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 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.     

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.     

Comparisons of control schemes for monitoring the means of processes subject to drifts

Although statistical process control (SPC) techniques have been focused mostly on detecting step (constant) mean shift, drift which is a time-varying change frequently occurs in industrial applications. In this research, for monitoring drift change, the following five control schemes are compared: the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) charts which are recommended detecting drift change in the literature; the generalized EWMA (GEWMA) chart proposed by Han and Tsung (2004) and two generalized likelihood ratio based schemes, GLR-S and GLR-L charts which are respectively under the assumption of step and linear trend shifts. Both the asymptotic estimation and the numerical simulation of the average run length (ARL) are presented. We show that when the in-control (IC) ARL is large (goes to infinity), the GLR-L chart has the best overall performance among the considered charts in detecting linear trend shift. From the viewpoint of practical IC ARL, based on the simulation results, we show that besides the GLR-L chart, the GEWMA chart offers a good balanced protection against drifts of different size. Some computational issues are also addressed.     

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.     

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.     

Using frailty models to account for heterogeneity in multistage manufacturing and service processes

Statistical process control has been widely applied to manufacturing and service operations with the aim of monitoring and improving the reliability of products. The existing monitoring procedures were introduced following the assumption that a single-stage process with independent quality characteristic is under consideration. However, in multistage processes with dependent variables, quality characteristics of interest should be optimally monitored only after they have been adjusted for the effect of influential covariates. In general, it is impossible to include all relevant covariates because measuring such values entails great financial costs. The neglect of such covariates results in having unobserved heterogeneity which dampens the detection ability of the monitoring procedure. The more complicated picture arises when the values corresponding to the reliability-related quality variable are censored due to the time and cost constraints. Thus, to deal with the effect of observed and unobserved covariates together with the censoring issue, the frailty and the proportional hazard models are used and some model-based monitoring schemes are devised. The surveillance procedures are proposed in both the presence and absence of a censoring mechanism. The performance analysis shows that the monitoring procedure based on the cumulative sum chart is superior in detecting shifts while the exponentially weighted moving average chart is effective in some cases.     

电渣重熔炉自动控制系统设计

电渣重熔的自耗电极电流大小取决于电极与渣池的距离,而该距离大小又取决于电极驱动电机的转速。只要实时测量电极的电流,对实测值和设定值进行比较,用增量式PID控制原理对电机转速进行控制,并摸索出合适的PID参数,即可获得稳定的电极电流。     

电渣重熔炉自动控制系统设计

电渣重熔的自耗电极电流大小取决于电极与渣池的距离,而该距离大小又取决于电极驱动电机的转速。只要实时测量电极的电流,对实测值和设定值进行比较,用增量式PID控制原理对电机转速进行控制,并摸索出合适的PID参数,即可获得稳定的电极电流。     

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).     

Cusums for tracking arbitrary functionals

Cusum charts are widely used for detecting deviations of a process about a target value and also for finding evidence of change in the mean of a process. The testing theory approximates the process by a Wiener process or a Brownian bridge, respectively. For quality control, it is important that other aspects are monitored in addition to or instead of the mean. Here, we show that cusum theory is easily adapted when the target is not the mean but some other aspect of the distribution.     

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.     

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。     

A new procedure for monitoring the range and standard deviation of a quality characteristic

The Shewhart and the Bonferroni-adjustment R and S chart are usually applied to monitor the range and the standard deviation of a quality characteristic. These charts are used to recognize the process variability of a quality characteristic. The control limits of these charts are constructed on the assumption that the population follows approximately the normal distribution with the standard deviation parameter known or unknown. In this article, we establish two new charts based approximately on the normal distribution. The constant values needed to construct the new control limits are dependent on the sample group size (k) and the sample subgroup size (n). Additionally, the unknown standard deviation for the proposed approaches is estimated by a uniformly minimum variance unbiased estimator (UMVUE). This estimator has variance less than that of the estimator used in the Shewhart and Bonferroni approach. The proposed approaches in the case of the unknown standard deviation, give out-of-control average run length slightly less than the Shewhart approach and considerably less than the Bonferroni-adjustment approach.     

Quality control for structural credit risk models

Over the last four decades, a large number of structural models have been developed to estimate and price credit risk. The focus of the paper is on a neglected issue pertaining to fundamental shifts in the structural parameters governing default. We propose formal quality control procedures that allow risk managers to monitor fundamental shifts in the structural parameters of credit risk models. The procedures are sequential — hence apply in real time. The basic ingredients are the key processes used in credit risk analysis, such as most prominently the Merton distance to default process as well as financial returns. Moreover, while we propose different monitoring processes, we also show that one particular process is optimal in terms of minimal detection time of a break in the drift process and relates to the Radon–Nikodym derivative for a change of measure.     

Run length distributions for estimated attributes charts

Attributes control charts, such as c and p charts, are popular methods for detecting out of control signals when it is practical only to obtain qualitative information about a process; in such cases, variables control charts, such as the , s and R charts, cannot be used. The run length distributions have previously been studied for variables charts when the control limits have been estimated. Little has been done in the case of attributes charts. In this paper, the run length distributions for the c chart and p chart are derived for the case when the control limits are estimated. It is shown that, as for variables charts, the effect of estimation on quantities such as the average run length (ARL) can be quite dramatic, but when the underlying process is in control, the ARL is potentially misleading as a basis for comparison. Received: September 1998     

Estimation in Shewhart control charts: effects and corrections

The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied.Acknowledgements. The authors would like to thank Sri Nurdiati for doing the Monte Carlo studies.     

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.     

AFT regression-adjusted monitoring of reliability data in cascade processes

Today’s competitive market has witnessed a growing interest in improving the reliability of products in both service and industrial operations. A large number of monitoring schemes have been introduced to effectively control the reliability-related quality characteristics. These methods have focused on single-stage processes or considered quality variables which are independent. However, the main feature of multistage processes is the cascade property which needs to be justified for the sake of optimal process monitoring. The problem becomes complicated when the presence of censored observations is pronounced. Therefore, both the effects of influential covariates and censored data must be taken into account while presenting a monitoring scheme. In this paper, the accelerated failure time models are used and two regression-adjusted control schemes based on Cox-Snell residuals are devised. Two different scenarios with censored and non-censored data are considered respectively. The competing control charts are compared in terms of zero-state and steady-state average run length criteria using Markov chain approach. The comparison study reveals that the cumulative sum based monitoring procedure is superior and more effective. It should be noted that the application of the proposed monitoring schemes are not restricted to manufacturing processes and thus service operations such as healthcare systems can benefit from them.     

Valuing technological synergies in mergers

Technological synergy in mergers and acquisitions (M&As) is achieved when there is an increase in value generated by combining the stock of complementary technologies of acquirers and targets, as well as utilizing target’s patents to initiate or defend lawsuits against competitors. Using U.S. patent data, we provide quantitative measures of these two sources of technological synergy. We find that these measures of technological synergy are important considerations of acquiring firms and capital market in valuing target firms’ innovative assets, as the measures are positive determinants of merger premium and total synergy gain. The expected total gains of acquirers’ and targets’ shareholders from technological synergy decrease with the difficulties of post-merger integration as proxied by geographical distance between acquirer and target. Our technological synergy measures are also good predictors of post-merger realized synergy, i.e., increase in patent outputs in the overlapped technology classes and market share.