A distribution-free tabular CUSUM chart for autocorrelated data

A distribution-free tabular CUSUM chart called DFTC is designed to detect shifts in the mean of an autocorrelated process. The chart's Average Run Length (ARL) is approximated by generalizing Siegmund's ARL approximation for the conventional tabular CUSUM chart based on independent and identically distributed normal observations. Control limits for DFTC are computed from the generalized ARL approximation. Also discussed are the choice of reference value and the use of batch means to handle highly correlated processes. The performance of DFTC compared favorably with that of other distribution-free procedures in stationary test processes having various types of autocorrelation functions as well as normal or nonnormal marginals.     

与控制点方法论相结合的V-mask累积和控制图

V-mask累积和控制图虽然能够有效地监控过程中发生的微小偏移,但是因为它需要存储大量统计量且计算时间较长,所以在计算机中实施起来比较困难.为了解决这一问题,介绍了将控制点方法论应用于V-mask累积和控制图这一方法,并通过实例来进一步说明.结果表明,与控制点方法论结合的控制图减少了存储量,缩短了计算时间,而且将在顾客满意度控制中得到广泛应用.     

Estimating the Change Point of the Process Fraction Non‐conforming with a Monotonic Change Disturbance in SPC

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we propose a maximum‐likelihood estimator for the change point of the process fraction non‐conforming without requiring knowledge of the exact change type a priori. Instead, we assume the type of change present belongs to a family of monotonic changes. We compare the proposed change‐point estimator to the maximum‐likelihood estimator for the process change point derived under a simple step change assumption. We do this for a number of monotonic change types and following a signal from a binomial cumulative sum (CUSUM) control chart. We conclude that it is better to use the proposed change point estimator when the type of change present is only known to be monotonic. The results show that the proposed estimator provides process engineers with an accurate and useful estimate of the time of the process change regardless of the type of monotonic change that may be present. Copyright © 2006 John Wiley & Sons, Ltd.     

基于流量统计特征的端口扫描检测算法

根据网络流量的统计特征提出一种慢速端口扫描行为检测算法，以主机数和端口数的比值及被访问主机端口集合之间的相似度为基础，采用非参数累积和CUSUM算法及小波变换方法对流量统计特征进行分析，进而判断是否存在端口扫描行为。实验结果表明，所提取的网络流量特征及算法可以有效地检测异常行为，该方法和Snort相比较具有低的漏报率和误报率。     

基于累积和控制图的监控软件开发

统计过程控制是保证现代生产制造业产品或服务质量水平的重要工具。传统的统计过程控制图对于监控过程出现大波动有很好的效果,但是对于过程的小波动并不灵敏。累积和控制图对过程出现的小偏移应用累积放大原理,能够及时的发现偏移并产生报警,避免产生严重的后果。本文对累积和控制图的原理和实现工具做了说明。给出了计算机实现累积和控制图比较完整的设计方案,此方案可以完成对统计过程控制系统的搭建,实现对过程的监控预警。     

New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.     

The Generalized Synthetic Chart

Abstract

The Generalized Synthetic chart is presented and mathematical expressions for its average run length and variance of the run length are developed. The methodology is applied to the EWMA and CUSUM charts and near-optimization procedures are discussed. The synthetic EWMA and CUSUM charts are compared with their standard counterparts, the original synthetic chart, and the Shewhart chart. Significant improvements in detecting power are reported.     

Tests for change—points based on recursive u—statistics

Tests for change—points for the location as well as regression models are often based on cumulative sums of recursive residuals. These recursive residuals are also employed in the sequential detection problem. In the context of general estimable parameters (funtionals of the underlying distribution functions), such recursive residuals may be defined in terms of recursive U—statistics. A class of tests for the change—points based on recursive U—statistics has been considered. Along with some invariance principles for recursive U—statistics, asymptotic properties of the proposed tests are studied.     

ON‐LINE MONITORING OF POLLUTION CONCENTRATIONS WITH AUTOREGRESSIVE MOVING AVERAGE TIME SERIES

The concentration of aerosol particles, largely caused by traffic volume and often enhanced during temperature inversion episodes in the cold season, can be a concern for human health in the urban environment. This particulate matter is typically recorded as PM₁₀, the total mass of particles below 10 μm in diameter. It is suspected that, within the PM₁₀ class, ultrafine particles ( < 100 nm) may be responsible for causing respiratory and cardiovascular diseases. Because of their low mass, ultrafine particles are hard to detect, and researchers try to utilize PM₁₀ in combination with nitrogen oxides NO_x and other trace gases to monitor their dynamic evolution. To meet pollution standards set by national government and European Union regulation, the city of Klagenfurt, Austria, began using calcium magnesium acetate as a deicer on 11 January 2012, hoping to literally glue pollutants to the ground and thereby reducing pollution concentrations. With the statistical methodology developed in this article, the dynamic evolution of PM₁₀ and NO_x is traced for the time period starting 4 January and ending 25 January 2012, and a change in dynamics is found. The findings are based on on‐line monitoring procedures that sequentially detect structural breaks in the mean and the parameter values of an autoregressive moving average process. These are defined in terms of model residuals and one‐step ahead predictors. Theoretical properties are studied, and a simulation study shows that the proposed procedures work well in finite samples.     

Computing the Percentage Points of the Run-Length Distributions of Multivariate CUSUM Control Charts

Multivariate CUSUM control charts are often used instead of the standard Hotelling's control charts in many practical problems when detection of small shifts in the process mean is important. However, design of multivariate CUSUM control charts are usually based on the average run length (ARL). In this work, we will compute the percentage points of the run-length distributions of two multivariate CUSUM control charts. It will be shown that interpretations based on ARL can be misleading since the in-control run-length distribution of a multivariate CUSUM is highly skewed. On the other hand, the percentage points of the run-length distribution provide additional information such as the median run length, early false out-of-control signals, and the skewness of the run-length distribution for a particular scheme. These extra information might provide quality control engineers further knowledge of a particular multivariate CUSUM control chart scheme.