Surveillance of the mean behavior of multivariate time series

In this paper several cumulative sum (CUSUM) charts for the mean of a multivariate time series are introduced. We extend the control schemes for independent multivariate observations of crosier [ Technometrics (1988) Vol. 30, pp. 187–194], pignatiello and runger [ Journal of Quality Technology (1990) Vol. 22, pp. 173–186], and ngai and zhang [ Statistica Sinica (2001) Vol. 11, pp. 747–766] to multivariate time series by taking into account the probability structure of the underlying stochastic process. We consider modified charts and residual schemes as well. It is analyzed under which conditions these charts are directionally invariant. In an extensive Monte Carlo study these charts are compared with the CUSUM scheme of theodossiu [ Journal of the American Statistical Association (1993) Vol. 88, pp. 441–448], the multivariate exponentially weighted moving-average (EWMA) chart of kramer and schmid [ Sequential Analysis (1997) Vol. 16, pp. 131–154], and the control procedures of bodnar and schmid [ Frontiers of Statistical Process Control (2006) Physica, Heidelberg]. As a measure of the performance, the maximum expected delay is used.     

Monitoring the cross-covariances of a multivariate time series

In this paper sequential procedures are proposed for jointly monitoring all elements of the covariance matrix at lag 0 of a multivariate time series. All control charts are based on exponential smoothing. As a measure of the distance between the target values and the actual values the Mahalanobis distance is used. It is distinguished between residual control schemes and modified control schemes. Several properties of these charts are proved assuming the target process to be a stationary Gaussian process. Within an extensive Monte Carlo study all procedures are compared with each other. As a measure of the performance of a control chart the average run length is used. An empirical example about Eastern European stock markets illustrates how the autocovariance and the cross-covariance structure of financial assets can be monitored by these methods.     

基于Wilcoxon秩和检验的多元非参数控制图

在统计过程控制(SPC)中,对多元数据的监测仍然是一个重要且具有挑战性的问题。当缺乏或有限的关于潜在过程分布的认知时,特别是当过程测量是多变量的时候,非参数控制图在统计过程控制(SPC)中是有用的。文章基于Wilcoxon秩和检验结合广义加权移动平均(GWMA)控制方案来制定图表统计量,得到一个新的多元非参数控制图,用于监测多元数据的位置参数变化。文章的理论和数值研究表明,所提出的控制图能够为任意数据分布位置偏移检测提供令人满意的性能。     

Industrial statistics and its recent contributions to total quality in the Netherlands

The use of statistical methods in quality management has a long history. Most of the pioneers, such as Walter A. Shewhart and W. Edwards Deming, refer to themselves as statisticians. Statistical thinking in industry means that all work is a series of interconnected processes, that all processes show variation, and that a reduction in variation is the key for continuous improvement. In the statistical literature we find several approaches to achieve this: quality by inspection, quality by process control and quality by design. In this paper we give a survey of the contributions of Dutch statisticians during the last five years.     

Using On-Line Process Data to Improve Quality: Challenges for Statisticians*

In the process industries measurements on a large number of process variables are routinely collected at regular intervals by on-line computers. This paper makes a case for incorporating these process variables into Statistical Process Control (SPC) schemes. Multivariate statistical methods such as Principal Component Analysis (PCA) and Partial Least Squares (PLS) can be used to project these data down into low dimensional spaces where analysis, monitoring and diagnosis are easily performed. Strong justifications for taking this approach are presented and examples are given. The statistical process control community has been slow in adapting to the data explosion brought about by the computer era. It has continued to stick with traditional control charts on the quality variables and ignored this rich source of additional information on the process. This paper explores some of the reasons for this and argues that the SPC community must adapt rapidly or lose control of the field to scientists and engineers. The paper also tries to induce statisticians into looking more seriously at the many unsolved problems in this area of reduced rank multivariate statistics.     

Control Charts for One-sided Capability Indices

There are many industrial product characteristics are desired to be the bigger the best and the smaller the best. The two well-know processes capability indices C _pl and C _pu, which measure larger-the-better and smaller-the-better process capabilities. Obviously, the formulae for the two indices C _pl and C _pu are easy to understand and straightforward to apply. Thus, indices C _pl and C _pu have been utilized by a number of Japanese companies and the U.S. automotive industry by Ford Motor Company. Boyles (1991, Journal of Quality Technology. 23: 17–26) and Spring (1995, Total Quality Management 6(3): 427–438.) point out that as soon as and S control charts are in statistical control, the control charts of process capability indices can be used to monitor the quality of process. In the previous, we know that if the process is not in control, the process capability index control chart can be used to monitor the differences of process capability, and as soon as the process is in control the stable process capability can be identified. Therefore, process capability index control chart not only can be used to monitor the stability of process’s quality but also can be used to monitor the quality of process. Since Boyles (1991, Journal of Quality Technology 23: 17–26.) and Spiring (1995, Total Quality Management 6(1): 21–33.) had had research about control chart of the bilateral specification index C _pm., but there are many kinds of products, which meet unilateral quality specification. Therefore, we will construct the control chart of unilateral specification index C _pl and C _pu to monitor and evaluate the stability of process and process capability.     

Extending monitoring methods to textual data: a research agenda

Textual data has become increasingly common in business analytic data sets. While concept-based text mining offers a method of extracting meaningful information from text data, methods for monitoring of customer perceptions of business processes and products that are discussed in customer-generated documents are not immediately available. We explore the results of two text-mining algorithms and review issues observed in the data that affect uploading the results onto a newly proposed methodological monitoring platform analogous to statistical process control charts. Finally, we discuss several topics for future research in text mining.     

Economic Process Management and Its Application on Bank Industry

A renewal equation approach is proposed to derive the multiple special-cause cost model for a system with two dependent subprocesses. The economic individual X control chart and simple cause-selecting control chart are thus constructed to monitor the two subprocesses. They may be used to maintain the whole process with minimum cost and effectively distinguish which component of the subprocesses is out of control. The economic design parameters of these two control charts can be determined by minimizing the cost model using a simple grid search method. An example of its application on controlling service quality in the bank industry is given to illustrate the design procedure and its application. It shows that these control charts may be used to control not only manufacturing dependent subprocesses but also service organisations with dependent subprocesses.     

Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.     

Performance assessment and improvement of control charts for statistical batch process monitoring

This paper describes the concepts of statistical batch process monitoring and the associated problems. It starts with an introduction to process monitoring in general which is then extended to batch process monitoring. The performance of control charts for batch process monitoring is discussed by means of two performance indices: the overall type I error and the action signal time. Problems associated with the existing approach are discussed and highlighted. Improvements are suggested and checked with the performance indices. To evaluate the effect of the proposed improvements as well as to assess the performance of the existing approach, an industrial batch production process is used.     

Monitoring process mean level using auxiliary information

In this study, a Shewhart‐type control chart is proposed for the improved monitoring of process mean level (targeting both moderate and large shifts which is the major concern of Shewhart‐type control charts) of a quality characteristic of interest Y. The proposed control chart, namely the M_r chart, is based on the regression estimator of mean using a single auxiliary variable X. Assuming bivariate normality of (Y, X), the design structure of M_r chart is developed for phase I quality control. The comparison of the proposed chart is made with some existing control charts used for the same purpose. Using power curves as a performance measure, better performance of the proposedM_r chart is observed for detecting the shifts in mean level of the characteristic of interest.     

Why and how to use vector autoregressive models for quality control: the guideline and procedures

While quality control on multivariate and serially correlated processes has attracted research attentions, a number of very detailed problems need to be overcome in order to construct practical control charts. We suggest guidelines for construction of control charts based on vector autoregressive (VAR) residuals. We discuss why VAR model is reasonable for real processes in nature, the use of VAR models to approximate multivariate serially correlated processes, residual estimation, selecting the number of variables, and selecting appropriate orders, among other issues. In addition, we illustrate an example employing VAR techniques to approximate a multivariate process previously examined and construct a control chart to monitor residuals. Last, we illustrate the potential development and use of the VAR residual chart to assist quality control and improvement.     

Health Effects of Air Pollution: A Statistical Review

We critically review and compare epidemiological designs and statistical approaches to estimate associations between air pollution and health. More specifically, we aim to address the following questions:

• 1 Which epidemiological designs and statistical methods are available to estimate associations between air pollution and health?
• 2 What are the recent methodological advances in the estimation of the health effects of air pollution in time series studies?
• 3 What are the the main methodological challenges and future research opportunities relevant to regulatory policy?

In question 1, we identify strengths and limitations of time series, cohort, case‐crossover and panel sampling designs. In question 2, we focus on time series studies and we review statistical methods for: 1) combining information across multiple locations to estimate overall air pollution effects; 2) estimating the health effects of air pollution taking into account of model uncertainties; 3) investigating the consequences of exposure measurement error in the estimation of the health effects of air pollution; and 4) estimating air pollution‐health exposure‐response curves. Here, we also discuss the extent to which these statistical contributions have addressed key substantive questions. In question 3, within a set of policy‐relevant‐questions, we identify research opportunities and point out current data limitations.     

Developing a multivariate approach to monitor fuzzy quality profiles

Referring to several applications in which the response quality characteristic is fuzzy, this paper studies how the profile functional relationship between a fuzzy response variable and a predictor variable can be monitored by using a fuzzy regression model which is referred to as profile. The purpose of this paper is to develop a multivariate approach for monitoring process/product fuzzy quality profiles in phase I for applications where the quality characteristic is linguistic, imprecise, vague or deficient. The multivariate approach includes three fuzzy multivariate control charts which are developed by using fuzzy set theory to monitor fuzzy profiles in order to achieve an in-control process. The performance of developed approach is investigated on the basis of signal probability in various out-of-control scenarios through a simulation study. Compared with univariate approach, the results indicate a good performance of our multivariate approach in detecting all sized shifts in process profiles. A real case in tourism industry is utilized to show the applicability of the proposed approach.     

A process control method based on five-parameter generalized lambda distribution

The use of control charts in statistical quality control, which are statistical measures of quality limits, is based on several assumptions. For instance, the process output distribution is assumed to follow a specified probability distribution (normal for continuous measurements and binomial or Poisson for attribute data) and the process supposed to be for large production runs. These assumptions are not always fulfilled in practice. This paper focuses on the problem when the process monitored has an output which has unknown distribution, or/and when the production run is short. The five-parameter generalized lambda distributions (GLD) which are subject to estimating data distributions, as a very flexible family of statistical distributions is presented and proposed as the base of control parameters estimation. The proposed chart is of the Shewhart type and simple equations are proposed for calculating the lower and upper control limits (LCL and UCL) for unknown distribution type of data. When the underlying distribution cannot be modeled sufficiently accurately, the presented control chart comes into the picture. We develop a computationally efficient method for accurate calculations of the control limits. As the vital measure of performance of SPC methods, we compute ARL’s and compare them to show the explicit excellence of the proposed method.     

Economically optimalc- andnp-control charts

In v. Collani (1981, 1986, 1987a and 1987b) simple procedures are developed to determine the approximately optimal economic design of control charts for measurements. Applying these procedures to the case of control charts for attributes, nomograms are obtained from which the approximately optimal design ofc-charts, i.e. charts for defects, is readily available. Furthermore it is shown that this method also provides good approximately optimalnp-charts, i.e. charts for defectives. Research supported by the DFG (Deutsche Forschungsgemeinschaft).     

Analysing Multivariate Spatial Point Processes with Continuous Marks: A Graphical Modelling Approach

This paper discusses the application of graphical modelling in the statistical analysis of marked point patterns. We consider a multivariate planar point process with quantitative marks. After a survey of statistical methods for marked point processes, a new graphical model is presented. The sub‐processes of marked points with identical discrete marks are identified with nodes of a graph, which is used to describe aspects of the spatial relationship: If two sub‐patterns are similar, then an arc is made between the corresponding nodes. Similarity is defined based on spectral densities, which makes the computations efficient. The resulting graph presents all these pairwise similarities simultaneously. We demonstrate the application of our method in the analysis of a multi‐species forest, where the points are tree locations, the discrete marks tree species and the quantitative marks are the diameters at breast height.     

企业物流成本控制模式研究

本文系统回顾了关于企业物流成本控制的文献并对其进行整理,针对物流成本的控制模式进行了归纳总结。归纳出其中三种重要的控制模式:基于会计核算方法的物流成本控制,基于供应链管理的物流成本控制以及从战略角度进行的物流成本控制。基于此,本文对现有研究的特点和局限性进行了分析、总结,并展望其未来可能的研究趋向,以期为国内相关研究提供参考。     

Self-adapting control charts

When the distributional form of the observations differs from normality, standard control charts are often prone to serious errors. Such model errors can be avoided by using (modified) nonparametric control charts. Unfortunately, these control charts suffer from large stochastic errors caused by estimation. In between these two types are the so-called parametric control charts. All three of them, as well as a combined chart, which chooses one of the three control charts according to the appropriate model assumption on the underlying distribution are discussed in this paper. The data indicate which of the three control charts to select. Readymade formulas for the several control charts are presented accompanied by an application on real data. Apart from bias removal, criteria based on exceedance probability and semi-variance are investigated.     

On multivariate higher order von Mises expansions

In this paper we review the von Mises calculations of higher order for statistical functionals of one variable. For the functionals of several variables, the higher order Gateaux differentials are defined leading to the corresponding multivariate higher order von Mises expansions. These expansions are used to analyze the bias of the corresponding statistical functionals. The second and third order derivatives are computed for M-estimates. Applications of these expansions to study the bias of M-estimates of location and to simultaneous M-estimates of location and scale are also given. Received: July 2000