Effect of Autocorrelation on Performance of the MCUSUM Control Chart

Control charts are designed to detect assignable causes of variation that may occur in production processes. When traditional control charts are used there is the implicit assumption that observations are independently and identically distributed over time. It is also assumed that the probability distribution representing the observations has a known functional form and is constant over time. However, in practice, observations generated by continuous as well as discrete production processes are often serially correlated. Autocorrelation not only violates the independence assumption of traditional control charts but also can affect the performance of control charts adversely. This point has received considerable attention in the past few decades. In this paper, we investigate the performance of the multivariate cumulative sum (MCUSUM) control chart in the presence of autocorrelation. Using an average run length (ARL) criterion, it is shown that autocorrelation can deteriorate the performance of MCUSUM control charts. A solution based on a time series model is presented that improves ARL properties of MCUSUM control charts. Copyright © 2005 John Wiley & Sons, Ltd.     

A Robust Bivariate Control Chart Alternative to the Hotelling's T2 Control Chart

In this paper, we proposed a new bivariate control chart denoted by based on the robust estimation as an alternative to the Hotelling's T² control chart. The location vector and the variance‐covariance matrix for the new control chart are obtained using the sample median, the median absolute deviation from the sample median, and the comedian estimator. The performance of the proposed method in detecting outliers is evaluated and compared with the Hotelling's T² method using a Monte‐Carlo simulation study. A numerical example is considered to illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A 2‐Stage Attribute‐Variable Control Chart to Monitor a Vector of Process Means

The aim of this paper is to propose a combined attribute‐variable control chart, namely M a x D  ? T ², to monitor a vector of process means μ  = [μ ₁,…,μ _q ] in a multivariate process control. The procedure consists of splitting a sample of size n into two sub‐samples of sizes n ₁ and n ₂(n  = n ₂ + n ₂), determined by an optimized process. Units of the first sub‐sample are evaluated by an attribute inspection. Using a device like a gauge ring, each unit of the first sub sample is considered approved related to the quality characteristic i if X _i ∈[ ; ]; otherwise, it is disapproved in the characteristic i , where and (obtained by an optimization) are respectively the lower and upper discriminating limits of the quality dimension X _i . If the number of disapproved items in any quality characteristic is higher than a control limit, then the measurement of the q quality characteristics is taken on each unit of the second sub‐sample and the statistic T ² is calculated. If T ² < L (L , the control limit) the process is judged as in control. The process will suffer intervention if both charts signal. The procedure has an advantage to not inspect the units of the second sub‐sample if the first sub‐sample indicates that the process is in control. This proposal shows a better performance than T ² control chart for a large number of scenarios. The two control limits and discriminant limits are optimized to reach a desired value of A R L ₀ and to minimize A R L ₁. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimal T2 Control Chart with a Double Sampling Scheme – An Alternative to the MEWMA Chart

Recent studies have shown that a double sampling (DS) scheme yields improvements in detection times of process shifts over variable ratio sampling (VRS) methods that have been extensively studied in the literature. Additionally, a DS scheme is more practical than some of the VRS methods since the sampling interval is fixed. In this paper, we investigate the effect of double sampling on cost, a criterion as important as detection rate. We study economic statistical design of the DS T² chart (ESD DS T²) so that designs are found that are economically optimal but yet meet desired statistical properties such as having low probabilities of false searches and high probabilities of rapid detection of process shifts. Through an illustrative example, we show that relatively large benefits can be achieved in a comparison with the classical T² chart and the statistical DS T² charts with our ESD DS T² approach. Furthermore, the economic performance of the ESD DS T² charts is favorably compared to the MEWMA and other VRS T² control charts in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

统计过程控制在微电脑控制器生产中的应用:案例研究

以某电子集团生产的某类型控制器的实际生产为例,采用因果分析法对其生产过程中造成质量缺陷的原因从5M1E(人、机、料、法、测、环)方面进行综合分析.通过对其测量系统进行监控,在其稳定可靠的情况下采集数据.运用SPC技术对波峰焊工序进行控制图监控,对失控原因进行分析并在线调整.有效地保证了控制器的质量,为其质量改善指明了方向.     

Statistical monitoring performance for startup operations in a feedback control system

Previously, it has been held that statistical process control (SPC) and engineering process control (EPC) were two distinct domains for process improvement. However, we specifically consider the impact for integrating the two approaches on a first‐order dynamic system with ARIMA disturbances. We show how to model and analyze this system over a range of practical conditions. Our work results in a set of response surfaces that characterize the performance of the integrated design. We also compare these results to the case where the SPC and EPC policies are applied separately. In general, we find that the EPC approach performs best in terms of minimizing error, but that we can reduce the number and magnitude of adjustments using the integrated monitoring and control approach. This work also further supports our earlier findings that the integrated design is effective on complex dynamic systems during the initial transient or startup period. Copyright © 2001 John Wiley & Sons, Ltd.     

多品种小批量生产的SPC应用研究

综述了多品种小批量生产方式的特点以及该生产方式下SPC(统计过程控制)的应用现状,指出常规控制图不适用于多品种小批量生产的问题,提出结合通用控制图、累积和(Cumulative-Sum,CUSUM)控制图和指数加权移动平均(Exponentially Weighted Moving-Averages,EWMA)控制图的解决方法,并总结出该SPC方法用于处理多品种小批量生产中微小偏差的步骤。     

An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

We evaluate the performance of the Crosier's cumulative sum (C‐CUSUM) control chart when the probability distribution parameters of the underlying quality characteristic are estimated from Phase I data. Because the average run length (ARL) under estimated parameters is a random variable, we study the estimation effect on the chart performance in terms of the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL). Previous evaluations of this control chart were conducted while assuming known process parameters. Using the Markov chain and simulation approaches, we evaluate the in‐control performance of the chart and provide some quantiles for its in‐control ARL distribution under estimated parameters. We also compare the performance of the C‐CUSUM chart to that of the ordinary CUSUM (O‐CUSUM) chart when the process parameters are unknown. Our results show that large number of Phase I samples are required to achieve a quite reasonable performance. Additionally, the performance of the C‐CUSUM chart is found to be superior to that of the O‐CUSUM chart. Finally, we recommend the use of a recently proposed bootstrap procedure in designing the C‐CUSUM chart to guarantee, at a certain probability, that the in‐control ARL will be of at least the desired value using the available amount of Phase I data. Copyright © 2015 John Wiley & Sons, Ltd.     

A Multivariate T2 Control Chart for Skewed Populations Using Weighted Standard Deviations

This paper proposes a heuristic method of constructing multivariate T² control charts for skewed populations based on ‘weighted standard deviations’, obtained by decomposing the standard deviation into upper and lower deviations according to the direction and degree of skewness. The proposed method adjusts the variance–covariance matrix of quality characteristics and modifies the ellipsoidal probability density function contour of the multivariate normal distribution to a shape similar to that of the skewed distribution. False alarm rates and out‐of‐control average run lengths of the proposed control chart are compared with those of the standard control chart for multivariate lognormal, Weibull and gamma distributions, and the results show that considerable improvement over the standard method can be achieved when the distribution is skewed. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of Parameter Estimation on the Multivariate Distribution‐free Phase II Sign EWMA Chart

Multivariate nonparametric control charts can be very useful in practice and have recently drawn a lot of interest in the literature. Phase II distribution‐free (nonparametric) control charts are used when the parameters of the underlying unknown continuous distribution are unknown and can be estimated from a sufficiently large Phase I reference sample. While a number of recent studies have examined the in‐control (IC) robustness question related to the size of the reference sample for both univariate and multivariate normal theory (parametric) charts, in this paper, we study the effect of parameter estimation on the performance of the multivariate nonparametric sign exponentially weighted moving average (MSEWMA) chart. The in‐control average run‐length (ICARL) robustness and the out‐of‐control shift detection performance are both examined. It is observed that the required amount of the Phase I data can be very (perhaps impractically) high if one wants to use the control limits given for the known parameter case and maintain a nominal ICARL, which can limit the implementation of these useful charts in practice. To remedy this situation, using simulations, we obtain the “corrected for estimation” control limits that achieve a desired nominal ICARL value when parameters are estimated for a given set of Phase I data. The out‐of‐control performance of the MSEWMA chart with the correct control limits is also studied. The use of the corrected control limits with specific amounts of available reference sample is recommended. Otherwise, the performance the MSEWMA chart may be seriously affected under parameter estimation. Copyright © 2016 John Wiley & Sons, Ltd.     

面向半导体制造业的统计过程分析与控制

传统的统计过程控制方法不能完全适应半导体制造业生产形式需要。本文在分析半导体光电封装制造模式的特点和实施过程控制所面临的问题的基础上,提出一种基于聚类分析的统计质量控制方法。通过实证分析,证实了该方法的可操作性并取得了良好的实际效果。     

Effect of Phase I Estimation on Phase II Control Chart Performance with Profile Data

This paper illustrates how phase I estimators in statistical process control (SPC) can affect the performance of phase II control charts. The deleterious impact of poor phase I estimators on the performance of phase II control charts is illustrated in the context of profile monitoring. Two types of phase I estimators are discussed. One approach uses functional cluster analysis to initially distinguish between estimated profiles from an in‐control process and those from an out‐of‐control process. The second approach does not use clustering to make the distinction. The phase II control charts are established based on the two resulting types of estimates and compared across varying sizes of sustained shifts in phase II. A simulated example and a Monte Carlo study show that the performance of the phase II control charts can be severely distorted when constructed with poor phase I estimators. The use of clustering leads to much better phase II performance. We also illustrate that the performance of phase II control charts based on the poor phase I estimators not only have more false alarms than expected but can also take much longer than expected to detect potential changes to the process. Copyright © 2014 John Wiley & Sons, Ltd.     

Simultaneous Monitoring of Sample and Group Autocorrelations

Most statistical process control (SPC) methods for detecting the presence of special causes of variation when process observations are inherently autocorrelated are focused on studying changes in the mean or variance of a time series. It is seldom emphasized in the quality literature that the presence of special causes of variation is manifested not only by the changes in mean or variance of a time series but also by the changes in its stochastic behavior. An approach to detect this type of change can be based on the sample autocorrelation function (ACF) or the Ljung-Box-Pierce portmanteau statistic applied to the residuals of the chosen time series model. In this article, we discuss the reasons why the residual ACF and portmanteau statistic give different sensitivities in terms of testing model adequacy and, hence, of detecting changes in stochastic behavior of a process. The problem is shown to be related to the multivariate SPC problem of deciding whether to monitor the individual observations using separate control charts or Hotelling's T² statistic. Here, we present a graphical scheme for simultaneously monitoring the residual ACF and the portmanteau statistic.     

A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Implementation of the Shewhart, CUSUM, and EWMA charts requires estimates of the in-control process parameters. Many researchers have shown that estimation error strongly influences the performance of these charts. However, a given amount of estimation error may differ in effect across charts. Therefore, we perform a pairwise comparison of the effect of estimation error across these charts. We conclude that the Shewhart chart is more strongly affected by estimation error than the CUSUM and EWMA charts. Furthermore, we show that the general belief that the CUSUM and EWMA charts have similar performance no longer holds under estimated parameters.     

The Design of the ARL‐Unbiased S2 Chart When the In‐Control Variance Is Estimated

The S² chart has been known as a powerful tool to monitor the variability of the normal process. When the variance of the process is unknown, it needs to be estimated by Phase I samples. It is well known that there are serious effects of parameter estimation on the performance of the S² chart based on known parameter assumption. If the effects of parameter estimation are not considered, it can lead to an increase in the number of false alarms and a reduction in the ability of the chart to detect process changes except for very small shifts in the variance. Based on the criterion of average run length (ARL) unbiased, a S² control chart is developed when the in‐control variance is estimated. The performance of the proposed control chart is also evaluated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control chart. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Cuscore control charts for generalized feedback‐control systems

The cumulative score (Cuscore) statistic is devised to ‘resonate’ with deviations or signals of an expected type. When a process signal subject to feedback control occurs, it results in a fault signature in the output error. In this paper, Cuscore statistics are designed to monitor process parameters and characteristics measured by a generalized minimum variance (GMV) feedback‐control system sensitive to the fault signature of a spike, step, and bump signal. In this study, the GMV considered is a first‐order dynamic system with autoregressive moving average (ARMA) noise. We show theoretically that the performance of Cuscore charts is independent of the amount of variability transferred from the output quality characteristic to the adjustment actions in the GMV control system. Simulation is used to test the performance using the Cuscore charts. In general, the Cuscore can detect signals over a broad range of system parameter values. However, areas of low detection capability occur for certain fault signatures. In these cases, a tracking signal test is combined with the Cuscore statistics to improve detection performance. This study provides several illustrations of the underlying behavior and shows how the methodology developed can be easily applied in practice. Copyright © 2006 John Wiley & Sons, Ltd.