Univariate Statistical Process Control Research Articles

Predictive Process Control Framework for Online Quality Control in a Hot Rolling Mill

Recent data science advances in statistical classification techniques, and in particular, machine learning techniques, have resulted in more efficient and robust ways of continuously monitoring and managing processes to achieve continuous quality improvement. With increased automation and process data outputs in industrial processes, traditional univariate Statistical Process Control (SPC) is proving impractical in some aspects and slowly loosing overall relevance. The main aim of this study is to develop a predictive process control framework for online quality control. This framework was validated for efficacy when compared to univariate SPC in a selected metal rolling plant based in South Africa. This predictive process control framework employs data science approaches through machine learning techniques and algorithms from the Python programming language. The research methodology is a single case study. An experiment approach was undertaken at hot roughing and hot finishing processes. The results of the study revealed a marginal 17 percent improvement in the predictive process control defect rate compared to the univariate SPC defect rate. The predictive model was based on the Random Forest algorithm and achieved an AUC of 0.84 compared to a 0.81 AUC for the neural network model. Factors found to have a positive impact on the success and sustainability of predictive process control were compliance with predictive model prescriptions, data science knowledge, senior management commitment, and the Extract, Transform, and Load (ETL) approach. These results contribute to the theory of online quality control and can be used as a guide by rolling mill process engineers and quality practitioners. Doi: 10.28991/HEF-2022-03-03-01 Full Text: PDF

Detection of Gear Wear and Faults in Spur Gear Systems Using Statistical Parameters and Univariate Statistical Process Control Charts

Detection of Gear Wear and Faults in Spur Gear Systems Using Statistical Parameters and Univariate Statistical Process Control Charts

An Algorithm for Early Outbreak Detection in Multiple Data Streams

An Algorithm for Early Outbreak Detection in Multiple Data Streams

Monitoring biological processes using univariate statistical process control

AbstractBiological modelling is a challenging task specifically when state variables are difficult or even impossible to be measured. Consequently, monitoring quality of biological process will be impacted negatively due to the lack of an accurate model capable of reflecting precisely the process dynamics. Moreover, the faults in such systems cannot be detected robustly. The current work proposes a novel approach that combines state estimation with process monitoring techniques. The developed approach, named as particle filter (PF)'based multiscale maximum double exponentially weighted moving average (MS‐M‐DEWMA) chart, includes two main phases. In the first phase, the PF technique is applied to estimate the unknown nonlinear states of the biological processes. In the second phase, the statistical univariate chart, MS‐M‐DEWMA is adopted to address fault detection in biological processes. Therefore, in this work, we propose a monitoring approach capable of detecting shifts in mean and/or variance in biological systems (pre‐defined structure obtained using material and energy balances) where the variables are estimated using state estimation techniques. The detection chart MS‐M‐DEWMA is applied to the residuals computed using the PF. The advantages of PF‐based MS‐M‐DEWMA method are threefold: (i) extract features and decorrelate measurements using dynamical multiscale representation; (ii) estimate the state of nonlinear biological processes using the PF technique; and (iii) enhance monitoring of biological processes through detecting shifts of both variance and mean using MS‐M‐DEWMA chart. The proposed approach is validated using a Cad system in E. coli (CSEC) model.

Using a Computational Intelligence Hybrid Approach to Recognize the Faults of Variance Shifts for a Manufacturing Process

Statistical Process Control (SPC) chart is effective in monitoring a process. When an SPC chart monitors a univariate process, it is not difficult to determine the assignable causes due to the fact that a univariate SPC chart only monitors a single quality characteristic. However, when a Multivariate Statistical Process Control (MSPC) chart is used to monitor a multivariate process, it is complicated to determine which quality characteristic(s) at fault. This study proposes a hybrid classification model to recognize the quality characteristic(s) at fault when the variance shifts occurred in a multivariate process. The proposed mechanism includes the hybridization of Artificial Neural Network (ANN) and analysis of variance (ANOVA). The performance of the proposed approach is evaluated by conducting a series of experiments. 

Univariate statistical process control of super saver beans: a case of RMV supermarket, zimbabwe.

Statistical Process Control (SPC) uses statistical techniques to improve the quality of a process reducing its variability. The main tools of SPC are the control charts. The basic idea of control charts is to test the hypothesis that there are only common causes of variability versus the alternative that there are special causes. Control charts are designed and evaluated under the assumption that the observations from the process are independent and identically distributed (IID) normal. However, the independence assumption is often violated in practice. Autocorrelation may be present in many procedures, and may have a significant effect on the properties of the control charts.Thus, traditional SPC charts are inappropriate for monitoring process quality. In this study, wepresent methods for process control that deal with auto correlated data and a method based on time series ARIMA models (Box Jenkins Methodology). We apply the typical Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts as SPC techniques and the time-series method in determining packaging process quality.

Improving the rapidity of responses to pipe burst in water distribution systems: a comparison of statistical process control methods

A pipe burst is a major water distribution system failure. Water escapes the network through the break increasing the total flow entering the network. These higher flows, in turn, increase the head losses in pipes and result in lower water pressures at customer taps. This study focuses on burst detection by seeking to identify anomalies in net system demand, pipe flow rates, and nodal pressure heads. Three univariate statistical process control (SPC) methods (the Western Electric Company rules, the cumulative sum (CUSUM) method, and the exponentially weighted moving average [EWMA]) and three multivariate SPC methods (Hotelling T2 method and multivariate versions of CUSUM and EWMA) are compared with respect to their detection effectiveness and efficiency. First, the three univariate methods are tested using real system burst detection and then the six SPC methods are compared using synthetic data. The real application using net system demand shows that burst flows are proportionally too small to be detected. Synthetic data analyses suggest that the univariate EWMA method using nodal pressure provides the highest detectability. The method's long record length helps detect small bursts and avoid false detection. SPC methods require consistent system operations for measurements beyond total area flow.

Statistical Process Control Using a Dynamic Sampling Scheme

This article considers statistical process control (SPC) of univariate processes, and tries to make two contributions to the univariate SPC problem. First, we propose a continuously variable sampling scheme, based on a quantitative measure of the likelihood of a process distributional shift at each observation time point, provided by the p-value of the conventional cumulative sum (CUSUM) charting statistic. For convenience of the design and implementation, the variable sampling scheme is described by a parametric function in the flexible Box–Cox transformation family. Second, the resulting CUSUM chart using the variable sampling scheme is combined with an adaptive estimation procedure for determining its reference value, to effectively protect against a range of unknown shifts. Numerical studies show that it performs well in various cases. A real data example from a chemical process illustrates the application and implementation of our proposed method. This article has supplementary materials online.

A Comparison of Statistical Process Control (SPC) and On-Line Multivariate Analyses (MVA) for Injection Molding

Abstract Manufacturing process automation is often impeded by limitations related to automatic quality assurance. Many plastics manufacturers use univariate statistical process control (SPC) for quality control by charting the critical process states relative to defined control limits. Alternatively, principal component analysis (PCA) and projection to latent stuctures (PLS) are multivariate methods that measure the process variance by the distance to the model (DModX) and the Hotelling t-squared (T2) values. A methodology for robust model development is described to perturb the manufacturing process for process characterization based on a design of experiments; best subset analysis is used to provide an optimal set of regressors for univariate SPC. Four different statistical models were derived from the same data set for a highly instrumented injection molding process. The performance of these models was then assessed with respect to fault diagnosis and defect identification when the molding process was subjected to twelve common process faults. Across two hundred molding cycles, the univariate SPC models correctly diagnosed five of the twelve process faults with one false positive, detecting only eighteen of twenty four defective products while indicating two false positives. With the same molding cycles, PCA and PLS provided nearly identical performance by correctly diagnosing ten of the twelve process faults and detecting twenty three of the twenty four defective products; PCA indicated two false positives while PLS indicated only one false positive.

A change point model for the location parameter of exponential family densities

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. In this research a maximum likelihood change point estimator is proposed for the natural location parameter of densities belonging to the exponential family. It is assumed that the behavior in the location parameter over discrete sampling intervals is adequately modeled by a linear predictor. The estimator is intended to be applied to data obtained following signals from univariate statistical process control charts in an effort to aid process engineers diagnose the root cause of process change.

Multiple criteria intelligence tracking for detecting extremes from sequences of risk incidents

A number of quantitative methods have emerged to identify and track precursors to risk for engineering systems. While data mining and statistical inference identify patterns from information of historical events, they may not address features of extreme events that have never occurred. While, event and fault-tree analyses synthesize important information on basic and initiating risk events, they fall short of addressing incident data in real time. Accident precursor analyses refine event and fault tree analyses by considering near-misses or precursors from system operational data. Complementing precursor analysis is an existing method of detecting anomalies in a sequence of risk incident reports to (a) identify and count patterns in the reports, (b) measure and track the complexity of the reports with univariate statistical process control, and (c) identify specific periods of instability. This paper extends the existing method to (d) introduce two additional measurements of patterns, (e) apply multiple criteria statistical process control to track the multiple measurements of the reports, and (f) use optimal search parameters to generate a watch list of system components for input to accident precursor analyses. The extension is demonstrated for a sequence of four observation periods of incident reports in a power distribution system.

Fault Detection Using the k-Nearest Neighbor Rule for Semiconductor Manufacturing Processes

It has been recognized that effective fault detection techniques can help semiconductor manufacturers reduce scrap, increase equipment uptime, and reduce the usage of test wafers. Traditional univariate statistical process control charts have long been used for fault detection. Recently, multivariate statistical fault detection methods such as principal component analysis (PCA)-based methods have drawn increasing interest in the semiconductor manufacturing industry. However, the unique characteristics of the semiconductor processes, such as nonlinearity in most batch processes, multimodal batch trajectories due to product mix, and process steps with variable durations, have posed some difficulties to the PCA-based methods. To explicitly account for these unique characteristics, a fault detection method using the k-nearest neighbor rule (FD-kNN) is developed in this paper. Because in fault detection faults are usually not identified and characterized beforehand, in this paper the traditional kNN algorithm is adapted such that only normal operation data is needed. Because the developed method makes use of the kNN rule, which is a nonlinear classifier, it naturally handles possible nonlinearity in the data. Also, because the FD-kNN method makes decisions based on small local neighborhoods of similar batches, it is well suited for multimodal cases. Another feature of the proposed FD-kNN method, which is essential for online fault detection, is that the data preprocessing is performed automatically without human intervention. These capabilities of the developed FD-kNN method are demonstrated by simulated illustrative examples as well as an industrial example.

On-line monitoring of a sugar crystallization process

The present paper reports a comparative evaluation of four multivariate statistical process control (SPC) techniques for the on-line monitoring of an industrial sugar crystallization process. The process itself is challenging since it is carried out in multiple phases and there exists strong non-linear and dynamic effects between the variables. The methods investigated include classical on-line univariate statistical process control, batch dynamic principal component analysis (BDPCA), moving window principal component analysis (MWPCA), batch observation level analysis (BOL) and time-varying state space modelling (TVSS). The study is focused on issues of on-line detection of changes in crystallization process operation, the early warning of process malfunctions and potential production failures; problems that have not been directly addressed by existing statistical monitoring schemes. The results obtained demonstrate the superior performance of the TVSS approach to successfully detect abnormal events and periods of bad operation early enough to allow bad batches and related losses in amounts of recycled sucrose to be significantly reduced.

Statistical Process Control Charts for Batch Operations Based on Independent Component Analysis

A significant step forward in recent years, in regard to multivariate statistical process control (MSPC) for operational condition monitoring and fault diagnosis, has been the introduction of principal component analysis (PCA) for the compression of process data. An alternative technique that has been studied more recently for data compression is independent component analysis (ICA). Published work has shown that, in some applications of statistical process monitoring, ICA-based methods have exhibited advantages over those based on other data compression techniques. However, it is inappropriate to use ICA in the same way as PCA to derive Hotelling's T2 and SPE (squared prediction error) charts, because the independent components are separated by maximizing their non-Gaussianity, whereas the satisfying Gaussian distribution is the basis of T2 and SPE monitoring charts, as well as univariate statistical process control (SPC) charts. In this paper, we propose a new method for deriving SPC charts based on ICA...

Integrating novelty detection, neural networks and conventional tools for pattern recognition in multivariate processes

Statistical process control (SPC) charts are powerful tools that are used to improve quality, increase uniformity and minimize production costs in manufacturing. Neural networks (NNs) have been successfully applied to interpret univariate SPC charts. Despite the growing importance and popularity of multivariate SPC (MSPC), the published literature on the application of NNs to SPC has not adequately discussed the issues related to application of NNs to MSPC for pattern recognition. This paper uses the chi-squared ( x2) statistic as a compact format for representing the input to NNs specialized in positive identification of selected subclasses of multivariate non-random patterns. It is imperative to maintain the reliability of decisions by such specialist NNs in order to convince process operators of their benefits. Therefore, to address the above requirement, this report also shows how novelty detection (ND) can be used as a filter to allow only relevant abnormal patterns to be processed by appropriate specialist NNs. Finally, a new framework within which specialist NNs can complement the decisions of ND and other MSPC techniques is outlined.

Using novelty detection to identify abnormalities caused by mean shifts in bivariate processes

Non-random (abnormal) behaviour indicates that a process is under the influence of special causes of variation. Detection of abnormal patterns is well established in univariate statistical process control (SPC). Various solutions including heuristics, traditional computer programming, expert systems and neural networks (NNs) have been successfully implemented. In multivariate SPC (MSPC), on the other hand, there is a clear need for more investigations into pattern detection. Bivariate SPC is a special case of MSPC where the number of variates is two and is studied here in terms of identification of shift patterns. In this work, an existing NN classification technique—known as novelty detection (ND)—whose application for MSPC has not been reported is applied for pattern recognition. ND successfully detects non-random bivariate time-series patterns representing shifts of various magnitudes in the process mean vector. The investigation proposes a simple heuristic approach for applying ND as an effective and useful tool for pattern detection in bivariate SPC with potential applicability for MSPC in general.

Univariate and Multivariate Process Monitoring and Improvement

The authors demonstrate the application of traditional process monitoring and control methods such as parameter estimation, alongside Univariate Statistical Process Control techniques that have traditionally been used for quality control and monitoring. Further work is also presented on the use of Multivariate Statistical Process Control methods for process monitoring and improvement. A restriction on this work is that only the data currently used by the process monitoring and control system is considered. This is a realistic constraint, as many companies will not be able to provide a bank of additional sensors for the purposes of fault detection. This paper is of interest to researchers and practitioners alike whose ultimate aim is to apply process monitoring, fault detection and isolation in 'real world" contexts rather than in the confmes of the laboratory. It provides a useful step forward in the provision of guidelines for the selection of techniques for particular process types and desired outcomes.

Non-parametric confidence bounds for process performance monitoring charts

Statistical Process Control (SPC) provides a tool for achieving and maintaining product quality. In today's climate of major data monitoring campaigns there has been an increase in interest in the multivariate statistical projection techniques of principal components analysis and projection to latent structures for process performance monitoring. Within univariate SPC, techniques for identifying when a process is moving out of control are well established. Similar guidelines are required for multivariate statistical process control (MSPC). Two approaches will be discussed - Hotelling's T2 statistic and a new approach, the M2 statistic. Both approaches will be illustrated by application to a high pressure low density polyethylene tubular reactor and to a batch methyl methacrylate polymerisation reactor.

Multivariate Statistical Process Control in Batch Process Monitoring

Batch processing was widely practised long before the advent of the modern chemical industry. A number of limitations have inhibited the success of batch monitoring:- the finite duration of a batch, the presence of significant non-linearities, the lack of on-line sensors for measuring quality variables, the absence of steady-state operation, the difficulty of developing accurate mechanistic models and finally, process measurements are autocorrelated in time as well as being correlated with one another at any given time. Recent approaches to the monitoring of batch behaviour have been based on the extension of univariate statistical process control (SPC) philosophy to handle multivariate processes. These tools have been the statistical projection methods of principal components analysis (PCA) and projection to latent structures (PLS), and their extensions to batch operation, i.e. multiway PCA and PLS.In this paper, multiway PCR is applied to the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process using two alternative approaches. These tools have been found to be an effective method for monitoring industrial processes when the data is of high dimension and ill-conditioned. Furthermore, they provide a useful modelling technique for predicting key quality variables which are either not measured on-line or else are monitored at a much slower frequency than the process variables.

Confidence Bounds for Multivariate Process Performance Monitoring Charts

Statistical Process Control (SPC) provides a tool for achieving and maintaining product quality. Traditional methods have focused on the monitoring of one quality variable at a time. However, in todays climate of major data monitoring exercises this approach is unrealistic and as a result there has been an increase in interest in the multivariate statistical projection techniques of principal components analysis and projection to latent structures for process performance monitoring. There still remain a number of questions which require to be addressed before these new approaches to monitoring can be widely adopted by industry. Within univariate SPC, techniques for identifying when the process is moving out of control are well established and are based both on sound statistical practice and engineering knowledge built up over a number of years. Similar underpinning guidelines require to be established for multivariate statistical process control (MSPC). Two approaches to this problem of defining control limits will be discussed - those based upon Hotelling's T2 statistic and a new approach based upon kernel density estimation and the standard bootstrap, the M2 statistic. Both approaches will be illustrated by application to a high pressure low density polyethylene tubular reactor and to a batch methyl methacrylate polymerisation reactor.