Conventional Statistical Process Control Research Articles

A nonparametric EWMA control chart for monitoring mixed continuous and count data

ABSTRACT Conventional statistical process control tools monitor either continuous or count data but rarely both simultaneously. While process data are becoming increasingly complex, there will be more data points containing both continuous and count information. In the case of mixed continuous and count data with unknown distributions, the traditional parameter control chart cannot be used to monitor them. It is proposed in this paper a novel nonparametric EWMA control chart to monitor mixed continuous and count data. The mixed continuous and count data are first transformed into categorical data, and then a log-linear model is utilized to analyze correlations between variables, followed by the construction of an EWMA statistic that is used to monitor mixed continuous and count data. Next, the proposed control chart is compared with several improved control charts for monitoring mixed continuous and count data. Based on the numerical simulation results, the control chart presented in this paper provides a superior method of detecting alarm signals in the process compared to some improved control charts. Finally, the proposed control chart is demonstrated to be effective and applicable using the semiconductor manufacturing process dataset from the UC Irvine Machine Learning Repository.

A General Framework for Robust Monitoring of Multivariate Correlated Processes

Statistical process control (SPC) charts provide an important analytic tool for online monitoring of sequential processes. Conventional SPC charts are designed for cases when in-control (IC) process observations are independent and identically distributed at different observation times and the IC process distribution belongs to a parametric (e.g., normal) family. In practice, however, these model assumptions are rarely valid. To address this issue, there have been some existing discussions in the SPC literature for handling cases when the IC process distribution cannot be described well by a parametric form, and some nonparametric SPC charts have been developed based on data ranking and/or data categorization. However, both data ranking and data categorization would lose information in the original process observations. Consequently, the effectiveness of the nonparametric SPC charts would be compromised. In this article, we make another research effort to handle this problem by developing a general process monitoring framework that is robust to the IC process distribution and short-ranged serial correlation. The new method tries to preserve as much information in the original process observations as possible. Instead of using data ranking and/or data categorization, it is based on intensive data pre-processing, including data decorrelation, data transformation, and data integration. Because the distribution of the pre-processed data can be approximated well by a parametric distribution, the design and implementation of the new method is relatively simple. Numerical studies show that it is indeed robust to the IC process distribution and effective for online monitoring of multivariate processes with short-ranged serial correlation.

High-Speed Monitoring of Multidimensional Processes Using Bayesian Updates

The advent of modern data acquisition and computing techniques has enabled high-speed monitoring of high-dimensional processes. The short sampling interval makes the samples temporally correlated, even if there is no underlying autocorrelation among covariates. In this study, we introduce a new process monitoring scheme in a Bayesian framework. The key strategy of this study is to incorporate sequential observations into the estimation procedure for the parameters of interest to update the prior distribution. Based on the updated prior, we obtain the most appropriate estimation of the process parameters at each sampling epoch by maximizing the posterior probability. In addition, conventional statistical process control and monitoring methodologies suffer from the “curse of dimensionality.” The closed form of the estimate developed in this study through Bayesian updates enables the proposed method to be effective for high-dimensional process monitoring. Various simulation studies demonstrate the superiority of the proposed scheme in the high-speed monitoring of high-dimensional processes. Moreover, a few sample paths of the estimated mean in a procedure of the proposed method are illustrated to provide practitioners with insights into the monitoring and control of the process. Finally, we provide a real-life application to illustrate the proposed method.

Online monitoring of high-dimensional binary data streams with application to extreme weather surveillance

With the rapid development of modern sensor technology, high-dimensional data streams appear frequently nowadays, bringing urgent needs for effective statistical process control (SPC) tools. In such a context, the online monitoring problem of high-dimensional and correlated binary data streams is becoming very important. Conventional SPC methods for monitoring multivariate binary processes may fail when facing high-dimensional applications due to high computational complexity and the lack of efficiency. In this paper, motivated by an application in extreme weather surveillance, we propose a novel pairwise approach that considers the most informative pairwise correlation between any two data streams. The information is then integrated into an exponential weighted moving average (EWMA) charting scheme to monitor abnormal mean changes in high-dimensional binary data streams. Extensive simulation study together with a real-data analysis demonstrates the efficiency and applicability of the proposed control chart.

Machine learning–driven in situ process monitoring with vibration frequency spectra for chemical mechanical planarization

The objective of this work is to tackle the challenges of monitoring and detecting subtle process changes in chemical mechanical planarization (CMP), an ultraprecision manufacturing process. Monitoring ultraprecision processes is usually of difficulty due to their innate complexity and low signal-to-noise ratio in sensor signals. Especially for subtle signal variations during small process changes, the conventional statistical process control charts could fail to detect such process anomalies from the sensor signals in the time domain. In this paper, frequency spectra representation of the microelectromechanical systems (MEMS) vibration sensor signals during subtle process changes is investigated, and the signal patterns uncovered by frequency spectra are utilized to formulate a machine learning–driven in situ process monitoring approach to detect process anomalies in CMP. The proposed approach overcomes the obstacles of differentiating subtle signal changes by transforming them into the frequency domain with Fourier transform and Hilbert-Huang transform and classifying the resulted frequency spectra with random forest. Based on frequency analysis, it can unveil the differences in the signals obscured in the time domain and suppress the high-frequency noise. Consequently, the presented machine learning–driven in situ process monitoring approach detects process anomalies by differentiating the deviated frequency spectra with machine learning. It is validated on our experimental CMP testbed for anomaly detection, and outperforms three benchmark statistical process control charts. For instance, it detects a slurry shutoff anomaly in CMP about ten times faster than the benchmark methods.

Statistical process control and process capability analysis for non-normal volumetric modulated arc therapy patient-specific quality assurance processes.

Applying statistical process control (SPC) to intensity-modulated radiotherapy (IMRT)/volumetric modulated arc therapy (VMAT) patient-specific quality assurance (PSQA) program was recommended by the American Association of Physics in Medicine Task Group 218 report, but a comprehensive analysis of PSQA processes with non-normal distributions is lacking. This study investigates SPC and process capability analysis (PCA) methods for non-normal IMRT/VMAT PSQA processes. 1119 VMAT PSQAs were performed on three beam-matched linear accelerators (linacs), using gamma analysis. The Anderson-Darling statistic was used to test normality. The control charts for each PSQA process were obtained using three non-normal-based methods and compared with the conventional Shewhart method. The ability of each PSQA process to produce an output within the specification limit was measured using the index; in this study, the index was calculated using two transformation methods and compared with that calculated using the conventional method. The performances of the three linacs were assessed using SPC and PCA methods. All three PSQA processes were non-normal (P<0.005). Compared to the non-normal-based SPC and PCA methods, the false alarm rates of the conventional method for linac1, linac2, and linac3 were 0.83%, 3.77%, and 4.95% respectively; the minimum overestimated values were 0.59, 0.87, and 1.49, respectively. The process capabilities of the three beam-matched linacs were at different levels. For non-normal VMAT PSQA processes, the conventional SPC and PCA methods increase the false alarm rates and overestimate process capabilities. Instead, non-normal-based SPC and PCA methods are more reliable and accurate in non-normal PSQA processes. Statistical process control and PCA are useful tools for assessing the performance of beam-matched linacs.

Adaptive radiotherapy based on statistical process control for oropharyngeal cancer.

PurposeThe purpose of this study is to quantify dosimetric changes throughout the delivery of oropharyngeal cancer treatment and to investigate the application of statistical process control (SPC) for the management of significant deviations during the course of radiotherapy.MethodsThirteen oropharyngeal cancer patients with daily cone beam computed tomography (CBCT) were retrospectively reviewed. Cone beam computed tomography images of every other fraction were imported to the Velocity software and registered to planning CT using the 6 DOF (degrees of freedom) couch shifts generated during patient setup. Using Velocity “Adaptive Monitoring” module, the setup‐corrected CBCT was matched to planning CT using a deformable registration. Volumes and dose metrics at each fraction were calculated and rated with plan values to evaluate interfractional dosimetric variations using a SPC framework. T‐tests between plan and fraction volumes were performed to find statistically insignificant fractions. Average upper and lower process capacity limits (UCL, LCL) of each dose metric were derived from these fractions using conventional SPC guidelines.ResultsGross tumor volume (GTV) and organ at risk (OAR) volumes in the first 13 fractions had no significant changes from the pretreatment planning CT. The GTV and the parotid glands subsequently decreased by 10% at the completion of treatment. There were 3–4% increases in parotid mean doses, but no significant differences in dose metrics of GTV and other OARs. The changes were organ and patient dependent. Control charts for various dose metrics were generated to assess the metrics at each fraction for individual patient.ConclusionsDaily CBCT could be used to monitor dosimetric variations of targets and OARs resulting from volume changes and tissue deformation in oropharyngeal cancer radiotherapy. Treatment review with the guidance of a SPC tool allows for an objective and consistent clinical decision to apply adaptive radiotherapy.

Bulanık İstatistiksel Proses Kontrol Tekniği İle 19x39x19 cm Bims Hafif Yapı Malzemesi Üretiminin Analizi

Statistical Process Control (SPC) is the most important a math-based tool used by engineers to control non-standard production and to ensure that production outputs are performed at specified quality ranges. However, in cases where conventional SPC is inadequate, fuzzy statistical process control approaches have been developed which enable more precise statistical process control using fuzzy set theory. In this study, fuzzy statistical process control techniques have been used to determine whether a 19x39x19 cm pumice brick, which is a product of a pumice brick factory, with fuzzy observation values is under control of the production process.

Short-run univariate quality control approaches

Short-run control charts are used in situations where limited or no data exist about the process, and conventional statistical process control (SPC) charts are considered ineffective for estimating parameters, such as control limits, because they cannot be established in most cases. This study presents a contemporary review on developing various short-run univariate quality control approaches. Considerable literature is systematically collected on the basis of content analysis. Techniques are differentiated on the basis of repetitive and non-repetitive processes. Subsequently, the principles, data sample collection, performance criteria, robustness and applications of quality control approaches are reviewed.

A REVIEW ON SHORT-RUN UNIVARIATE QUALITY CONTROL APPROACHES

Short-run control charts are used in situations where limited or no data exist about the process, and conventional statistical process control (SPC) charts are considered ineffective for estimating parameters, such as control limits, because they cannot be established in most cases. This study presents a contemporary review on developing various short-run univariate quality control approaches. Considerable literature is systematically collected on the basis of content analysis. Techniques are differentiated on the basis of repetitive and non-repetitive processes. Subsequently, the principles, data sample collection, performance criteria, robustness and applications of quality control approaches are reviewed.

Real-time quality monitoring and diagnosis for manufacturing process profiles based on deep belief networks

A large number of real-time quality data are collected through various sensors in the manufacturing process. However, most process data are high-dimension, nonlinear and high-correlated, so that it is difficult to model the process profiles, which restricts the application of conventional statistical process control technique. Motivated by the powerful ability of deep belief network (DBN) to extract the essential features of input data, this paper develops a real-time quality monitoring and diagnosis scheme for manufacturing process profiles based on DBN. The profiles collected from a manufacturing process are mapped into quality spectra. A novel DBN recognition model for quality spectra is established in the off-line learning phase, which can be applied to monitor and diagnose the process profiles in the on-line phase. The effectiveness of DBN recognition model for manufacturing process profiles is demonstrated by simulation experiment, and a real injection molding process example is applied to analyze the performance. The results show that the proposed DBN model outperforms alternative methods.

An Algorithm for Early Outbreak Detection in Multiple Data Streams

An Algorithm for Early Outbreak Detection in Multiple Data Streams

A New Process Control Chart for Monitoring Short-Range Serially Correlated Data

–Statistical process control (SPC) charts are critically important for quality control and management in manufacturing industries, environmental monitoring, disease surveillance, and many other applications. Conventional SPC charts are designed for cases when process observations are independent at different observation times. In practice, however, serial data correlation almost always exists in sequential data. It has been well demonstrated in the literature that control charts designed for independent data are unstable for monitoring serially correlated data. Thus, it is important to develop control charts specifically for monitoring serially correlated data. To this end, there is some existing discussion in the SPC literature. Most existing methods are based on parametric time series modeling and residual monitoring, where the data are often assumed to be normally distributed. In applications, however, the assumed parametric time series model with a given order and the normality assumption are often invalid, resulting in unstable process monitoring. Although there is some nice discussion on robust design of such residual monitoring control charts, the suggested designs can only handle certain special cases well. In this article, we try to make another effort by proposing a novel control chart that makes use of the restarting mechanism of a CUSUM chart and the related spring length concept. Our proposed chart uses observations within the spring length of the current time point and ignores all history data that are beyond the spring length. It does not require any parametric time series model and/or a parametric process distribution. It only requires the assumption that process observation at a given time point is associated with nearby observations and independent of observations that are far away in observation times, which should be reasonable for many applications. Numerical studies show that it performs well in different cases.

Surrogate model–based optimal feed-forward control for dimensional-variation reduction in composite parts' assembly processes

ABSTRACTDimension control and variation reduction are vital for composite parts' assembly processes. Due to the nonlinear properties of composites, physics-based models cannot accurately and efficiently approximate the assembly processes. In addition, conventional robust parameter design (RPD) and statistical process control (SPC) cannot actively compensate for dimensional errors or prevent defects. This article proposes a surrogate model–based optimal feed-forward control strategy for dimensional-variation reduction and defect prevention in the assembly of composite parts. The objective is accomplished by (i) developing a grouped Latin hypercube sampling approach tailored to the problem; (ii) adopting a universal Kriging model for dimensional prediction and then embedding the model into an optimal feed-forward control algorithm; and (iii) conducting a multiobjective optimization to determine the control actions. A case study reveals that the developed methodology can effectively reduce the mean and standard deviation of dimensional deviations for the assembly of composite parts.

Bivariate SPC Chart Pattern Recognition Using Modular-Neural Network

In statistical process control (SPC), monitoring and identifying unnatural variation in manufacturing process is challenging when dealing with two correlated quality variables (bivariate). The conventional multivariate SPC charts were designed only for triggering unnatural variation but it is not provide information towards diagnosis. In recent years, several SPC chart pattern recognition schemes were proposed to provide information towards diagnosis based on various category of unnatural variation. In this paper, the modular neural-network scheme was developed to identify nine category of bivariate SPC chart patterns. The success factor for the scheme is outlined as a new perspective in realizing accurate monitoring-diagnosis in quality control.

Case study: statistical monitoring for the moisture content of the cut tobacco

The moisture content of cut tobacco in Tobacco industry affects directly the quality of tobacco. To prevent the abnormal changes of the moisture content of cut tobacco, effective surveillance systems would be extremely helpful to give out-of-control (OC) signals as quickly as possible. The conventional statistical process control charts are not suitable to use due to complex structures, such as semiparametric trend, within-batch correlation in the moisture content data. In this paper, we propose a four-step procedure in which Semiparametric longitudinal model, time series analysis methods and normal transformation methods are utilized to eliminate the impact of the complex structures. And our procedure is demonstrated using the moisture content data of cut tobacco at the outlet (MCCTO) collected in Shanghai tobacco group co., LTD of China. The results show that our procedure is effective in detecting the abnormal changes of the MCCTO data.

Multivariate statistical process control in product quality review assessment – A case study

According to the Food and Drug Administration and the European Good Manufacturing Practices (GMP) guidelines, Annual Product Review (APR) is a mandatory requirement in GMP. It consists of evaluating a large collection of qualitative or quantitative data in order to verify the consistency of an existing process. According to the Code of Federal Regulation Part 11 (21 CFR 211.180), all finished products should be reviewed annually for the quality standards to determine the need of any change in specification or manufacturing of drug products. Conventional Statistical Process Control (SPC) evaluates the pharmaceutical production process by examining only the effect of a single factor at the time using a Shewhart's chart. It neglects to take into account the interaction between the variables. In order to overcome this issue, Multivariate Statistical Process Control (MSPC) can be used. Our case study concerns an APR assessment, where 164 historical batches containing six active ingredients, manufactured in Morocco, were collected during one year. Each batch has been checked by assaying the six active ingredients by High Performance Liquid Chromatography according to European Pharmacopoeia monographs. The data matrix was evaluated both by SPC and MSPC. The SPC indicated that all batches are under control, while the MSPC, based on Principal Component Analysis (PCA), for the data being either autoscaled or robust scaled, showed four and seven batches, respectively, out of the Hotelling T2 95% ellipse. Also, an improvement of the capability of the process is observed without the most extreme batches. The MSPC can be used for monitoring subtle changes in the manufacturing process during an APR assessment.

Ensemble-Bayesian SPC: Multi-mode process monitoring for novelty detection

ABSTRACTWe propose a monitoring method based on a Bayesian analysis of an ensemble-of-classifiers for Statistical Process Control (SPC) of multi-mode systems. A specific case is considered, in which new modes of operations (new classes), also called “novelties,” are identified during the monitoring stage of the system. The proposed Ensemble-Bayesian SPC (EB-SPC) models the known operating modes by categorizing their corresponding observations into data classes that are detected during the training stage. Ensembles of decision trees are trained over replicated subspaces of features, with class-dependent thresholds being computed and used to detect novelties. In contrast with existing monitoring approaches that often focus on a single operating mode as the “in-control” class, the EB-SPC exploits the joint information of the trained classes and combines the posterior probabilities of various classifiers by using a “mixture-of-experts” approach. Performance evaluation on real datasets from both public repositories and real-world semiconductor datasets shows that the EB-SPC outperforms both conventional multivariate SPC as well as ensemble-of-classifiers methods and has a high potential for novelty detection including the monitoring of multimode systems.

Dynamic network monitoring and control of in situ image profiles from ultraprecision machining and biomanufacturing processes

AbstractIn modern industries, advanced imaging technology has been more and more invested to cope with the ever‐increasing complexity of systems, to improve the visibility of information and enhance operational quality and integrity. As a result, large amounts of imaging data are readily available. This presents great challenges on the state‐of‐the‐art practices in process monitoring and quality control. Conventional statistical process control (SPC) focuses on key characteristics of the product or process and is rather limited to handle complex structures of high‐dimensional imaging data. New SPC methods and tools are urgently needed to extract useful information from in situ image profiles for process monitoring and quality control. In this study, we developed a novel dynamic network scheme to represent, model, and control time‐varying image profiles. Potts model Hamiltonian approach is introduced to characterize community patterns and organizational behaviors in the dynamic network. Further, new statistics are extracted from network communities to characterize and quantify dynamic structures of image profiles. Finally, we design and develop a new control chart, namely, network‐generalized likelihood ratio chart, to detect the change point of the underlying dynamics of complex processes. The proposed methodology is implemented and evaluated for real‐world applications in ultraprecision machining and biomanufacturing processes. Experimental results show that the proposed approach effectively characterize and monitor the variations in complex structures of time‐varying image data. The new dynamic network SPC method is shown to have strong potentials for general applications in a diverse set of domains with in situ imaging data.

Pierre Gy’s development of the Theory of Sampling: a retrospective summary with a didactic tutorial on quantitative sampling of one-dimensional lots

Author Summary: Corrected version with changes to Table 3 published 14 March 2017. This paper presents an overview of the pioneering work of Pierre Gy on the Theory of Sampling (TOS) over a period of 66 years—a monumental legacy of dedicated work to the science of sampling. It starts with the early years, beginning in 1949, when Gy worked tirelessly, often in isolation, and not without resistance from other scientists, to create a systematic, mathematically based framework within which every error arising from sampling of a heterogeneous material can be identified (named), analysed and explained. Gy is widely remembered for “The Formula”, which expresses the variance of the fundamental sampling error (FSE) in terms of the mass, fragment top-size and various other compositional attributes of the minerals of interest. But as early as 1947 the seeds of two related questions were planted: “How... to sample” and “How much... material should one take”, which eventually evolved to become the Theory of Sampling, essentially completed in 1975. Presentation of this famous equation to the scientific community led to a period of intense practical experimentation on stationary lots that continues to this day. Gy also addressed the challenge of sampling from fluxes and here identified the variability due to autocorrelation between samples taken from flowing streams that led ultimately to the discipline of chronostatistics, a study of variability in one-dimensional streams. The scope and depth of Gy’s research endeavours grew during the 1960s and led to his encounter with metallurgical balance and reconciliation. As a result, Gy developed the idea of proportional sampling that allows several material streams to be sampled according to the same selection probability with very efficient reconciliation benefits. The TOS was also further extended to include the problems that producers faced in regard to bed blending. Gy was a prolific writer and published over 250 different articles and books, with his last four papers published in the Proceedings of the First World Conference on Sampling and Blending, WCSB1 (2003), Esbjerg, Denmark. In these papers, Gy left us a personal history of the development of TOS as well as three fundamental tutorials, with practical examples, summarising how to manage both the qualitative and quantitative aspects of sampling of discrete materials. This tribute focuses especially on Pierre Gy“s pioneering applications of variography to understanding the large-scale variability in process plants and process control from as early as the 1950s, and he devoted a major part of the development period of TOS to this critically important subject. The variogram allows one to identify sources of variability and provides valuable insight into correlations between successive samples. Poor understanding of the analytical capabilities of the variogram mean that it has not been widely applied in process control. Failure to address the concept of stream heterogeneity means that conventional statistics and statistical process control (SPC) fail to identify and distinguish the sources of variability in a process stream. For each type of heterogeneity, there is a matching variety of process variability. Although the method is powerful in terms of the insights one is able to gain in regard to plant performance and management, there are surprisingly few examples of its application in the literature, although there has been greater acceptance of the method. The authors believe the concluding didactic presentation of Pierre Gy’s approach to process sampling may be a useful starting point for newcomers to TOS.