可变抽样区间的多变量自相关过程VAR控制图

基于批量-均值法的思想,向量自回归(VAR)控制图对多变量自相关过程的较小偏移可以进行有效控制。为了提高多变量自相关过程监控效率,本文研究可变抽样区间的VAR控制图。首先,对多变量自相关过程的VAR控制图进行可变抽样区间设计;然后,用蒙特卡洛模拟方法计算其平均报警时间;最后,以平均报警时间为评价准则,对所设计的可变抽样区间VAR控制图与固定抽样区间的VAR控制图进行比较研究。研究结果表明:所设计的可变抽样区间多变量自相关过程VAR控制图较固定抽样区间的多变量自相关过程VAR控制图能更好的监控过程的变化。     

联合监测过程位置参数和尺度参数的非参数Shewhart控制图

用于检测生产服务过程的传统控制图多数都假定过程的分布是已知的。这些控制困经常是在正态分布的假设下构建的,然而在服务质量实时监控中数据往往是非正态的。在这种情况下,基于正态分布假设的控制图的结果是不可靠的。为了解决这个问题,通常考虑非参数方法,因为在过程分布未知情况下,非参数控制图比参数图更加稳健有效。本文提出一个新的基于Van der Waerden和Klotz检验的Lepage型非参数Shewhart控制图(称为LPN图)用于同时检测未知连续过程分布的位置参数和尺度参数。文中给出了LPN图在不同参数下的控制限。依据运行长度分布的均值,方差和分位数,分析了LPN图在过程受控和失控时的性能,并与其他一些现有的非参数控制图进行比较。基于蒙特卡洛的模拟结果表明,LPN图对非正态分布具有很好的稳健性,并且在不同的过程分布下对检测位置参数和尺度参数,尤其对检测尺度参数的漂移都具有很好的性能。最后通过监控出租车服务质量说明LPN图在实际中的应用。     

具有可变抽样区间的EWMA标准差控制图

对指数加权滑动平均即EWM A标准差控制图进行了可变抽样区间设计,用M arkov-cha in方法给出了该控制图的平均报警时间的计算公式,并同固定抽样区间的常规EWM A标准差控制图进行比较,数据显示,所设计的控制图能较快的发现过程变化从而减少产品的不合格率.     

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

多元自相关过程的VAR控制图

为了解决多元自相关过程的残差T~2控制图对小偏移不灵敏的问题,本文利用批量-均值法的思想,结合VAR模型的渐近分布,设计了多元自相关过程的向量自回归(VAR)控制图.只要子组样本量足够大,VAR控制图可以对过程出现的各种偏移进行有效控制.通过对比残差T~2控制图的控制效果,得出VAR控制图对小偏移灵敏、残差T~2控制图对大偏移灵敏的结论,联合使用VAR控制图和残差T~2控制图可更有效地监控多元自相关过程。     

An approximation method to model multivariate interpolation problems: Indexing HDMR

Dealing with univariate or bivariate data sets instead of a multivariate data set is an important concern in interpolation problems and computer-based applications. This paper presents a new data partitioning method that partitions the given multivariate data set into univariate and bivariate data sets and constructs an approximate analytical structure that interpolates function values at arbitrarily distributed points of the given grid. A number of numerical implementations are also given to show the performance of this new method.     

A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems

When complex systems are monitored, multi-observations from several sensors or sources may be available. These observations can be fused through Bayesian theory to give a posterior probabilistic estimate of the underlying state which is often not directly observable. This forms the basis of a Bayesian control chart where the estimated posterior probability of the state can be compared with a preset threshold level to assess whether a full inspection is needed or not. Maintenance can then be carried out if indicated as necessary by the inspection. This paper considers the design of such multivariate Bayesian control chart where both the transition between states and the relationship between observed information and the state are not Markovian. Since analytical or numerical solutions are difficult for the case considered in this paper, Monte Carlo simulation is used to obtain the optimal control chart parameters, which are the monitoring interval and the upper control limit. A two-stage failure process characterised by the delay time concept is used to describe the underlying state transition process and Bayesian theory is used to compute the posterior probability of the underlying state, which is embedded in the simulation algorithm. Extensive examples are shown to demonstrate the modelling idea.     

Monitoring change point for diffusion parameter based on discretely observed sample from stochastic differential equation models

Stochastic differential equation (SDE) models are useful in describing complex dynamical systems in science and engineering. In this study, we consider a monitoring procedure for an early detection of dispersion parameter change in SDE models. The proposed scheme provides a useful diagnostic analysis for phase I retrospective study and develops a flexible and effective control chart for phase II prospective monitoring. A standardized control chart is constructed, and a bootstrap method is used to estimate the mean and variance of the monitoring statistic. The control limit is obtained as an upper percentile of the maximum value of a standard Wiener process. The proposed procedure appears to have a manageable computational complexity for online implementation and also to be effective in detecting changes. We also investigate the performance of the exponentially weighted mean squared control charts for the continuous SDE processes. A simulation method is used to study the empirical sizes and the average run length characteristics of the proposed scheme, which also demonstrates the effectiveness of our method. Finally, we provide an empirical example for illustration. Copyright © 2014 John Wiley & Sons, Ltd.     

可变抽样区间的二项EWMA控制图

在制造过程中,对产品的不合格品数进行监控时,通常选用计数性控制图-np图,它是基于过程服从二项分布建立的,一般对于过程中出现的较大波动效果明显。为了提高控制图对不合格品数较小波动的监控效果,本文设计了产品不合格品数服从二项分布的EWMA控制图。提出可变抽样区间的二项EWMA控制图,并采用马可夫链法计算其平均报警时间。对固定抽样区间以及可变抽样区间二项EWMA控制图对比研究,表明当过程失控时,可变抽样区间二项EWMA控制图具有较小的失控平均报警时间,能够迅速监测出过程中的异常波动,明显优于固定抽样区间的二项EWMA控制图。     

Multivariate nonparametric control chart with variable sampling interval

This paper proposes an adaptive, multivariate, nonparametric, exponentially weighted moving average control chart with variable sampling interval. A number of studies have discussed multivariate nonparametric control charts. However, the proposed multivariate nonparametric control charts usually have strict requirements. In this paper, we construct a control chart for multivariate processes that is based on the Mahalanobis depth. Specifically, we use the concept of the Mahalanobis depth to reduce each multivariate measurement to a univariate index. It is worth mentioning that this approach is completely nonparametric. We also discuss the optimal strategy for the parameters. This chart is an adaptive chart and has a variable sampling interval. A simulation study demonstrates that the proposed chart is efficient in detecting various magnitudes of shifts. A gravel data and a wine quality detection example are given to introduce the proposed control chart.     

Multivariate dynamic information

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.     

The range inter‐event process in a symmetric birth–death random walk

This paper provides new results for the range inter‐events process of a birth–death random walk. Motivations for determining and using the inter‐range event distribution have two sources. First, the analytical results we obtain are simpler than the range process and make it easier, therefore, to use statistics based on the inter‐range event process. Further, most of the results for the range process are based on long‐run statistical properties which limits their practical usefulness while inter‐range events are by their nature ‘short‐term’ statistics. Second, in many cases, data on amplitude change are easier to obtain and calculate than range and standard deviation processes. As a results, the predicted statistical properties of the inter‐range event process can provide an analytical foundation for the development of statistical tests that may be used practically. Application to outlier detection, volatility and time‐series analysis is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

EWMA control charts for autoregressive processes

Many processes must be monitored by using observations that are correlated. An approach called algorithmic statistical process control can be employed in such situations. This involves fitting an autoregressive/moving average time series model to the data. Forecasts obtained from the model are used for active control, while the forecast errors are monitored by using a control chart. In this paper we consider using an exponentially weighted moving average (EWMA) chart for monitoring the residuals from an autoregressive model. We present a computational method for finding the out-of-control average run length (ARL) for such a control chart when the process mean shifts. As an application, we suggest a procedure and provide an example for finding the control limits of an EWMA chart for monitoring residuals from an autoregressive model that will provide an acceptable out-of-control ARL. A computer program for the needed calculations is provided via the World Wide Web.     

基于马尔可夫链模型的B&L VSSI控制图的经济设计

在已有VSSI控制图基础上,本文结合B&L转换规则,提出了新的控制图运行方式。运用马尔可夫链方法,推导出新运行方式下控制图的性能指标ATS和AATS,给出了相应的费用函数。通过数值实例,本文将改进的控制图与现有的SS、VSI和VSSI控制图进行了比较分析,发现在缩短报警时间、节约费用方面,改进控制图有着明显的优势。进一步,本文运用遗传算法搜索出了改进控制图的最优参数解。     

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。     

Design of a multivariate exponentially weighted moving average control chart with variable sampling intervals

This study develops a procedure for the statistical design of the variable sampling intervals (VSI) multivariate exponentially weighted moving average (MEWMA) chart. The VSI MEWMA chart is compared with the corresponding fixed sampling interval (FSI) MEWMA chart, in terms of the steady-state average time to signal for different magnitude of shifts in the process mean vector. It is shown that the VSI MEWMA chart performs better than the corresponding standard FSI MEWMA chart for detecting a wide range of shifts in the process mean vector.     

A generally weighted moving average control chart for monitoring the coefficient of variation

This paper proposes a generally weighted moving average control chart with adjusted time-varying control limits for monitoring the coefficient of variation of a normally distributed process variable. This control chart is constructed by combining the generally weighted moving average procedure with a resetting model.The implementation of the proposed chart is presented. Some numerical comparison of the proposed chart with several relevant competing control charts is performed. In general, as demonstrated by extensive simulation results, our chart is clearly more sensitive than other competing procedures for each combination of the in-control target value of the coefficient of variation, the sample size and the shift size. Detection examples are given for two industrial manufacturing processes to introduce the proposed control chart.     

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。     

Nonparametric estimation of the spectral measure,and associated dependence measures,for multivariate extreme values using a limiting conditional representation

The traditional approach to multivariate extreme values has been through the multivariate extreme value distribution G, characterised by its spectral measure H and associated Pickands’ dependence function A. More generally, for all asymptotically dependent variables, H determines the probability of all multivariate extreme events. When the variables are asymptotically dependent and under the assumption of unit Fréchet margins, several methods exist for the estimation of G, H and A which use variables with radial component exceeding some high threshold. For each of these characteristics, we propose new asymptotically consistent nonparametric estimators which arise from Heffernan and Tawn’s approach to multivariate extremes that conditions on variables with marginal values exceeding some high marginal threshold. The proposed estimators improve on existing estimators in three ways. First, under asymptotic dependence, they give self-consistent estimators of G, H and A; existing estimators are not self-consistent. Second, these existing estimators focus on the bivariate case, whereas our estimators extend easily to describe dependence in the multivariate case. Finally, for asymptotically independent cases, our estimators can model the level of asymptotic independence; whereas existing estimators for the spectral measure treat the variables as either being independent, or asymptotically dependent. For asymptotically dependent bivariate random variables, the new estimators are found to compare favourably with existing estimators, particularly for weak dependence. The method is illustrated with an application to finance data.     

Multivariate Bayesian process control for a finite production run

Most industrial products and processes are characterized by several, typically correlated measurable variables, which jointly describe the product or process quality. Various control charts such as Hotelling’s T², EWMA and CUSUM charts have been developed for multivariate quality control, where the values of the chart parameters, namely the sample size, sampling interval and the control limits are determined to satisfy given economic and/or statistical requirements. It is well known that this traditional non-Bayesian approach to a control chart design is not optimal, but very few results regarding the form of the optimal Bayesian control policy have appeared in the literature, all limited to a univariate chart design. In this paper, we consider a multivariate Bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent, normally distributed vectors of random variables. The problem is formulated in the POMDP (partially observable Markov decision process) framework and the objective is to determine a control policy minimizing the total expected cost. It is proved that under standard operating and cost assumptions the control limit policy is optimal. Cost comparisons with the benchmark chi-squared chart and the MEWMA chart show that the Bayesian chart is highly cost effective, the savings are larger for smaller values of the critical Mahalanobis distance between the in-control and out-of-control process mean.