A Distribution-Free Multivariate Control Chart

Monitoring multivariate quality variables or data streams remains an important and challenging problem in statistical process control (SPC). Although the multivariate SPC has been extensively studied in the literature, designing distribution-free control schemes are still challenging and yet to be addressed well. This article develops a new nonparametric methodology for monitoring location parameters when only a small reference dataset is available. The key idea is to construct a series of conditionally distribution-free test statistics in the sense that their distributions are free of the underlying distribution given the empirical distribution functions. The conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point can be guaranteed to attain a specified false alarm rate. The success of the proposed method lies in the use of data-dependent control limits, which are determined based on the observations online rather than decided before monitoring. Our theoretical and numerical studies show that the proposed control chart is able to deliver satisfactory in-control run-length performance for any distributions with any dimension. It is also very efficient in detecting multivariate process shifts when the process distribution is heavy-tailed or skewed. Supplementary materials for this article are available online.     

Multivariate Control Chart for Process Dispersion Based on Individual Observations

In this paper, we will discuss a simple way for monitoring shifts in the covariance matrix of a p-dimensional multivariate normal process distribution, N_p(μ,Σ). An exact method based on the chi-square distribution for constructing multivariate control limits will also be shown. We will illustrate the proposed procedure at work based on an example.     

A Note on the Lower-Sided Synthetic Chart for Exponentials

The synthetic control chart for exponential data is discussed and an expression is derived for its average run length, as well as its design parameters. The synthetic control chart for exponentials is shown analytically to be a two-in-a-row rule. This chart is compared with the Shewhart chart for individuals and with the worst-case, lower-sided exponential EWMA and CUSUM charts. While the synthetic control chart for exponentials outperforms the Shewhart chart for individuals, the EWMA and CUSUM charts are shown to be far superior in detecting decreases in the exponential mean.     

A New Two-Sided Cumulative Sum Quality Control Scheme

A new two-sided cumulative sum quality control scheme is proposed. The new scheme was developed specifically to be generalized to a multivariate cumulative sum quality control scheme. The multivariate version will be examined in a subsequent paper; this article evaluates the univariate version. A comparison of the conventional two-sided cumulative sum scheme and the proposed scheme indicates that the new scheme has slightly better properties (ratio of on-aim to off-aim average run lengths) than the conventional scheme. Steady state average run lengths are discussed. The new scheme and the conventional two-sided cumulative sum scheme have equivalent steady state average run lengths. Methods for implementing the fast initial response feature for the new cumulative sum scheme are given. A comparison of average run lengths for the conventional and proposed schemes with fast initial response features is also favorable to the new scheme. A Markov chain approximation is used to calculate the average run lengths of the new scheme.     

The Generally Weighted Moving Average Control Chart for Detecting Small Shifts in the Process Mean

A generalization of the exponentially weighted moving average (EWMA) control chart is proposed and analyzed. The generalized control chart we have proposed is called the generally weighted moving average (GWMA) control chart. The GWMA control chart, with time-varying control limits to detect start-up shifts more sensitively, performs better in detecting small shifts of the process mean. We use simulation to evaluate the average run length (ARL) properties of the EWMA control chart and GWMA control chart. An extensive comparison reveals that the GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in the mean of a process. To enhance the detection ability of the GWMA control chart, we submit the composite Shewhart-GWMA scheme to monitor process mean. The composite Shewhart-GWMA control chart with/without runs rules is more sensitive than the GWMA control chart in detecting small shifts of the process mean. The resulting ARLs obtained by the GWMA control chart when the assumption of normality is violated are discussed.     

Increasing the Sensitivity of Multivariate EWMA Control Chart

A multivariate exponentially weighted moving average (MEWMA) control chart is used for fast detection of small shifts in multivariate statistical quality control. However, for ease of computation, the MEWMA control chart statistics are computed based on the asymptotic form of their covariance matrix in most cases. Another reason that justifies the design of the MEWMA control chart using the asymptotic covariance matrix is that the chart will be insensitive at start-up since processes are more likely to be away from the target value when the control scheme is initiated due to start-up problems. However, if initial out-of-control conditions are deemed important for quick detection, then the MEWMA statistics should be computed based on the exact covariance matrix, as it leads to a natural fast initial response for the MEWMA chart. It will also be shown in this paper the importance of computing the MEWMA statistics based on the exact form of their covariance matrix to further enhance the MEWMA control chart's sensitivity for detecting small shifts. The MEWMA statistics based on the asymptotic and the exact form of their covariance matrix will be referred to as the asymptotic and the exact MEWMA statistics, respectively. Plots and factors that simplify the design of the exact MEWMA control chart are also given.     

Alternatives to the Multivariate Control Chart for Process Dispersion

In this article, we compare the performances of six new multivariate control chart schemes for process dispersion to the standard multivariate process dispersion control chart. The six new schemes are designed by transforming the standard multivariate control chart statistic for process dispersion into a standard scale so that runs rules can be incorporated into these schemes. This article discusses a simple extension for using runs rules in a multivariate control chart for process dispersion. The extension is deemed important since the use of runs rules is always confined to univariate control charts only. The performances of the six control chart schemes together with the standard control chart are based on the computed average run length (ARL) profiles. Five of the six schemes have shown better ARL performances than the standard multivariate process dispersion control chart.     

A Neural Network Method for Modelling the Parameters of a CUSUM Chart

The cumulative sum (CUSUM) chart is widely employed in quality control to monitor a process or to evaluate historic data. CUSUM charts are designed to exhibit acceptable average run lengths both when the process is in and out of control. This paper introduces a functional technique for generating the parameters h and k for such a chart that will have specified average run lengths. It employs the method of artificial neural networks to derive the appropriate coefficients. An EXCEL spreadsheet to assist computing the parameters is presented.     

A Quality Control Chart for Work Performance Appraisal

A substantial disagreement between total quality management/Deming's principles and traditional management falls in the area of work performance appraisal. In fact, Deming ranks the traditional “evaluation of performance, merit rating, or annual review” third in his list of the Seven Deadly Diseases of the western style of management. Deming advocates argue that many of the faulty management practices in performance appraisal originate from a failure to understand variation among workers and a failure to distinguish between the “common causes” and the “special causes” of variation. Deming emphasized quality control charts as a proper tool for monitoring the stability of a system, for distinguishing the special causes from the common causes, and for detecting who among the workers is performing within the system, out of the system on the good side, or out of the system on the poor side. However, the implementation of most control charts requires that the performance ratings be quantitative on the interval scale of measurement, which may not be the case in practice. Some merit systems use ratings that are only categorical on the ordinal scale of measurement (e.g., excellent, good, fair, and poor) or rank workers by arranging them in order of merit from 1, 2, last.

Deming, however, did not show how to construct a control chart for performance appraisal when the performance ratings are reported only on the ordinal scale of measurement. In this article, we propose a quality control chart that is particularly useful in the area of performance appraisal when the workers' ratings are categorical on the ordinal scale of measurement. The proposed chart can aid managers in implementing Deming's teachings on performance appraisal. The manager will then be able to understand variation among workers and to distinguish between the “common causes” and the “special causes” affecting a certain work system. The manager can then determine who among the workers is performing within the bounds of the system, out of the system on the good side, or out of the system on the poor side.     

基于鲁棒LS-SVM的控制图模式识别

提出一种基于鲁棒最小二乘支持向量机(LS-SVM)的控制图模式识别方法,并研究其应用于过程质量诊断的可行性、有效性.理论研究和仿真试验结果表明,该方法对于标准的6种控制图模式都具有很高的模式识别率,训练模式识别器所需样本少,且训练结果泛化能力强,计算方法简单迅速.     

A New Bivariate Control Chart to Monitor the Multivariate Process Mean and Variance Simultaneously

In this article a new control chart which enables a simultaneous monitoring of both the process mean and process variance of a multivariate data will be proposed. A thorough discussion in identifying whether the process mean or variability shifts is also given. Simulation studies will be performed to study the performance of the new chart by means of its average run length (ARL) profiles. Numerous examples are also given to show how the new chart is put to work in real situations.     

基于神经网络的质量控制图模式识别技术的研究

提出了一种用于质量控制图模式识别的新的神经网络模型，它与以往的神经网络模型相比，具有较强的识别能力和较短的训练时间。     

基于投影寻踪方法的多元质量控制图

应用遗传规划方法对投影方向进行优化,得到最佳投影方向,在此基础上,分析了多元样本数据与投影数据之间的映射关系,并且验证当多元样本数据服从正态分布时,其投影也服从正态分布.可以通过对多元质量数据的投影进行控制,达到多元质量控制的目的.通过仿真对所研究的方法进行了验证.     

A Dual Purpose Cost Based Quality Control System

This paper considers the development of a cost based industrial quality control system which functions both as an acceptance sampling plan and as a means for determining an assignable cause of quality variation in the manufacturing process. The manufacturing faci1ity studied normally produces items at a relatively constant proportion defective. The facility is subject, however, to random failures in time which cause the proportion defective to shift upwards. The objective of the paper is to develop a sampling plan which minimizes the expected total annual cost of quality control by determining t)he sample size, acceptance number, and time period between successive samples. The optimization technique employed is a combination of a multivariate search technique and a partial enumeration.     

Design of Runs Rules Schemes

Runs rules are often used to increase the sensitivity of a Shewhart control chart. In this work, plots of various runs rules schemes are given to simplify the determination of control limits based on a desired in-control average run length (ARL₀).