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。     

Approximation and contamination bounds for probabilistic programs

In many applications of manufacturing and service industries, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. In some situations, multiple profiles are required in order to model the quality of a product or process effectively. General multivariate linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. However, in such situations, the existing parametric profile monitoring methods suffer from a drawback in that when the profile parameter dimensionality is large, the detection ability of the procedures commonly used T ²-type charting statistics is likely to decline substantially. Moreover, it is also challenging to isolate the type of profile parameter change in such high-dimensional circumstances. These issues actually inherit from those of the conventional multivariate control charts. To resolve these issues, this paper develops a new methodology for monitoring general multivariate linear profiles, including the regression coefficients and profile variation. After examining the connection between the parametric profile monitoring and multivariate statistical process control, we propose to apply a variable-selection-based multivariate control scheme to the transformations of estimated profile parameters. Our proposed control chart is capable of determining the shift direction automatically based on observed profile data. Thus, it offers a balanced protection against various profile shifts. Moreover, the proposed control chart provides an easy but quite effective diagnostic aid. A real-data example from the logistics service shows that it performs quite well in the application.     

The efficiency of CUSUM schemes for monitoring the coefficient of variation

Continuous surveillance of the coefficient of variation is a quality control issue worthy of consideration in several manufacturing and service‐oriented companies. In this paper, we present a new method to monitor the squared coefficient of variation by means of two one‐sided cumulative sum‐type control charts. We study the run length properties of the proposed charts using a Markov chain approach. Several tables are given in order to show the sensitivity of the proposed charts for different deterministic shift sizes and their performance for the random shift size condition. The results show that the proposed control charts have attractive performance compared with some competing charts and are better in many cases. An illustrative example is discussed on a real dataset. Copyright © 2016 John Wiley & Sons, Ltd.     

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。     

Analysis of ordered categorical data to develop control charts for monitoring customer loyalty

In the highly competitive business environment of today, the cost to attract new customers is much higher than the cost required to maintain the existing ones. To keep the balance between the acquisition rate and defection rate through executing offensive and defensive marketing policies, it is required to have real time information using an efficient method to monitor customer loyalty. The relationship between customer loyalty and customer satisfaction should be kept in mind when one develops a method for loyalty monitoring. This paper presents several control charts classified in two groups based on the scale used to assess customer loyalty. In the first group of control charts, customer loyalty is considered as a binary random variable modeled by Bernoulli distribution whilst in the second group, an ordinal scale is considered to report loyalty level. Performance comparison of the proposed techniques using ARL criterion indicates that chi‐square and likelihood‐ratio control charts developed based on Pearson chi‐square statistic and ordinal logistic regression model respectively are able to rapidly detect the significant changes in loyalty behavior. To show how to apply the procedures and how to interpret their results, two illustrative synthetic cases are also explained. Copyright © 2009 John Wiley & Sons, Ltd.     

Covariate-Adjusted Nonparametric Regression for Time Series

The covariate-adjusted regression model was initially proposed for the situations where both the predictors and the response variables are not directly observed, but are distorted by some common observable covariates. In this paper, we investigate a covariate-adjusted nonparametric regression (CANR) model and consider the proposed model on time series setting. We develop a two-step estimation procedure to estimate the regression function. The asymptotic property of the proposed estimation is investigated under the -mixing conditions. Both the real data and simulated examples are provided for illustration.     

基于正态分布的逐批抽样检验贝叶斯控制图控制限研究

在生产条件受控的状态下,先验分布与后验分布应服从同一分布,在假设该分布为正态分布的前提下,根据贝叶斯理论推导出均值、极差和标准差的迭代计算公式,并依此计算控制图的控制限,使有效的先验批检验信息得到充分运用,弥补传统控制图在小批量生产环境下样本信息不足的缺点。研究发现,基于贝叶斯原理的统计控制图控制限随着检验批次的逐渐增加,更接近控制界限的实际值,比传统控制图的控制效果更加可靠、有效。     

A new control chart in contaminated data of t‐Student distribution for individual observations

Control charts are the most popular tool for monitoring production quality. In traditional control charts, it is usually supposed that the observations follow a multivariate normal distribution. Nevertheless, there are many practical applications where the normality assumption is not fulfilled. Furthermore, the performance of these charts in the presence of measurement errors (outliers) in the historical data has been improved using robust control charts when the observations follow a normal distribution. In this paper, we develop a new control chart for t‐Student data based on the trimmed T² control chart () through the adaptation of the elements of this chart to the case of this distribution. Simulation studies show that a control chart performs better than T² in t‐Student samples for individual observations. Copyright © 2012 John Wiley & Sons, Ltd.     

A hybrid wrapper–filter approach to detect the source(s) of out-of-control signals in multivariate manufacturing process

With modern data-acquisition equipment and on-line computers used during production, it is now common to monitor several correlated quality characteristics simultaneously in multivariate processes. Multivariate control charts (MCC) are important tools for monitoring multivariate processes. One difficulty encountered with multivariate control charts is the identification of the variable or group of variables that cause an out-of-control signal. Expert knowledge either in combination with wrapper-based supervised classifier or a pre-filter with wrapper are the standard approaches to detect the sources of out-of-control signal. However gathering expert knowledge in source identification is costly and may introduce human error. Individual univariate control charts (UCC) and decomposition of T²$T^2$ statistics are also used in many cases simultaneously to identify the sources, but these either ignore the correlations between the sources or may take more time with the increase of dimensions. The aim of this paper is to develop a source identification approach that does not need any expert-knowledge and can detect out-of-control signal in less computational complexity. We propose, a hybrid wrapper–filter based source identification approach that hybridizes a Mutual Information (MI) based Maximum Relevance (MR) filter ranking heuristic with an Artificial Neural Network (ANN) based wrapper. The Artificial Neural Network Input Gain Measurement Approximation (ANNIGMA) has been combined with MR (MR-ANNIGMA) to utilize the knowledge about the intrinsic pattern of the quality characteristics computed by the filter for directing the wrapper search process. To compute optimal ANNIGMA score, we also propose a Global MR-ANNIGMA using non-functional relationship between variables which is independent of the derivative of the objective function and has a potential to overcome the local optimization problem of ANN training. The novelty of the proposed approaches is that they combine the advantages of both filter and wrapper approaches and do not require any expert knowledge about the sources of the out-of-control signals. Heuristic score based subset generation process also reduces the search space into polynomial growth which in turns reduces computational time. The proposed approaches were tested by exhaustive experiments using both simulated and real manufacturing data and compared to existing methods including independent filter, wrapper and Multivariate EWMA (MEWMA) methods. The results indicate that the proposed approaches can identify the sources of out-of-control signals more accurately than existing approaches.     

Economic design of attribute np control charts using a variable sampling policy

To use a control chart, the quality engineer should specify three decision variables, namely the sample size, the sampling interval and the critical region of the chart. A significant part of recent research relaxed the constraint of using fixed design parameters to open the way to a new type of control charts called adaptive ones where at least one of the decision variables may change in real time based on the last data information. These adaptive schemes have proven their effectiveness from economical and statistical point of views. In this paper, the economic design of an attribute np control chart using a variable sampling interval (VSI) is treated. A sensitivity analysis is conducted to search for optimal design parameters minimizing the expected total cost per hour and to reveal the impact of the process and cost parameters on the behavior of optimal solutions. An economic comparison between the classical np chart, variable sample size (VSS) np control chart and VSI chart is conducted. It is found that switching from the classical attribute chart to the VSI sampling strategy results in notable cost savings and in reduction of the average time to signal and the average number of false alarms. In most cases of the sensitivity analysis, the VSI np chart outperforms the VSS np chart based on economical and statistical considerations. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

A discontinuous interpolated finite volume approximation of semilinear elliptic optimal control problems

In this article, we describe a discontinuous finite volume method with interpolated coefficients for the numerical approximation of the distributed optimal control problem governed by a class of semilinear elliptic equations with control constraints. The proposed distributed control problem involves three unknown variable: control, state and costate. For the approximation of control, we have adopted three different methodologies: variational discretization, piecewise constant and piecewise linear discretization, while the approximation of state and costate variables is based on discontinuous piecewise linear polynomials. As the resulted scheme is non‐symmetric, optimize‐then‐discretize approach is used to approximate the control problem. Optimal a priori error estimates in suitable natural norms for state, costate and control variables are derived. Moreover, numerical experiments are presented to support the derived theoretical results. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2090–2113, 2017     

稀土分离联产品质量控制研究

以稀土分离企业为背景,抽取联产品特点及质量属性,绘制单一产品的指数加权移动平均控制图和联产品的多元残差T²控制图,并将两类控制图进行对比分析,分析表明和EWMA控制图相比,联产品多元残差T²控制图能降低控制图虚发警报的概率。针对多元残差T²控制图发现的异常模式,采用支持向量机模型对异常模式进行分类处理,寻找分类规则,构造PSO-SVM分类器,运用粒子群算法对SVM参数寻优,并对得出的结果进行对比分析。分析表明该分类器能提高分类正确率,模式识别可以用于诊断稀土企业引起联产品多元残差T²控制图出现异常的原因,从而提高过程质量管理水平。     

Model-free conditional independence feature screening for ultrahigh dimensional data

Feature screening plays an important role in ultrahigh dimensional data analysis. This paper is concerned with conditional feature screening when one is interested in detecting the association between the response and ultrahigh dimensional predictors (e.g., genetic makers) given a low-dimensional exposure variable (such as clinical variables or environmental variables). To this end, we first propose a new index to measure conditional independence, and further develop a conditional screening procedure based on the newly proposed index. We systematically study the theoretical property of the proposed procedure and establish the sure screening and ranking consistency properties under some very mild conditions. The newly proposed screening procedure enjoys some appealing properties. (a) It is model-free in that its implementation does not require a specification on the model structure; (b) it is robust to heavy-tailed distributions or outliers in both directions of response and predictors; and (c) it can deal with both feature screening and the conditional screening in a unified way. We study the finite sample performance of the proposed procedure by Monte Carlo simulations and further illustrate the proposed method through two real data examples.     

Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.     

Robust sampled‐data control of uncertain switched neutral systems with probabilistic input delay

This article focuses on the robust sampled‐data control for a class of uncertain switched neutral systems based on the average dwell‐time approach. In particular, the system is considered with probabilistic input delay using sampled state vectors, which are described by the stochastic variables with a Bernoulli distributed white sequence and time‐varying norm‐bounded uncertainties. By constructing a novel Lyapunov–Krasovskii functional which involves the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities for ensuring the robust exponential stability of the uncertain switched neutral system about its equilibrium point. Moreover, based on the stability criteria, a state feedback sampled‐data control law is designed for the considered system. Finally, a numerical example based on the water‐quality dynamic model for the Nile River is given to illustrate the effectiveness of the proposed design technique. © 2015 Wiley Periodicals, Inc. Complexity 21: 308–318, 2016     

Control charts for monitoring ship operating conditions and CO2 emissions based on scalar‐on‐function regression

To respond to the compelling air pollution programs, shipping companies are nowadays setting‐up on their fleets modern multisensor systems that stream massive amounts of observational data, which can be considered as varying over a continuous domain. Motivated by this context, a novel procedure is proposed, which extends classical multivariate techniques to the monitoring of multivariate functional data and a scalar quality characteristic related to them. The proposed procedure is shown to be also applicable in real time and is illustrated by means of a real‐case study in the maritime field on the continuous monitoring of operating conditions (ie, the multivariate functional data) and total CO₂ emissions (ie, the scalar quality characteristic) at each voyage of a cruise ship. The real‐time monitoring is particularly helpful for promptly supporting managerial decision making by indicating if and when an anomaly occurs during the navigation.     

基于惩罚似然比的高维空间相关过程EWMA质量监控模型

变量选择控制图是高维统计过程监控的重要方法。针对传统变量选择控制图较少考虑高维过程空间相关性而造成监控效率低的问题,提出一种基于Fused-LASSO的高维空间相关过程监控模型。首先,利用Fused LASSO算法对似然比检验进行改进;然后,推导出基于惩罚似然比的监控统计量;最后,通过仿真模拟和真实案例分析所提监控模型的性能。仿真实验和真实案例均表明:在高维空间相关过程中,当相邻监控变量同时发生异常时,利用所提监控方法能够准确识别潜在异常变量,取得较好的监控效果。     

一种多指标质量动态控制图及其应用

研究了将多指标在一个图上标示的多指标控制图。提出了三种质量控制限并作了比较。控制上限(UCL)取Hotelling的T2统计量的α/2上侧分位数。预控上限(UPCL)取Hotelling的T2统计量的λα/2上侧分位数。当第k个观测点的T2k值超过UPCL时,则接下去的抽样区间将缩短,以便及早发现失控状态。对超出控制限的情况下如何确定哪一个质量指标发生异常的问题,提出了一种可靠的分析方法。用这种方法解决了某卷烟厂的烟丝生产过程中的多指标质量控制和管理问题。