Variables control chart limits and tests for special causes

Control charts are used to detect problems in control such as outliers, shifts in levels or excess variability in subgroup means that may have a special cause. This paper addresses itself to deriving control chart limits based on past data and based on initial samples in a current control situation. We present a general setting for control charts. Furthermore, an overview is given of tests for special causes. The tests are standardized so that the asymptotic type I error does not exceed a fixed level. The distributions of the run lengths of the tests and combinations of tests are also evaluated. We propose to use a low percen-tile of the run length distribution, instead of the average run length, to study the performance of the tests. These indicate that, in particular when tests are combined, the run length percentiles may be too small for practical purposes. It is shown that (nearly) exact control chart limits for observations from a normal distribution exist. The traditional limits differ considerably from the proposed ones and correspond to even smaller run length percentiles.     

Run length distributions and economic design of [`(X)]\bar X charts with unknown process variance

The run length distribution of charts with unknown process variance is analized using numerical integration. Both traditional chart limits and a method due to Hillier are considered. It is shown that setting control limits based on the pooled standard deviation, as opposed to the average sample standard deviation, provides better run length performance due to its smaller mean square error. The effect of an unknown process variance is shown to increase the area under both tails of the run length distribution. If Hillier’s method is used instead, only the right tail of the run length distribution is increased. Collani’s model for the economic design of charts is extended to the case of unknown process variance by writing his standardized objective function in terms of average run lengths.     

爱尔朗排队模型在配送中心车辆调度中的应用研究

利用随机过程和排队论的相关知识,通过对爱尔朗排队模型进行性能分析以及参数求解,给出其在配送中心中的具体应用,并通过实例求解。通过求解系统空闲的概率、系统平均队长、排队等候平均队长、车辆在配送中心中的逗留时间、平均排队时间,比较单路排队和多路排队的区别,以此判断配送中心的车辆调度系统建设是否合理。     

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.     

Run length analysis of Shewhart charts applied to drifting processes under an integrative SPC/EPC model

Engineering Process Controllers (EPC) are frequently based on parametrized models. If process conditions change, the parameter estimates used by the controllers may become biased, and the quality characteristics will be affected. To detect such changes it is adequate to use Statistical Process Control (SPC) methods. The run length statistic is commonly used to describe the performance of an SPC chart. This paper develops approximations for the first two moments of the run length distribution of a one-sided Shewhart chart used to detect two types of process changes in a system that is regulated by a given EPC scheme: i) changes in the level parameter; ii) changes in the drift parameter. If the drift parameter shifts, it is further assumed that the form of the drift process changes from a linear trend under white noise (the in-control drift model) into a random walk with drift model. Two different approximations for the run length moments are presented and their accuracy is numerically analyzed. Received: August 1998     

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.     

变样本容量比例控制图设计及应用

针对单边休哈特比例控制图失控状态下平均报警时间长的问题,提出一种单边变样本容量比例控制图来监控两个正态变量间比例的偏移。采用马尔可夫链方法计算了该控制图的平均运行链长。在保证过程处于受控状态的统计性能基础上,使失控状态下的平均运行链长最小,从而获得控制图的最优决策变量和最优性能指标。仿真结果表明,单边变样本容量比例控制图的性能明显优于单边休哈特比例控制图。最后将该方法应用于港口皮带机配煤比例监控的问题,通过仿真实验说明了该方法能够对煤炭配比过程中的比例偏移做出有效反应。     

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.     

Queue control using a historically developed stochastic model

This paper applies a stochastic model to determine the optimal or ideal average planned queue level. The ideal average planned queue level is defined to be the minimum average queue level necessary to ensure that in the long run the probability of work center idle time over a specified planning horizon is no greater than some value α chosen by management. Also discussed is the usefulness of the ideal planned queue level, not only for controlling work-in-process inventories, but also for obtaining better work center lead time estimates.     

Asymptotic confidence intervals for the length of the shortt under random censoring

A short t of a one dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a show and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note a non-parametric asymptotic confidence interval for the length of the (uniqueness is assumed) short t is established in the random censorship from the right model. The estimator of the length of the short t is based on the product-limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko-Cantelli theorem and the functional central limit theorem for the PL estimator.     

Model choice and value-at-risk estimation

Value at risk (VaR) is a commonly used tool to measure market risk. In this paper, we discuss the problems of model choice and VaR performance. The VaRs of daily returns of the Shanghai and Shenzhen indexes are calculated using equally weighted moving average (EQMA), exponentially weighted moving average (EWMA), GARCH(1,1), empirical density estimation method, and the Pareto-type extreme-value distribution methods. Considering the length of the window and the requirement for adequate capital, back testing indicates that the Pareto-type extreme-value distribution method reflects the real market risk more accurately than the other models.     

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     

Bootstrapping sequential change-point tests for linear regression

Bootstrap methods for sequential change-point detection procedures in linear regression models are proposed. The corresponding monitoring procedures are designed to control the overall significance level. The bootstrap critical values are updated constantly by including new observations obtained from the monitoring. The theoretical properties of these sequential bootstrap procedures are investigated, showing their asymptotic validity. Bootstrap and asymptotic methods are compared in a simulation study, showing that the studentized bootstrap tests hold the overall level better especially for small historic sample sizes while having a comparable power and run length.     

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.     

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.     

Learning,information processing and order submission in limit order markets

By introducing a genetic algorithm learning with a classifier system into a limit order market, this paper provides a unified framework of microstructure and agent-based models of limit order markets that allows traders to determine their order submission endogenously according to market conditions. It examines how traders process and learn from market information and how the learning affects limit order markets. It is found that, measured by the average usage of different group of market information, trading rules under the learning become stationary in the long run. Also informed traders pay more attention to the last transaction sign while uninformed traders pay more attention to technical rules. Learning of uninformed traders improves market information efficiency, but not necessarily when informed traders learn. Opposite to the learning of informed traders, learning makes uninformed traders submit less aggressive limit orders and more market orders. Furthermore private values can have significant impact in the short run, but not in the long run. One implication is that the probability of informed trading (PIN) is positively related to the volatility and the bid-ask spread.     

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。     

Should banks diversify or focus? Know thyself: The role of abilities

The paper investigates whether diversification/focus across assets, industries and borrowers affects bank performance when banks’ abilities (screening and monitoring) are considered. The initial results show that diversification (focus) at the asset, industry and borrower levels is expected to decrease (increase) returns. However, once banks’ screening and monitoring abilities are controlled for, the effect of diversification/focus either gets weaker or disappears. Further, in some cases, these abilities enhance banks’ long-run performance, but in others they prove to be costly, at least, in the short run. Thus, the level of monitoring and screening abilities should be taken into consideration in understanding, planning and implementing diversification/focus strategies.     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

The Likelihood Ratio Test for the Rank of a Cointegration Submatrix*

This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent–transitory decompositions and of subhypotheses related to neutrality and long‐run Granger noncausality. The proposed test has a chi‐squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable.