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.     

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.     

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.     

Joint economic design of EWMA control charts for mean and variance

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi’s quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.     

Comparison of control charts for Poisson count data in health‐care monitoring

Statistical surveillance is a noteworthy endeavor in many health‐care areas such as epidemiology, hospital quality, infection control, and patient safety. For monitoring hospital adverse events, the Shewhart u‐control chart is the most used methodology. One possible issue of the u‐chart is that in health‐care applications the lower control limit (LCL) is often conventionally set to zero as the adverse events are rare and the sample sizes are not sufficiently large to obtain LCL greater than zero. Consequently, the control chart loses any ability to signal improvements. Furthermore, as the area of opportunity (sample size) is not constant over time, the in‐control and out‐of‐control run length performances of the monitoring scheme are unknown. In this article, on the basis of a real case and through an intensive simulation study, we first investigate the in‐control statistical properties of the u‐chart. Then we set up several alternative monitoring schemes with the same in‐control performances and their out‐of‐control properties are studied and compared. The aim is to identify the most suitable control chart considering jointly: the ability to detect unexpected changes (usually worsening), the ability to test the impact of interventions (usually improvements), and the ease of use and clarity of interpretation. The results indicate that the exponentially weighted moving average control chart derived under the framework of weighted likelihood ratio test has the best overall performance.     

Control charts for monitoring correlated counts with a finite range

Correlated count data processes with a finite range can be adequately described by a first‐order binomial autoregressive model. However, in several practical applications, these data demonstrate extra‐binomial variation, and a more appropriate choice is the first‐order beta‐binomial autoregressive model. In this paper, we propose and study control charts that can be used for the monitoring of these 2 processes. Practical guidelines concerning their statistical design are provided, whereas the effect of the extra‐binomial variation is investigated as well. Finally, the practical application of the proposed schemes is illustrated via a real‐data example.     

Individuals control schemes for monitoring the mean and variance of processes subject to drifts

This paper investigates control chart schemes for detecting drifts in the process mean μ and/or process standard deviation σ when individual observations are sampled. Drifts may be due to causes such as gradual deterioration of equipment, catalyst aging, waste accumulation, or human causes, such as operator fatigue or close supervision. The standard Shewhart X chart and moving range (MR) chart are evaluated, as well as several types of exponentially weighted moving average (EWMA) charts and combinations of charts involving these EWMA charts. We show that the combinations of the EWMA charts detect slow-rate and moderate-rate drifts much faster than the combined X and MR charts. We also show that varying the sampling interval adaptively as a function of the process data results in notable reductions in the detection delay of drifts in μ and/or σ.     

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.     

联合检测过程位置参数和尺度参数的非参数Cusum控制图

用于检测生产过程的多数传统控制图都假定过程的受控分布是已知的,并假定数据服从正态分布。然而在很多情况下,由于没有足够的数据来估计过程的分布,这种假定就变得不现实,而非参数控制图却不需要任何关于分布的特殊形式的假定。另外,多数的已有控制图都是使用两个单独的均值与方差控制图来同时检测生产过程.本文中,我们提出一个新的基于Cramer-von-Mises(CvM)检验的非参数累积和控制图(称为CvM图)来同时检测过程位置参数和尺度参数。文中给出了基于不同受控平均运行长度(ARL)下的CvM图的控制限,通过步长的均值、方差及分位数来研究控制图的性能表现。最后用一个实例来说明CvM图的实际应用。     

Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap

This paper considers the problem of finding limits for a statistical process control (SPC) chart for the process mean, when the process distribution is unknown. The bootstrap method estimates these limits relying on Monte Carlo methods, which are subject to simulation errors. Therefore this paper develops a computationally efficient enumeration method for exact calculations of the control limits.     

监测L\'{e}vy稳定过程均值变点的平均运行时间估计

平均运行长度(时间) (ARL)是判断一控制图监测变点效果好坏的一个重要工具\bd 本文主要研究L\'{e}vy 稳定过程的均值变点监测问题\bd 我们给出了三个控制图, 即EWMA, GEWMA和GLR的ARL 估计, 并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

自相关对常规控制图影响的模拟研究与案例分析

常规统计控制图的基本假设前提是观测值独立同分布,而在实际生产过程中,质量指标值常表现出自相关现象,违背独立性假定。本文运用平均链长(ARL)研究自相关过程为AR(1)时对常规控制图的影响,并比较了常规控制图和残差控制图对序列相关过程的控制效果。模拟结果和实例分析表明:当过程序列相关时,使用常规作图法估计出的标准差是有偏的,致使控制限设置错误和常规控制图检测能力降低。因此,在一些统计过程控制中,须考虑自相关现象并采用适当的控制图方法。     

兼顾效率和成本的ARMA控制图多目标优化设计

ARMA控制图是一种有效的自相关过程质量监控方法,为了能够同时对ARMA控制图监控方案的效率和成本进行优化,本文分别研究了ARMA控制图的平均运行长度和质量成本的计算方法,并由此建立了ARMA控制图的多目标优化设计模型。采用NSGA-Ш智能优化算法,通过一个具体的算例对该模型的计算方法进行了说明,针对不同程度的过程偏移给出了多目标优化设计的非劣解解集。然后通过灵敏度分析的方法研究了模型中的主要设计参数对监控方案的效率和成本的影响程度。最后,通过与其它几种ARMA控制图优化设计方案的比较分析,说明了本文提出的设计方法的优势。     

自相关过程的残差控制图

由于自相关过程违背了过程输出数据独立性的假定,使得传统休哈特图的有效性受到质疑。本文首先讨论控制图设计基本思想,然后分析了对自相关过程监控的残差控制图原理;进而以平均链长和各链点检出概率为准则,系统研究了AR(1)过程残差控制图的检测能力,并与休图进行了比较。最后,通过一个模拟验证了该方法的有效性。     

On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.     

Nonparametric tests for a change in the coefficient of variation

We consider the problem of testing the null hypothesis of no change against the alternative of exactly one change point when the change is expressed in terms of the value of the coefficient of variation. We propose a number of nonparametric test statistics for this problem. The asymptotic theory of the proposed tests is developed.      

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.     

On the compactness method in general ergodic impulsive control of markov processes

In this paper the impulsive control of Feller Markov processes on compact state space with long run average cost criterion is studied. Under the assumption of compactness of the resolvent operator the optimal strategies corresponding to general cost for impulses are constructed. Also the case of purely jump Markov processes is considered     

A new distribution-free adaptive sample size control chart for a finite production horizon and its application in monitoring fill volume of soft drink beverage bottles

Nonparametric control charts have received increasing attention in process monitoring. In this article, a new nonparametric sign (SN) control chart with variable sample size (VSS) for a finite horizon process is developed. The novelty of this research lies in the incorporation of the VSS technique into the nonparametric SN chart for a finite horizon process, hence, resulting in the development of a more sensitive nonparametric short run chart. The statistical performance of the new nonparametric VSS SN control chart is evaluated and compared with the existing fixed sample size (FSS) SN chart for a finite horizon process. The charts' performances are compared using the truncated average run length (TARL) and truncated standard deviation of the run length (TSDRL) criteria. The results obtained show that the nonparametric VSS SN short run chart is always quicker than the FSS SN short run chart in detecting process shifts for various underlying process distributions, hence, reducing scrap and rework cost. Finally, an application of the proposed control charting scheme is shown through a real-life example on the fill volume of soft drink beverage bottles.     

A statistical process control approach to selecting a warm-up period for a discrete-event simulation

The selection of a warm-up period for a discrete-event simulation continues to be problematic. A variety of selection methods have been devised, and are briefly reviewed. It is apparent that no one method can be recommended above any other. A new approach, based upon the principles of statistical process control, is described (SPC method). Because simulation output data are often highly autocorrelated and potentially non-normal, the batch means method is employed in constructing the control chart. The SPC method is tested on seven data sets and encouraging results are obtained concerning its accuracy. The approach is also discussed with respect to its ease of implementation, simplicity, generality of use and requirements for parameter estimation.