On the Run Length of a State-Space Control Chart for Multivariate Autocorrelated Data

The literature on statistical process control (SPC) describes the negative effects of autocorrelation in terms of the increase in false alarms. This has been treated by the individual modeling of each series or the application of VAR models. In the former case, the analysis of the cross correlation structure between the variables is altered. In the latter, if the cross correlation is not strong, the filtering process may modify the weakest relations. In order to improve these aspects, state-space models have been introduced in multivariate statistical process control (MSPC). This article presents a proposal for building a control chart for innovations, estimating its average run length to highlight its advantages over the VAR approach mentioned above.     

One-sided EWMA control charts for monitoring Poisson processes with varying sample sizes

ABSTRACT

Recently considerable research has been devoted to monitoring increases of incidence rate of adverse rare events. This paper extends some one-sided upper exponentially weighted moving average (EWMA) control charts from monitoring normal means to monitoring Poisson rate when sample sizes are varying over time. The approximated average run length bounds are derived for these EWMA-type charts and compared with the EWMA chart previously studied. Extensive simulations have been conducted to compare the performance of these EWMA-type charts. An illustrative example is given.     

三坐标雷达实际垂直探测威力模型及算法研究

在考虑阵地反射和地物遮蔽的情况下,针对分米波段和厘米波段的三坐标雷达,建立了雷达垂直探测威力模型.文中对模型中参数的获取、近似处理等问题进行了详细的讨论,并根据三坐标雷达的工作模式和天线扫描方式,深入研究了天线垂直方向性函数的取值问题.最后给出了一种三坐标雷达实际垂直探测威力算法,实现了雷达在任意方位实际垂直探测威力的自动仿真生成.     

Residual-based specification of the random-effects distribution for cluster data

We propose a method for specifying the distribution of random effects included in a model for cluster data. The class of models we consider includes mixed models and frailty models whose random effects and explanatory variables are constant within clusters. The method is based on cluster residuals obtained by assuming that the random effects are equal between clusters. We exhibit an asymptotic relationship between the cluster residuals and variations of the random effects as the number of observations increases and the variance of the random effects decreases. The asymptotic relationship is used to specify the random-effects distribution. The method is applied to a frailty model and a model used to describe the spread of plant diseases.     

广义范数残差判据

本文讨论了利用正交变换方法的最小二乘递推算法,提出了广义范数残差的概念,建立了相应的广义范数残差判据,用来离线或在线评价参数和模型结构估计的可靠程度。仿真结果证实了这种判据在解决系统辨识问题时的可行性。     

An adaptive empirical Bayesian thresholding procedure for analysing microarray experiments with replication

Summary.  A typical microarray experiment attempts to ascertain which genes display differential expression in different samples. We model the data by using a two-component mixture model and develop an empirical Bayesian thresholding procedure, which was originally introduced for thresholding wavelet coefficients, as an alternative to the existing methods for determining differential expression across thousands of genes. The method is built on sound theoretical properties and has easy computer implementation in the R statistical package. Furthermore, we consider improvements to the standard empirical Bayesian procedure when replication is present, to increase the robustness and reliability of the method. We provide an introduction to microarrays for those who are unfamilar with the field and the proposed procedure is demonstrated with applications to two-channel complementary DNA microarray experiments.     

Reduction of control-chart signal variablity for high-quality processes

The design of a control chart is often based on the statistical measure of average run length (ARL). A longer in-control ARL is ensured by the design, but the variance run length distribution may also be large for such a design. In practical terms, the variability in false alarms and true signals may be large. If the sample size for plotting a point is not constant, then the focus is on the average number inspected as against the ARL. This article considers two well-known attribute control chart procedures for monitoring high quality based on the number inspected, and shows how the variability in false alarms and correct signals can be reduced.     

Control chart for monitoring multivariate COM-Poisson attributes

Statistical process control of multi-attribute count data has received much attention with modern data-acquisition equipment and online computers. The multivariate Poisson distribution is often used to monitor multivariate attributes count data. However, little work has been done so far on under- or over-dispersed multivariate count data, which is common in many industrial processes, with positive or negative correlation. In this study, a Shewhart-type multivariate control chart is constructed to monitor such kind of data, namely the multivariate COM-Poisson (MCP) chart, based on the MCP distribution. The performance of the MCP chart is evaluated by the average run length in simulation. The proposed chart generalizes some existing multivariate attribute charts as its special cases. A real-life bivariate process and a simulated trivariate Poisson process are used to illustrate the application of the MCP chart.     

Nonparametric Estimation of the Geometric Vitality Function

Recently, Nair and Rajesh (2000 Nair , K. R. M. , Rajesh , G. ( 2000 ). Geometric vitality function and its application to reliability . IAPQR Tran. 25 ( 1 ): 1 – 8 . [Google Scholar]) proposed a measure to describe the failure pattern of components/devices in terms of the geometric mean of the residual life. This measure find applications in modeling life time data. In the present work we provide a nonparametric kernel-type estimator for the geometric vitality function, both in the case of complete and censored samples. The properties of the estimator, under certain regularity conditions, are studied. The performance of the estimator is compared with the empirical estimator using a real data set and simulation studies are carried out using the Monte Carlo method.     

Some Comments Regarding the Synthetic Chart

The steady-state average run length (ARL) is a function of the in-control probabilities of being in each nonabsorbing state. Davis and Woodall (2002) tabulated values that are significantly smaller than the steady-state ARLs, because they used the out-of-control probabilities. The synthetic chart signals when a second sample point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it. The side-sensitive version of the synthetic chart does not signal when the points beyond the control limits are on opposite sides. With this rule, the chart detects mean changes more quickly.