A Double Moving Average Control Chart

The double exponentially weighted moving average (DEWMA) technique has been investigated in recent years for detecting shifts in the process mean and has been shown to be more efficient than the corresponding exponentially weighted moving average (EWMA) technique. In this article, we extend the DEWMA technique of performing exponential smoothing twice to the double moving average (DMA) technique by computing the moving average twice. Using simulation, we show that our proposed DMA chart improves upon the ARL performance of the moving average (MA) chart in detecting mean shifts of small to moderate magnitudes. It is also shown through simulation that, generally, the DMA charts with spans, w = 10 and 15 provide comparable average run length (ARL) performances to the EWMA and cumulative sum (CUSUM) charts, designed for detecting small shifts.     

关于单变量统计过程控制图某些研究结果简介

文章仅对一元连续变量的静态与动态控制图研究现状进行了简单的总结和介绍,并给出了较详细的参考文献,希望为国内开展此方向的研究抛砖引玉。     

Dual Nonparametric CUSUM Control Chart Based on Ranks

In this article, we provide a sequential rank-based dual nonparametric CUSUM (DNC) control chart for detecting arbitrary magnitude of shifts in the location parameter. It is a self-starting scheme and thus can be used to monitor processes at the start-up stages. Moreover, we do not require any prior knowledge of the underlying distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitudes of shifts. An illustrative example is given to introduce the implementation of our proposed DNC control chart. It is easy to construct and fast to compute.     

The Run Sum R Chart with Fast Initial Response

A fast initial response (FIR) feature for the run sum R chart is proposed and its ARL performance estimated by a Markov chain representation. It is shown that this chart is more sensitive than several R charts with runs rules proposed by different authors. We conclude that the run sum R chart is simple to use and a very effective tool for monitoring increases and decreases in process dispersion.     

Some Comments Regarding the Synthetic Chart

The steady-state average run length (ARL) is a function of the in-control probabilities of being in each nonabsorbing state. Davis and Woodall (2002) tabulated values that are significantly smaller than the steady-state ARLs, because they used the out-of-control probabilities. The synthetic chart signals when a second sample point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it. The side-sensitive version of the synthetic chart does not signal when the points beyond the control limits are on opposite sides. With this rule, the chart detects mean changes more quickly.     

A Sum of Squares Generally Weighted Moving Average Control Chart

In this article, we propose a new control chart called the sum of squares generally weighted moving average (SS-GWMA) control chart to simultaneously detect both the increase and decrease in the mean and/or variability. This new scheme is compared with the sum of squares exponentially weighted moving average (SS-EWMA) control chart. A simulation study is conducted to show that SS-GWMA control charts outperform SS-EWMA charts, in terms of the average run length (ARL), standard deviation of run length (SDRL), and diagnostic abilities. The design of SS-GWMA control charts is also discussed.     

Performance comparison of some likelihood ratio-based statistical surveillance methods

Using Markov chain representations, we evaluate and compare the performance of cumulative sum (CUSUM) and Shiryayev–Roberts methods in terms of the zero- and steady-state average run length and worst-case signal resistance measures. We also calculate the signal resistance values from the worst- to the best-case scenarios for both the methods. Our results support the recommendation that Shewhart limits be used with CUSUM and Shiryayev–Roberts methods, especially for low values of the size of the shift in the process mean for which the methods are designed to detect optimally.     

Modified Group Runs Control Charts to Detect Increases in Fraction Non Conforming and Shifts in the Process Mean

The nonparametric two-sample bootstrap is employed to compute uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, and so on. In this framework, the bootstrap variability was empirically studied without a normality assumption, exhaustively in five scenarios involving both high- and low-accuracy matching algorithms. With a tolerance 0.02 of the coefficient of variation, it was found that 2000 bootstrap replications were appropriate for ROC analysis on large datasets in order to reduce the bootstrap variance and ensure the accuracy of the computation.     

Effect of Inspection Error on Out-of-Control Average Run Length of CUSUM Charts

The cumulative sum (CUSUM) chart is commonly used for detecting small or moderate shifts in the fraction of defective manufactured items. However, its construction relies on the error-free inspection assumption, which can seldom be met in practice. In this article, we discuss the construction of an upward CUSUM chart in the presence of inspection error, study the effects of inspection error on the out-of-control ARL of the CUSUM chart, and present a formula for determining the sampling size that compensates for the effect of inspection error on the out-of-control ARL.     

Evaluation of control charts under linear trend

The performance of several control charting schemes is studied when the process mean changes as a linear trend. The control charts considered include the Shewhart chart, the Shewhart chart supplemented with runs rules, the cumulative sum (CUSUM) chart, the exponentially weighted moving average (EWMA) chart, and a generalized control chart.     

Grey Predictive Process Control Charts

The present article intends to develop some imputation methods to reduce the impact of non response at both the occasions in two-occasion successive (rotation) sampling. Utilizing the auxiliary information, which is only available at the current occasion, estimators have been proposed for estimating the population mean at the current occasion. Estimators for the current occasion are also derived as a particular case when there is non response either on the first occasion or second occasion. Behaviors of the proposed estimators are studied and their respective optimum replacement policies are also discussed. To study the effectiveness of the suggested imputation methods, performances of the proposed estimators are compared in two different situations, with and without non response. The results obtained are demonstrated with the help of empirical studies.     

On the Run Length of a State-Space Control Chart for Multivariate Autocorrelated Data

The literature on statistical process control (SPC) describes the negative effects of autocorrelation in terms of the increase in false alarms. This has been treated by the individual modeling of each series or the application of VAR models. In the former case, the analysis of the cross correlation structure between the variables is altered. In the latter, if the cross correlation is not strong, the filtering process may modify the weakest relations. In order to improve these aspects, state-space models have been introduced in multivariate statistical process control (MSPC). This article presents a proposal for building a control chart for innovations, estimating its average run length to highlight its advantages over the VAR approach mentioned above.     

两个系统因素影响下的联合动态均值图

本文研究了两个系统因素下过程控制中样本容量和抽样区间的联合动态均值图（VSSI）,并利用马氏链方法研究了动态均值图的性质。结果表明：VSSI图比VSS图,VSI图及FSSI图能更快地发现过程均值的漂移,因此,VSSI图对于快速检测遭受不同类型系统因素的过程更加有效,且对均值的敏感性增加,最后给出了联合动态均值图在生产中的一个应用实例。     

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.     

Economic Design of Cumulative Sum Control Charts for Monitoring a Process with Correlated Samples

The underlying assumption for the design of control charts is the measurements within a sample are independently distributed. However, there are many situations where the uncorrelation assumption may be unacceptable in practice. In this paper, the economic design of cumulative sum (CUSUM) control chart for correlated data within a sample is developed. The genetic algorithm is applied to find the optimal design parameters of the CUSUM control chart by minimizing the cost function. An illustrative example is given. A sensitivity analysis is then conducted to evaluate the effects of cost parameters, process parameters, and correlation coefficient on the economic design.     

A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this article, we provide a sequential rank-based nonparametric adaptive EWMA (NAE) control chart for detecting the persistent shift in the location parameter. This NAE chart is a self-starting scheme and thus can be used to monitor processes at the start-up stages rather than waiting for the accumulation of sufficiently large calibration samples. Moreover, we do not require any prior knowledge of the underlying distribution, and to prespecify any tuning parameter either. A Markov chain model is suggested to calibrate the run-length distribution of NAE, which is shown to have approximate tail probability as a geometric distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitude of shifts. A real-data example from manufacturing shows that it performs quite well in practical applications.     

Adaptive Hotelling's T 2 Control Charts with Run Rules

This study investigates the statistical properties of the adaptive Hotelling's T ² charts with run rules in which the sample size and sampling interval are allowed to vary according on the current and past sampling points. The adaptive charts include variable sample size (VSS), variable sampling interval (VSI), and variable sample size and sampling interval (VSSI) charts. The adaptive Hotelling's T ² charts with run rules are compared with the fixed sampling rate Hotelling's T ² chart with run rules. The numerical results show that the VSS, VSI, and VSSI features improve the performance of the Hotelling's T ² chart with run rules.