Multivariate Statistical Process Control Based on Principal Component Analysis (MSPC-PCA): Some Reflections and a Case Study in an Autobody Assembly Process

In modern manufacturing processes, massive amounts of multivariate data are routinely collected through automated in-process sensing. These data often exhibit high correlation, rank deficiency, low signal-to-noise ratio and missing values. Conventional univariate and multivariate statistical process control techniques are not suitable to be used in these environments. This article discusses these issues and advocates the use of multivariate statistical process control based on principal component analysis (MSPC-PCA) as an efficient statistical tool for process understanding, monitoring and diagnosing assignable causes for special events in these contexts. Data from an autobody assembly process are used to illustrate the practical benefits of using MSPC-PCA rather than conventional SPC in manufacturing processes.     

Autocorrelated SPC for Non‐Normal Situations

The importance of statistical process control (SPC) techniques in quality improvement is well recognized in industry. However, most conventional SPC techniques have been developed under the assumption of independent, identically and normally distributed observations. With advances in sensing and data capturing technologies, large volumes of data are being routinely collected from individual units in manufacturing industries. These data are often autocorrelated and skewed. Conventional SPC techniques can lead to false alarms or other types of poor performance monitoring of such data. There is a great need for process control techniques for variation reduction in these environments. Much recent research has focused on the development of appropriate SPC techniques for autocorrelated data, but few studies have considered the impact of non‐normality on these techniques. This paper investigates the effect of skewness on conventional autocorrelated SPC techniques, and provides an effective approach based on a scaled weighted variance approach to improve SPC performance in such an environment. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Comprehensive control charting applied to chromatography

Multivariate statistical process control (MSPC) based for example on principal component analysis (PCA) can make use of the information contained in multiple measured signals simultaneously. This can be much more powerful in detecting variations due to special causes than conventional single variable statistical process control (SPC). Furthermore, the PCA based SPC simplifies monitoring as it limits the number of control charts to typically two charts rather than one for each signal. However, the derived MSPC statistics may suffer from lack of sensitivity if only one or a few variables deviate in a given situation. In this paper we develop a new comprehensive control (COCO) chart procedure that considers both univariate statistics and multivariate statistics derived from PCA in a single plot that allows easy visualization of the combined data from a univariate and multivariate point of view. The method is exemplified using twenty analytical chromatographic peak areas obtained for purity analysis of a biopharmaceutical drug substance. The new control chart procedure detected two different types of faulty events in this study.     

Nonlinear Profile Monitoring of Reflow Process Data Based on the Sum of Sine Functions

In most statistical process control (SPC) applications, it is often assumed that the quality of a process or product can be adequately represented by the distribution of a univariate quality characteristic. However, in some particular situations, the quality‐related response of interest is not a single variable but a function of some independent variables. Such a functional relationship is called a profile. Recently, profile monitoring has drawn considerable attention in the statistical process control literature. This article proposes a new approach for the reflow process data, which applies the sum of sine functions to model the nonlinear profiles and then the vector of parameter estimates is monitored using the Hotelling T² and metric control charts. Through an actual data set of the reflow process, the proposed approach is compared with the polynomial regression approach in phase I and phase II analyses. The experimental results show that the proposed approach demonstrates good abilities to detect outlying profiles in phase I and provides better out‐of‐control average run length performances than the polynomial regression approach in phase II. Copyright © 2012 John Wiley & Sons, Ltd.     

Economic design of the integrated multivariate EPC and multivariate SPC charts

The goal of engineering process control (EPC) is to minimize variability by adjusting some manipulative process variables. The goal of statistical process control (SPC) is to reduce variability by monitoring and eliminating assignable causes of variation. As suggested by Box and Kramer and others, it is possible to reduce both special cause and common cause variations by integrating EPC and SPC. In the integrated multivariate EPC (MEPC) and multivariate SPC (MSPC) charts, we propose some statistical and economic criteria, such as the average Euclidean distance from the target vector and the average quality cost (AQC) to evaluate the performance of the MEPC/MSPC charts. The traditional average run length (ARL), average Euclidean distance and AQC of three MSPC charts are investigated and compared. The results of the simulations show that the MEPC/MGWMA chart is more effective and more economical than both the MEPC/MEWMA chart and the MEPC/Hotelling multivariate chart in detecting small shifts of the mean vector. Copyright © 2006 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.     

Effect of non‐normality on the monitoring of simple linear profiles

In some statistical process control (SPC) applications, it is assumed that a quality characteristic or a vector of quality characteristics of interest follows a univariate or multivariate normal distribution, respectively. However, in certain applications this assumption may fail to hold and could lead to misleading results. In this paper, we study the effect of non‐normality when the quality of a process or product is characterized by a linear profile. Skewed and heavy‐tailed symmetric non‐normal distributions are used to evaluate the non‐normality effect numerically. The results reveal that the method proposed by Kimtextitet al. (J. Qual. Technol. 2003; 35 :317–328) can be designed to be robust to non‐normality for both highly skewed and heavy‐tailed distributions. Copyright © 2010 John Wiley & Sons, Ltd.     

Statistical monitoring and diagnosis of automatic controlled processes using dynamic PCA

As manufacturing quality has become a decisive factor in competing in a global market, statistical quality techniques such as statistical process control (SPC) are becoming very popular in industries. With advances in sensing and data capture technology, large volumes of data are being routinely collected in automatic controlled processes. There is a growing need for SPC monitoring and diagnosis in these environments, but an effective implementing scheme is still lacking. This research provides an integrated approach to simultaneously monitor and diagnose an automatic controlled process by using dynamic principal component analysis (DPCA) and minimax distance classifier. Through a step-by-step implementation procedure, the proposed scheme is expected to have an impact on many manufacturing industries with automatic process control (APC) or engineering process control (EPC).     

The role of SPC in printed circuit board manufacture

This paper reports on research which examined the use of statistical process control (SPC) in the quality improvement process of a printed circuit board (PCB) manufacturer. The implementation of SPC is discussed along with the difficulties encountered and benefits achieved. The findings indicate that SPC is a tool which can be of considerable assistance in the quality improvement process of PCB manufacture. However, the variety of manufacturing technologies used and the number of interconnecting processes makes the application of SPC more difficult than in other traditional industries. The lessons learned include that the introduction of SPC must not be rushed, that discipline and support from all levels in the organization are crucial to its success, that SPC cannot be used in isolation—it needs the structure of a continuous improvement initiative, and that getting processes in a state of statistical control and capable, and keeping them there, is a difficult task which involves considerable effort and patience.     

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.     

一种保证预设质量和过程稳态的SPC方法

提出三种过程质量指数(PQI)的过程质量指数系统,基于过程质量指数的统计公差提供了一个过程质量要求和控制图设计之间的标准化界面.通过基于过程质量指数的统计公差带增加对x--R或x--s控制图中线的约束,建立一种保证预设质量和过程稳态的统计过程控制新方法.这不仅增强了控制图的功能,也为过程质量规划、统计公差和保证预设质量的SPC相关参数的并行设计提供了指导.     

Distribution-free multivariate process control based on log-linear modeling

This paper considers Statistical Process Control (SPC) when the process measurement is multivariate. In the literature, most existing multivariate SPC procedures assume that the in-control distribution of the multivariate process measurement is known and it is a Gaussian distribution. In applications, however, the measurement distribution is usually unknown and it needs to be estimated from data. Furthermore, multivariate measurements often do not follow a Gaussian distribution (e.g., cases when some measurement components are discrete). We demonstrate that results from conventional multivariate SPC procedures are usually unreliable when the data are non-Gaussian. Existing statistical tools for describing multivariate non-Gaussian data, or transforming the multivariate non-Gaussian data to multivariate Gaussian data, are limited, making appropriate multivariate SPC difficult in such cases. In this paper, we suggest a methodology for estimating the in-control multivariate measurement distribution when a set of in-control data is available, which is based on log-linear modeling and which takes into account the association structure among the measurement components. Based on this estimated in-control distribution, a multivariate CUSUM procedure for detecting shifts in the location parameter vector of the measurement distribution is also suggested for Phase II SPC. This procedure does not depend on the Gaussian distribution assumption; thus, it is appropriate to use for most multivariate SPC problems.     

Using an MQE chart based on a self-organizing map NN to monitor out-of-control signals in manufacturing processes

Control charts are recognized as one of the most important tools for statistical process control (SPC), used for monitoring any abnormal deviations in the state of manufacturing processes. However, the effectiveness of control charts is strictly dependent on statistical assumptions that in real applications are frequently violated. In contrast, neural networks (NNs) have excellent noise tolerance in real time, requiring no hypothesis on the statistical distribution of monitored processes. This feature makes NNs promising tools for quality control. In this paper, a self-organizing map (SOM)-based monitoring approach is proposed for enhancing the monitoring of processes. It is capable of providing a comprehensive and quantitative assessment value for the current process state, achieved by minimum quantization error (MQE) calculation. Based on MQE values over time series, a novel MQE chart is developed for monitoring process changes. The aim of this research is to analyse the performance of the MQE chart under the assumption that predictable abnormal patterns are not available. To this aim, the performance of the MQE chart in manufacturing processes (including non-correlated, auto-correlated and multivariate processes) is evaluated. The results indicate that the MQE chart may be a promising tool for quality control.     

A spatial variable selection method for monitoring product surface

Two-dimensional (2-D) data maps are generated in certain advanced manufacturing processes. Such maps contain rich information about process variation and product quality status. As a proven effective quality control technique, statistical process control (SPC) has been widely used in different processes for shift detection and assignable cause identification. However, charting algorithms for 2-D data maps are still vacant. This paper proposes a variable selection-based SPC method for monitoring 2-D wafer surface. The fused LASSO algorithm is firstly employed to identify potentially shifted sites on the surface; a charting statistic is then developed to detect statistically significant shifts. As the variable selection algorithm can nicely preserve shift patterns in spatial clusters, the newly proposed chart is proved to be both effective in detecting shifts and capable of providing diagnostic information for process improvement. Extensive Monte Carlo simulations and a real example have been used to demonstrate the effectiveness and usage of the proposed method.     

LRProb control chart based on logistic regression for monitoring mean shifts of auto-correlated manufacturing processes

With the growth of automation in manufacturing, process quality characteristics are being measured at higher rates and data is more likely to be auto-correlated. Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because process parameters are highly auto-correlated. Several attempts such as some time series based control charts have been made in the previous years to extend traditional SPC techniques. However, these extensions pose some serious limitations for monitoring the process mean shifts. These charts require that a suitable model has been identified for the time series of process observations before residuals can be obtained. In this paper, a logistic regression (LR)-based process monitoring model is proposed for enhancing the monitoring of processes. It is capable of providing a comprehensible and quantitative assessment value for the current process state, which is achieved by the event occurrence probability calculation of LR. Based on these probability values over the time series, a novel chart: LRProb chart, is developed for monitoring and visualising process changes. The aim of this research is to analyse the performance of the LRProb chart under the assumption that only a small number of predictable abnormal patterns are available. To such aim, the performance of the LRProb chart is evaluated on two real-world industrial cases and simulated processes. Given the simplicity, visualisation and quantification of the proposed LRProb chart, this approach is proved from the experiments to be a feasible alternative for quality monitoring in the case of auto-correlated process data.     

A Hybrid SPC Method with the Chi‐Square Distance Monitoring Procedure for Large‐scale,Complex Process Data

Standard multivariate statistical process control (SPC) techniques, such as Hotelling's T², cannot easily handle large‐scale, complex process data and often fail to detect out‐of‐control anomalies for such data. We develop a computationally efficient and scalable Chi‐Square ( ) Distance Monitoring (CSDM) procedure for monitoring large‐scale, complex process data to detect out‐of‐control anomalies, and test the performance of the CSDM procedure using various kinds of process data involving uncorrelated, correlated, auto‐correlated, normally distributed, and non‐normally distributed data variables. Based on advantages and disadvantages of the CSDM procedure in comparison with Hotelling's T² for various kinds of process data, we design a hybrid SPC method with the CSDM procedure for monitoring large‐scale, complex process data. Copyright © 2005 John Wiley & Sons, Ltd.     

Improving the performance of the multivariate exponentially weighted moving average control chart

Multivariate statistical process control (SPC) procedures are useful in cases where several process variables are monitored simultaneously. A significant disadvantage of these techniques is that the time required to detect a process shift increases with the number of variables being monitored. We show how the shift detection capability of one popular multivariate SPC scheme, the multivariate analogue of the exponentially weighted moving average control chart, can be significantly improved by transforming the original process variables to a lower‐dimensional subspace through the use of a U‐transformation. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

三坐标测量机的数据处理和分析

数据处理和分析是三坐标测量机应用的核心工作，而基于统计过程控制的SPC技术，则是测量机应用的高级阶段，SPC技术应用的基础性工作是对大量数据的汇总处理。本文提出了一种利用程序方法对数据进行汇总的数学模型和编程思路，结合工作中的经验，对SPC技术的实际应用进行了一些粗浅的探讨。通过使用这些技术和方法，可以实现数据采集、数据处理和数据分析的全程自动化。