Toward identifying the source of mean shifts in multivariate SPC: a neural network approach

To identify the source(s) of process shifts under a multivariate setting is a challenging problem. Though some statistical techniques have been proposed, they are limited or restricted in their level of success and ease of use. In this paper, we propose a neural-network based identifier (NNI) to detect process mean shifts as well as indicate the variable(s) responsible for the shifts in a process where variables are correlated. Various network configurations and training strategies were investigated to develop an effective network. This research demonstrates how the NNI with a simple network structure, i.e. without any hidden layers, can perform superiorly to the Hotelling T ² chart and comparably to the MEWMA chart in detecting small to moderate shifts for bivariate processes. The run length analysis also indicates that the NNI performs much more stably than the Hotelling T ² chart and the MEWMA chart. One of the great advantages of this approach is that the proposed identifier, aided with the NNI output chart, can indicate the source(s) of the shift(s), i.e. the variable(s) responsible for the shift(s). The NNI output chart allows this monitoring scheme to easily interpret the underlying structures of the process variables.     

基于GRU神经网络的自相关过程残差控制图

为提升自相关过程监控的效率,提出基于门控循环单元(gated recurrent unit,GRU)神经网络的自相关过程残差控制图。采用受控下的自相关过程数据对GRU网络进行离线训练与测试,对预测误差进行监控,形成控制用残差控制图。采用训练好的GRU网络预测当前过程波动,利用控制用残差控制图判定当前过程是否失控。运用蒙特卡洛仿真法,与基于一阶自回归模型、BP神经网络以及支持向量回归构建的残差控制图进行性能对比。研究表明,过程受控时,所提残差控制图与其他3种的稳态平均运行链长相差不大,即4者的性能表现相当;而在均值偏移异常过程中,所提残差控制图的平均运行链长远小于其他3种,对自相关过程均值偏移具有较好的监控性能。     

A New Cumulative Sum Quality Control Scheme for Monitoring the Process Mean

A control chart is a powerful statistical process monitoring tool that is frequently used in many industrial and service organizations to monitor in‐control and out‐of‐control performances of the manufacturing processes. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recognized as potentially powerful tool in quality and management control. These control charts are sensitive to both small and moderate changes in the process. In this paper, we propose a new CUSUM (NCUSUM) quality control scheme for efficiently monitoring the process mean. It is shown that the classical CUSUM control chart is a special case of the proposed controlling scheme. The NCUSUM control chart is compared with some of the recently proposed control charts by using characteristics of the distribution of run length, i.e. average run length, median run length and standard deviation of run length. It is worth mentioning that the NCUSUM control chart detects the random shifts in the process mean substantially quicker than the classical CUSUM, fast initial response‐based CUSUM, adaptive CUSUM with EWMA‐based shift, adaptive EWMA and Shewhart–CUSUM control charts. An illustrative example is given to exemplify the implementation of the proposed quality control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

A hybrid learning-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes

In multivariate statistical process control, most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon overall statistics. But these charts do not relieve the need for pinpointing the source(s) of the out-of-control signals. In addition, these charts cannot provide more detailed process information, such as quantitative abnormal assessment values and visualisation of process changes, which would be very useful for quality practitioners to locate the assignable causes that give rise to the out-of-control situation. In this study, a hybrid learning-based model has been investigated for monitoring and diagnosing out-of-control signals in a bivariate process. In this model, a minimum quantisation error (MQE) chart based on the self-organization map (SOM) neural network (NN) was developed for monitoring process changes (i.e., mean shifts), and a selective NN ensemble approach (DPSOEN) was developed for diagnosing signals that are judged as out-of-control signals by MQE charts. The simulation results demonstrate that the proposed model outperforms the conventional multivariate control scheme in terms of average run length (ARL), and can accurately classify the source(s) of out-of-control signals. An extensive experiment is also carried out to examine the effects of six statistical features on the performance of DPSOEN.     

A New Rank‐based Multivariate CUSUM Approach for Monitoring the Process Mean

In many cases, data do not follow a specific probability distribution in practice. As a result, a variety of distribution‐free control charts have been developed to monitor changes in the processes. An existing rank‐based multivariate cumulative sum (CUSUM) procedure based on the antirank vector does not quickly detect the large shift levels of the process mean. In this paper, we explore and develop an improved version of the existing rank‐based multivariate CUSUM procedure in order to overcome the difficulty. The numerical experiments show that the proposed approach dramatically outperforms the existing rank‐based multivariate CUSUM procedure in terms of the out‐of‐control average run length. In addition, the proposed approach particularly resolves the critical problem of the original approach, which occurs in the simultaneous shifts whose components are all the same but not 0. We believe that the proposed approach can be utilized for monitoring real data. Copyright © 2015 John Wiley & Sons, Ltd.     

On mixed memory control charts based on auxiliary information for efficient process monitoring

Control charts are popular monitoring tools in statistical process control toolkit. These are used to identify assignable causes in the process parameters (location and/or dispersion). These assignable causes result in a shift in the process parameter(s). The shift can be categorized into three sizes (small, moderate, and large). Memory control charts such as the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are effective for identifying small-to-moderate shift(s) in the process. Likewise, mixed memory control charts are useful for efficient process monitoring. In this study, we have proposed two new mixed memory control charts based on auxiliary information named MxMEC and MxMCE control charts to improve the efficiency of these mixed charts. The MxMEC chart is a merger of the auxiliary information based MxEWMA chart and the classical CUSUM chart. Likewise, the MxMCE chart integrates the auxiliary information based MxCUSUM with the classical EWMA chart. The proposed MxMEC and MxMCE charts are evaluated through famous performance measures including average run length, extra quadratic loss, relative average run length, and performance comparison index. The performance of the study proposals is compared with the existing counterparts such as the classical CUSUM and EWMA, MxCUSUM, MxEWMA, MEC, MCE, and runs rules-based CUSUM charts. The comparisons revealed the superiority of the proposed charts against other competing charts particularly for small-to-moderate shifts in the process location. Finally, a real-life data is used to show the implementation procedure of the proposed charts in practical situations.     

A two-stage neural network approach for process variance change detection and classification

Statistical process control charts (SPCC) have become one of the most commonly used tools for monitoring process variability in today's manufacturing environment. Meanwhile, neural networks have been gradually recommended as alternatives to SPCC due to their superior performances, especially in the case of monitoring process mean and unnatural patterns. Little attention has been given to the use of neural networks for monitoring the process variance. This paper describes a neural network approach to monitor process variance changes and to predict change-magnitudes. The performances of the proposed neural network monitoring scheme are compared to those of SPCC for a sample size of five and for individual observations. Simulation results show that the performance of the proposed method is comparable to that of SPCC in terms of average run lengths. In addition, the proposed neural network scheme has the capability to estimate the magnitude of the variance change by combining with a bootstrap resampling scheme. A robustness test is also applied to examine the performance of the proposed scheme for observations from a non-normal distribution.     

New Synthetic EWMA and Synthetic CUSUM Control Charts for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are potentially powerful statistical process monitoring tools because of their excellent speed in detecting small to moderate persistent process shifts. Recently, synthetic EWMA (SynEWMA) and synthetic CUSUM (SynCUSUM) control charts have been proposed based on simple random sampling (SRS) by integrating the EWMA and CUSUM control charts with the conforming run length control chart, respectively. These synthetic control charts provide overall superior detection over a range of mean shift sizes. In this article, we propose new SynEWMA and SynCUSUM control charts based on ranked set sampling (RSS) and median RSS (MRSS) schemes, named SynEWMA‐RSS and SynEWMA‐MRSS charts, respectively, for monitoring the process mean. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed control charts. The run length performances of these control charts are compared with their existing powerful counterparts based on SRS, RSS and MRSS schemes. It turns out that the proposed charts perform uniformly better than the Shewhart, optimal synthetic, optimal EWMA, optimal CUSUM, near‐optimal SynEWMA, near‐optimal SynCUSUM control charts based on SRS, and combined Shewhart‐EWMA control charts based on RSS and MRSS schemes. A similar trend is observed when constructing the proposed control charts based on imperfect RSS schemes. An application to a real data is also provided to demonstrate the implementations of the proposed SynEWMA and SynCUSUM control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

On‐line Identification and Quantification of Mean Shifts in Bivariate Processes using a Neural Network‐based Approach

Many statistical process control (SPC) problems are multivariate in nature because the quality of a given process or product is determined by several interrelated variables. Various multivariate control charts (e.g. Hotelling's , multivariate cumulative sum and multivariate exponentially weighted moving average charts) have been designed for detecting mean shifts. However, the main shortcoming of such charts is that they can detect an unusual event but do not directly provide the information required by a practitioner to determine which variable or group of variables has caused the out‐of‐control signal. In addition, these charts cannot provide more detailed shift information, for example the shift magnitude, which would be very useful for quality practitioners to search the assignable causes that give rise to the out‐of‐control situation. This work proposes a neural network‐based model that can identify and quantify the mean shifts in bivariate processes on‐line. The performance evaluation performed by the simulation demonstrates that the proposed model outperforms the conventional multivariate control schemes in terms of average run length, and can accurately estimate the magnitude of the shift of each of the shifted variables in a real‐time mode. Extensive simulation is also carried out to examine the effects of correlation on the performance of the proposed model. A numerical example is presented to illustrate the usage of the proposed model. Although a mean shift identification and quantification tool for bivariate SPC is the particular application presented here, the proposed neural network‐based methodology can be applied to multivariate SPC in general. Copyright © 2006 John Wiley & Sons, Ltd.     

Design of a t‐chart using generalized multiple dependent state sampling

In this article, a new t‐chart based on generalized multiple dependent state (GMDS) sampling is proposed for efficient monitoring of a process by assuming that the time between events follows the exponential distribution. The proposed t‐chart has two pair of control limits and utilizes the past sample information with the current sample information. The control chart coefficients are estimated by considering different values of the in‐control average run lengths. The proposed t‐chart is compared with the existing chart by using the out‐of‐control average run length and extra quadratic loss function. The comparison reveals that the proposed charting strategy has better shift detection ability in process mean. An illustrative example is given for the practical implementation of the proposed chart.     

基于神经网络的SPC/EPC整合过程监测方法研究

为解决统计过程控制(SPC)/工程过程调整(EPC)整合引起的传统SPC控制图监测异常扰动效率低的问题,提出了采用神经网络技术监测SPC/EPC整合过程的策略,并对神经网络模型结构和参数设置进行分析,构建过程输入、过程输出及两者的协方差为输入参数,异常扰动发生与否为输出参数的3层神经网络模型。为验证该方法的性能,进行了大量的比较实验:即对相同的样本,分别采用Shewhar图、CUSUM图和上述神经网络模型进行监测。实验结果表明:神经网络模型能准确监测幅度大于2的阶跃扰动和大于2的过程漂移,平均运行步长(ARL)为1;传统SPC监测技术只能较准确地(监测率大于90%)监测幅度大于5的阶跃扰动和大于2的过程漂移,ARL大于2。与传统监测方法相比,该方法能快速有效地监测异常扰动的发生。     

Weighted adaptive multivariate CUSUM control charts

An adaptive multivariate cumulative sum (AMCUSUM) control chart has received considerable attention because of its ability to dynamically adjust the reference parameter whereby achieving a better performance over a range of mean shifts than the conventional multivariate cumulative sum (CUSUM) charts. In this paper, we introduce a progressive mean–based estimator of the process mean shift and then use it to devise new weighted AMCUSUM control charts for efficiently monitoring the process mean. These control charts are easy to design and implement in a computerized environment compared with their existing counterparts. Monte Carlo simulations are used to estimate the run‐length characteristics of the proposed control charts. The run‐length comparison results show that the weighted AMCUSUM charts perform substantially and uniformly better than the classical multivariate CUSUM and AMCUSUM charts in detecting a range of mean shifts. An example is used to illustrate the working of existing and proposed multivariate CUSUM control charts.     

Efficient adaptive CUSUM control charts based on generalized likelihood ratio test to monitor process dispersion shift

In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out-of-control signal against these control charts. Moreover, real-life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts.     

A magnitude‐robust control chart for monitoring and estimating step changes for normal process means

Statistical process control charts are intended to assist operators of a usually stable system in monitoring whether a change has occurred in the process. When a change does occur, the control chart should detect it quickly. If the operator can also be provided information that aids in the search for the special cause, then critical off‐line time can be saved. We investigate a process‐monitoring tool that not only provides speedy detection regardless of the magnitude of the process shift, but also supplies useful change point statistics. A likelihood ratio approach can be used to develop a control chart for permanent step change shifts of a normal process mean. The average run length performance for this chart is compared to that of several cumulative sum (CUSUM) charts. Our performance comparisons show that this chart performs better than any one CUSUM chart over an entire range of potential shift magnitudes. The likelihood ratio approach also provides point and interval estimates for the time and magnitude of the process shift. These crucial change‐point diagnostics can greatly enhance special cause investigation. Copyright © 2002 John Wiley & Sons, Ltd.     

Process monitoring for correlated gamma‐distributed data using generalized‐linear‐model‐based control charts

A model‐based scheme is proposed for monitoring multiple gamma‐distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals. Copyright © 2003 John Wiley & Sons, Ltd.     

Monitoring type‐2 censored reliability data in multistage processes

In this paper, we propose control charts to monitor the Weibull scale parameter of type‐2 censored reliability data in multistage processes. A cumulative sum control chart and 2 exponentially weighted moving average control charts based on conditional expected values are devised to detect decreases in the mean level of reliability‐related quality characteristic. The proposed control schemes are based on standard smallest extreme value distributions derived from Weibull processes to effectively account for the cascade property, which is the main characteristic of multistage processes. Subsequently, simulation study is conducted to evaluate the performance of the control charts using average run length criterion. Extra quadratic loss, performance comparison index, and relative average run length are also used to compare the detect ability of our proposed monitoring procedures. Moreover, sensitivity analysis is done to study the impact of failure number in the sample size and to investigate the robustness of the proposed monitoring procedures against the shift in the previous stage. Finally, a real case study in a glass bottle–making company is investigated to illustrate the performance of the competing control charts. The results reveal the superiority of the cumulative sum control chart.     

Phase II monitoring of general linear profiles in the presence of between‐profile autocorrelation

In this paper, an approach based on the U statistic is first proposed to eliminate the effect of between‐profile autocorrelation of error terms in Phase‐II monitoring of general linear profiles. Then, a control chart based on the adjusted parameter estimates is designed to monitor the parameters of the model. The performance of the proposed method is compared with the ones of some existing methods in terms of average run length for weak, moderate, and strong autocorrelation coefficients under different shift scenarios. The results show that the proposed method provides significantly better results than the competing methods to detect shifts in the regression parameters, while the competing methods perform better in detecting shifts in the standard deviation. At the end, the applicability of the proposed method is illustrated by an example. Copyright © 2015 John Wiley & Sons, Ltd.     

Using independent component analysis to monitor 2‐D geometric specifications

Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.     

An adaptive EWMA control chart for monitoring the process mean in Bayesian theory under different loss functions

The Shewhart control chart is used for detecting the large shift and an exponentially weighted moving average (EWMA) control chart is used for detecting the small/moderate shift in the process mean. A scheme that combines both the Shewhart control chart and the EWMA control chart in a smooth way is called the adaptive EWMA (AEWMA) control chart. In this paper, we proposed a new AEWMA control chart for monitoring the process mean in Bayesian theory under different loss functions (LFs). We used informative (conjugate prior) under two different LFs: (1) squared error loss function and (2) linex loss function for posterior and posterior predictive distributions. We used the average run length and standard deviation of run length to measure the performance of the AEWMA control chart in the Bayesian theory. A comparative study is conducted for comparing the proposed AEWMA control chart in Bayesian theory with the existing Bayesian EWMA control chart. We conducted a Monte Carlo simulation study to evaluate the proposed AEWMA control chart. For the implementation purposes, we presented a real-data example.     

智能滑模变结构控制在定长控制系统中的应用

提出了一种基于智能滑模变结构的定长自动控制系统设计方法，利用模糊神经网络在线调整滑模变结构参数，在定长控制系统中的应用表明了该方法的优越性和实用性。