is made in the continuous-time case, which shows that by properly choosing the design parameters, the three plans can be made equally efficient in certain senses.     

QUALITY CONTROL WITH MULTIVARIATE DATA

The paper examines statistical process control of bivariate and multivariate data, using in particular the multivariate equivalents of the univariate Shewhart chart, CUSUM chart and the Exponentially Weighted Moving Average chart. This illustrates the usefulness of Principal Component methods in statistical process control with multivariate data.     

Monitoring Nonlinear Profiles with Random Effects by Nonparametric Regression

The monitoring of process/product profiles is presently a growing and promising area of research in statistical process control. This study is aimed at developing monitoring schemes for nonlinear profiles with random effects. We utilize the technique of principal components analysis to analyze the covariance structure of the profiles and propose monitoring schemes based on principal component (PC) scores. The number of the PC scores used in constructing control charts is crucial to the detecting power. In the Phase I analysis of historical data, due to the dependency of the PC-scores, we adopt the usual Hotelling T ² chart to check the stability. For Phase II monitoring, we study individual PC-score control charts, a combined chart scheme that combines all the PC-score charts, and a T ² chart. Although an individual PC-score chart may be perfect for monitoring a particular mode of variation, a chart that can detect general shifts, such as the T ² chart and the combined chart scheme, is more feasible in practice. The performances of the schemes under study are evaluated in terms of the average run length.     

A Multivariate Adaptive Exponentially Weighted Moving Average Control Chart

A multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed. The new multivariate scheme can detect small and large shifts in the process mean vector effectively. The proposed scheme can be viewed as a smooth combination of a multivariate exponentially weighted moving average (MEWMA) chart and a Shewhart χ²-chart. The optimal design of the proposed chart is given according to a pre-specified in-control average run length and two shift sizes; a small and large shift each measured in terms of the non centrality parameter. The signal resistance of the newly proposed multivariate chart is also given. Comparisons among the new chart, the MEWMA chart, and the combined Shewhart-MEWMA (S-MEWMA) chart in terms of the standard and worst-case average run length profiles are presented. In addition, the three charts are compared with respect to their worst-case signal resistance values. The proposed chart gives somewhat better worst-case ARL and signal resistance values than the competing charts. It also gives better standard ARL performance especially for moderate and large shifts. The effectiveness of our proposed chart is illustrated through an example with simulated data set.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Conditional Information in Projections of Gaussian Vectors

Conditional information measures the information in a sample for an interest parameter in the presence of nuisance parameter. In the context of Gaussian likelihoods this paper first derives conditions under which a projection of the data may reduce conditional information to zero. These are then applied in the context of time series regressions, and inference on a covariance parameter, such as with either autoregressive or moving average errors. It is shown that regressing out very common regressors, such as a linear trend or dummy variable, can imply that conditional information is zero in the case of non-stationary autoregressions or non-invertible moving averages, respectively.     

A Distribution-Free Control Chart Based on Order Statistics

In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004 Chakraborti , S. , van der Laan , P. , van de Wiel , M. A. ( 2004 ). A class of distribution-free control charts . J. Roy. Statist. Soc. Ser. C-Appl. Statist. 53 ( 3 ): 443 – 462 .[Web of Science ®] , [Google Scholar]).     

A New Control Scheme Always Better Than X-Bar Chart

A new control scheme is proposed by borrowing the idea of the Benjamini–Hochberg procedure for controlling the false discovery rate in multiple testing. It is shown theoretically that the proposed 2-span control scheme outperforms the Shewhart X-bar chart in terms of the average run length under any size of mean shifts. Some simulations are carried out to demonstrate that the proposed scheme having various span sizes always outperforms the X-bar chart in terms of the average run lengths.