基于回归调整CUSUM控制图的流感监测

流感事件的不可控将对公众健康构成威胁,控制图可以对流感进行监控并对流感爆发进行预警.在实际生活中,每天的流感人数不是同分布的,会受到如温度和湿度等相关因素影响,忽视这些因素可能会使控制图出现误报从而影响疾控部门的决策.考虑到这些因素,文章基于风险调整零膨胀泊松CUSUM控制图提出了一种针对于正常泊松分布的回归调整CUSUM控制图.并且通过蒙特卡洛随机模拟方法算出控制限,分析了文章提出的回归调整CUSUM控制图失控状态下的性能,并与传统CUSUM控制图进行了比较,模拟结果显示回归调整CUSUM控制图明显提高了对漂移的监测效率.最后基于文章提出的方法对香港一家医院的流感人数进行监测,并对流感爆发进行了准确的预警.     

CUSUM，GLR，GEWMA以及RFCuscore控制图监测稳定过程均值漂移的效果比较

本文给出了累积和控制图(CUSUM)监测稳定过程均值漂移的平均运行长度(ARL)的区间估计,并采用数字模拟的方法对CUSUM,GLR,GEWMA以及RFCuscore四种控制图监测稳定过程均值漂移的效果进行比较,结果显示CUSUM效果最好.     

CUSUM,GLR,GEWMA以及RFCuscore控制图监测稳定过程均值漂移的效果比较(英)

本文给出了累积和控制图(CUSUM)监测稳定过程均值漂移的平均运行长度(ARL)的区间估计,并采用数字模拟的方法对CUSUM,GLR,GEWMA以及RFCuscore四种控制图监测稳定过程均值漂移的效果进行比较,结果显示CUSUM效果最好.     

阶段Ⅱ监控手术表现的风险调整后的几何控制图（英文）

近年来,统计过程控制(SPC)己被广泛用于监测临床从业人员的表现.本文建立了两个阶段II的风险调整的几何控制图,即累积和(CUSUM)和加权似然比检验(WLRT)控制图,用来监控手术的表现.通过模拟实验,以平均运行长度(ARL)为标准,对所提出的控制图的性能进行了评估和比较.结果表明,所提出的控制图可以有效地检测到过程参数的变化.     

关于累积和(CUSUM)检验的改进

对连续检验问题，常用的检测方法有三大类其一是众所周知的Shewhartt控制图，它是最常用的对生产过程进行连续监控的控制方法，不过，如果过程均值有小的漂移(即μ-μo小)时，Shewhart控制图的检验效果不是很好，除了Shewhart控制图外，另有二类常用的控制图法，其一是累积和控制图(CUSUM)，由Page^[1]基于似然比导出，其二是指数加权移动平均控制图(EWMA)，由Roberts^[2]给出，它们已被证明在检测小的漂移时效果不错。许多人对CUSUM与EWMA进行了比较，总的来说。最好的CUSUM与最好的EWMA在检测小的漂移方面难分优劣，但CUSUM是由似然比导出的，且其平均运行长度的计算相对来说要简便些，因此，CUSUM在与EWMA的比较中更具优势，应用更广．我们分析了CUSUM的导出过程和公式。指出CUSUM有二个可以进一步改进的方面在此基础上，我们给出了二个新的累积和检验统计量及其判断难则，它们分别是PCUSUM检验统计量Pn和DCUSUM检验统计量Sn．在连续检验问题中判断一个检验方法好坏的最重要的标难是其平均运行长度比较标难是在要求具有相同的受控状态下平均运行长度ARL0的条件下，比较其失控状态下的平均运行长度ARL1，ARL1越小越好我们对PCUSUM检验和DCUSUM检验都建立了其平均运行长度ARL的计算公式．通过对CUSUM，PCUSUM，DCUSUM的平均运行长度的比较我们发现我们提出的新的累积和控制方法确比原来的CUSUM有较大改进。     

几类正态过程的CUSUM图

本文针对呈正态分布的过程数据, 讨论当过程参数$(\mu,\sigma^2)$已知或未知时单参数变化、双参数变化的过程控制问题. 针对均值未知情况,利用Quesenberry提出的$Q$统计量构造了一系列标准化的CUSUM图;对于方差未知时的复杂情形, 给出了一种构造更为简单的CUSUM图的方法;对于未知(或不关心) $(\mu,\sigma^2)$中何者变化的特殊情形, 文章提出了纯变化的概念, 给出了相应统计量及由该统计量构造的CUSUM-D图, 针对每个考虑的情形, 通过模拟计算本文给出了相应于统计量的条件期望延时(CED), 同时在文章最后给出了本文提出的CUSUM图与已有的CUSUM图($Q$图)的模拟比较, 结果表明新的CUSUM图是可行的.     

带马尔可夫均值估计量的非参数自适应CUSUM控制图

本文提供了一个带马尔可夫均值估计量的非参数自适应CUSUM控制图用于监测位置参数的持续性漂移。它可以通过马尔可夫均值估计量预测未知的漂移大小,自适应的调整控制图参数,来对不同大小的未知漂移进行一个很好的监控。这是一个自启动非参数控制图,可以用于监控开始阶段,并且不需要依赖于任何样本的分布.通过数据模拟研究显示出这个控制图不仅在各种不同分布下具有很好的稳健性,并且对各种大小的漂移都很有效。     

多元统计过程控制中的投影寻踪方法

投影寻踪（projection pursuit,简称PP）方法是通过高维数据在低维投影上的统计分析,由此充分获取高维数据本身的统计和信息的一类统计方法,并在统计过程控制中得到广泛应用,本文主要介绍利用投影寻踪方法在统计过程控制中所构造的新控制图及其优良性质,它们包括：监测线性趋势的M控制图,监测均值微小飘移的PP－CUSUM控制图以及矩链过程的多元控制图。     

基于改进加权Poisson CUSUM控制图的发病率监控研究

现代社会医疗质量管理的重要性不言而喻,如何科学有效地开展发病率监控,具有重要的研究意义和实用价值。本文主要研究加权Poisson CUSUM控制图的改进及其在发病率监控上的应用。通过引入"标准化"处理思想,即将对数似然比统计量除以对应样本容量,本文提出"标准化"对数似然比加权Poisson CUSUM控制图,用以提高对发病率的监控水平。通过设定合适的人口模型,模拟计算验证了本文设计的模型能够有效提高监控效果,且对于不同人口模型和不同加权函数均有显著优势。最后,基于美国新墨西哥州男性甲状腺癌患病数据开展的实证检验也印证了以上结论。     

监测均值变动的多重控制图方法

本文证明了当受控平均运行长度充分大时, 多重控制图有两个优点: 一是相比较GLR (广义似然比) 和GEWMA (广义指数权重移动平均)控制图它可以大大降低运算的复杂性; 二是能够较快地监测均值变化的大小. 数值模拟也表明: 多重控制图不仅优于其构成的单个控制图, 而且在监测未知的均值变动方面也优于单个的CUSUM, EWMA, 多重EWMA和GLR控制图.     

控制过程方差的CUSUMQ图及其性质

崔恒建．控制过程方差的ＣＵＳＵＭＱ图及其性质．数理统计与管理，１９９８，１７（４），３３～３８．Ｑｕｓｅｎｂｅｒｒｙ（１９９５）基于样本方差的标准化变换Φ－１［Ｈｎ－１（（ｎ－１）Ｓ２／σ２０）］提出了控制过程方差的累积和（ＣＵＳＵＭ）Ｑ控制图。本文我们描述了在控制过程方差变化中这种ＣＵＳＵＭＱ控制图的性质，并将控制图的设计方法用到单边及双边的ＣＵＳＵＭＱ图，说明它几乎是最优的。而且我们发现在控制过程方差的微小变化时，设计的ＣＵＳＵＭＱ图的性能要优于基于ｌｏｇ（Ｓ２）的ＣＵＳＵＭ和ＥＷＭＡ图     

The Monitoring of Exponentially Weighted Forecasts

By considering equivalences between various forecasting systems, the exact stochastic process followed by the one-step-ahead errors may be found. This process, the error process, is important for any monitoring scheme, and is a function of the forecasting system and the underlying data process. The error process is obtained for the most general form of exponential smoothing systems used in optimal conditions. The statistical properties are derived. In particular, the approximate variance of Trigg's smoothed error tracking signal is obtained explicitly for several exponential smoothing systems, and a procedure is given for obtaining it numerically for any such system. The use of different smoothing constants in the forecasting system and the tracking signal is discussed and it is found that suitable choice of the tracking signal constant greatly improves the performance of the signal, making it more comparable with CUSUM schemes.     

具有可变抽样区间的非正态累积和控制图

当过程存在小波动时,累积和控制图比传统的休哈特控制图监控效果灵敏。为了提高控制图的监控效率,本文针对非正态情形下的累积和控制图进行可变抽样区间设计。首先用Burr分布近似各种非正态分布,构造可变抽样区间的非正态累积和控制图;其次利用马尓可夫链方法计算其平均报警时间;最后研究结果表明, 所设计的可变抽样区间非正态累积和控制图较固定抽样区间的非正态累积和控制图能更好地监控过程的变化。     

Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance

In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose. It facilitates the determination of the charting parameters of the CUSUM charts and considerably or significantly increases their overall detection effectiveness. A single CUSUM chart (called the ABS CUSUM chart) has been developed by the holistic algorithm and fully investigated. This chart is able to detect two-sided mean shifts and increasing variance shifts by inspecting the absolute value of sample mean shift. The results of performance studies show that the overall performance of the ABS CUSUM chart is nearly as good as an optimal 3-CUSUM scheme (a scheme incorporating three individual CUSUM charts). However, since the ABS CUSUM chart is easier for implementation and design, it may be more suitable for many SPC applications in which both mean and variance of a variable have to be monitored.     

多元正态向量均值变点在线监测

在这篇文章中, 我们提出了监测多元独立向量均值变点的两种方法. 第一种方法是构造基于残差的CUSUM统计量; 第二种方法是构造基于递归残差的CUSUM统计量. 并分别得到了对应统计量的渐进分布.模拟表明本文提出的方法监测效果良好, 生产实例也说明该方法具有一定的实用性和有效性.     

On Average Run Lengths of Control Charts for Autocorrelated Processes

It is well known that statistical control charts such as Shewhart, CUSUM and EWMA charts have widespread applications in improving the quality for manufacturing and service systems. The average run length is a traditional measurement of a control chart’s performance. Usually, finding the run length distribution and the average run length is a difficult and tedious task. In this article, we develop a general and unified approach based on the use of discretization and the finite Markov chain imbedding technique to investigate the run length properties for various control charts when the process observations are autocorrelated. Numerical results are presented for illustrative purposes.     

Testing for changes in the mean or variance of long memory processes

In this paper, we study the asymptotic CUSUM tests for detecting changes in the mean or variance of a moving-average process with long memory. When there is no change over [O,T], the asymptotic distribution of the test statistic is derived, which allows us to find asymptotic critical values. When there is a change, the behavior of the test statistic is discussed. Conditions for the consistency of these tests are also discussed. Based on the asymptotic results, simulation studies of testing for changes in the mean show that the CUSUM test proposed performs well.     

A Hidden-Markov estimation method for mean-shift detection of fraction defective in production process control

This paper considers a statistical method of estimating mean shift for a fraction defective of population. One traditional method for this estimation problem has been known as the CUSUM (cumulative sum) method, and it provides a method of estimating the occurrence of a shift in the mean from the observed data. We consider this estimation problem of shift occurrence in a production process. It is assumed that the process has two states, one is good (fraction defective low) and the other bad (fraction defective high), and starts in good state with probability one. We are interested in judging when the state has moved to the bad state by analyzing the observed data.In this paper, we model such a phenomenon as a hidden-Markov model. The states which are unobservable in a hidden-Markov model can be analyzed from the sequence of observed results. Hence, the advantage of this modeling technique is that the unknown parameters which are included in the hidden states can be estimated. We compare the performance of this hidden-Markov model with the CUSUM method based on several simulation data sets.