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Are principal components with estimated parameters feasible in multivariate process control?

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2022年第8期38卷 4141-4156页

作者： Shepherd, Deborah K. Rigdon, Steven E. Louisiana State Univ Dept Math Shreveport LA 71105 USA St Louis Univ Dept Epidemiol & Biostat 3545 Lafayette Ave St Louis MO 63103 USA

Principal components have been used in conjunction with Hotelling's T-2 chart to monitor multivariate processes. It is known that prohibitively large sample sizes are needed to estimate the process parameters with enough precision to deploy the chart. We investigate whether principal components can be used to reduce the dimensionality of a process so that multivariate process control can be performed using estimated parameters. The chart based on the first k principal components, which we will refer to as the TPC,k2$T<^>2_{{\rm PC},k}$ chart, is investigated. Specifically, we explore three research questions in this paper: (1) can the TPC,k2$T<^>2_{{\rm PC},k}$ chart with estimated parameters be applied with moderate preliminary sample sizes?, (2) are there situations where the TPC,k2$T<^>2_{{\rm PC},k}$ charts are able to detect a shift in the mean vector quicker than the T-2 charts?, and (3) is it possible to exploit assumptions about the covariance matrix, such as equal covariances, to improve the performance of the TPC,k2$T<^>2_{{\rm PC},k}$ chart. Using simulation, we find that for high dimensions, the TPC,k2$T<^>2_{{\rm PC},k}$ chart with estimated parameters can be used to detect shifts in the direction of the first principal component. Otherwise, the chart requires very large preliminary sample sizes. When it is reasonable to assume equal covariances, the number of parameters to be estimated is substantially reduced and the performance of the TPC,k2$T<^>2_{{\rm PC},k}$ chart is improved.

关键词： multivariate statistical process control time to signal average run length preliminary sample

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Health Monitoring and Fault Detection Using Wavelet Packet Technique and multivariate process control Method

Health Monitoring and Fault Detection Using Wavelet Packet T...

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Prognostics and System Health Management Conference (PHM- Hunan)

作者： Jin, Xiaohang Sun, Yi Shan, Jihong Wang, Yu Xu, Zhengguo Zhejiang Univ Technol Coll Mech Engn Hangzhou Zhejiang Peoples R China Xi An Jiao Tong Univ Sch Mech Engn Xian Shaanxi Peoples R China Zhejiang Univ Dept Control Sci & Engn Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9781479979585

Generally, machines will undergo two stages: normal working stage and irreversible degradation stage, before they fail. The division of two these stages are helpful for remaining useful life (RUL) estimation. With the help of health monitoring technique, the start point of the degradation stage can be detected successfully, which facilitates the prognostic activities. This paper reports the work on the detection of start point of the degradation stage in machines. An approach, which combines the wavelet packet technique and multivariate statistical process control method, for fault detection was developed. Motor bearings and fans data are employed to illustrate the effectiveness of the proposed method. Results show that it is feasible for fault detection.

关键词： Fault detection cooling fan health monitoring motor bearing multivariate statistical process control wavelet packet

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multivariate process control by transition scheme in soft- drink process using 3-Way PLS approach

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Procedia Food Science 2011年 1卷 1181-1187页

作者： Jorge Saavedra Andres Córdova Research Group on Chemometrics Department of Food Engineering Pontificia Universidad Católica de Valparaíso Waddington 716 Valparaíso2360021 Chile Centro Regional de Estudios en Alimentos Saludables (CREAS) Blanco 1623 of 1402 Edificio Torres Mar del Sur II Valparaíso 2362396 Chile

Recently many attentions has been placed to process transitions, startups and restarts, since these abnormalities often arrives to the loss of production time, undesirable and not detectable variability increasing withproduction of off- grade materials. The present research deal with the modeling a continuous soft-drinks bottling process by a multivariate approach based on the 3-Way PLS. process was modeled, filtering the high grade of autocorrelation and cross-correlation within the studied variables. The responsible variables for that behavior were detected by 3-Way PLS which could be useful to separate autocorrelated sources of variability enable to control this kind of industrial process.

关键词： multivariate statistical process control Transitions 3-Way PLS Soft-drink bottling process PCA MPLS

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Real-time monitoring and fault detection of pulsed-spray fluid-bed granulation using near-infrared spectroscopy and multivariate process trajectories

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Particuology 2020年第6期18卷 112-123页

作者： Jie Zhao Wenlong Li Haibin Qu Geng Tian Yanding Wei Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang UniversityHangzhou 310058China Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province College of Mechanical EngineeringZhejiang UniversityHangzhou 310027China

Pulsed spray is a useful tool forgranule size control in fluid bed *** improve the quality control of pulsed-spray fluid bed granulation,a combination of in-line near-infrared(NIR)spectroscopy and p「incipal component analysis was used to develop multivariate statistical process control(MSPC)*** types of MSPC charts were developed,including principal component score charts,Hotelling's T2 control charts,and distance to model X control charts,to monitor the batch evolution throughout the granulation *** optimized warping was used as an alignment method to deal with the time variation in batches caused by the granulation mechanism in MSPC *** control charts developed in this study were validated on normal batches and tested on four batches that deviated from normal processing conditions to achieve real-time fault *** results indicated that the NIR spectroscopy-based MSPC model included the variability in the sample set constituting the model and could withstand external *** research demonstrated the application of synchronized NIR spectra in conjunction w让h multivariate batch modeling as an attractive tool for process monitoring and a fault diagnosis method for effective process control in pulsed-spray fluid bed granulation.

关键词： Pulsed-spray fluid bed granulation multivariate statistical process control Multiway principal component analysis Near-infrared spectroscopy Correlation optimized warping

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Variable sampling interval hotelling's T2 charts with runs rules for switching between sampling interval lengths

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2012年第2期28卷 131-140页

作者： Mahadik, Shashibhushan B. DRK Coll Commerce Dept Stat Kolhapur 416002 Maharashtra India

The use of runs rules is proposed for switching between the sampling interval lengths of variable sampling interval Hotelling's T2 charts. The purpose of applying these rules is to reduce the frequency of the switches which causes inconvenience in the administration of the charts. The expressions for the performance measures for the charts with these rules are derived. The effects of different runs rules on the performances are evaluated through numerical comparisons. The runs rules substantially reduce the frequency of switches during the in-control period and during the out-of-control periods due to the small to moderate shifts in the process mean vector. They also fairly improve the statistical performances of the charts in detecting the small shifts and do not affect that in detecting the large shifts. However, some runs rules slightly worsen the statistical performances in detecting the moderate shifts. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： adaptive control chart average time to signal average number of samples to signal average number of switches to signal multivariate statistical process control

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Determining the number of operational modes in baseline multivariate SPC data

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IIE TRANSACTIONS 2007年第12期39卷 1103-1110页

作者： Zhang, Hang Albin, Susan Rutgers State Univ Dept Ind & Syst Engn Piscataway NJ 08854 USA Arizona State Univ Dept Ind Engn Tempe AZ USA

When building a multivariate SPC model, it is commonly assumed that there is only one operational mode in the baseline data. However, multiple operational modes may exist. It is important to know the number of modes in the data in order to construct an effective process control system. Each operational mode appears as a cluster in the baseline data. This paper proposes a method to identify the correct number of clusters in baseline data. None of the existing methods for finding the number of clusters has all three of the following critical features: (i) the proposed method can determine if there is only one cluster, the most common case in baseline data;(ii) it can identify clusters that are convex or non-convex;and (iii) it is insensitive to user-specified parameters. The paper includes a comparison of the existing and proposed methods on four datasets. The proposed method consistently gives the correct number of clusters whereas the existing methods are unable to do so.

关键词： number of clusters clustering data mining multivariate statistical process control phase I

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A new proposal to solve the autocorrelation problem for monitoring processes in the cutlery industry

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2014年第2期31卷 323-333页

作者： Alfaro Navarro, Jose Luis Vargas Vargas, Manuel Andres Martinez, Maria Encarnacion Mondejar Jimenez, Jose Univ Castilla La Mancha Fac Ciencias Econ & Empresariales Albacete Albacete 02071 Spain Univ Castilla La Mancha Fac Ciencias Sociales Cuenca Cuenca 16071 Spain

Traditional multivariate control charts consider the observations to be independent. In many industrial applications, however, a certain autocorrelation level can normally be observed. This can be due to the nature of the process itself (inertia in the process), or to the way in which the sample is obtained. In the latter case, the problem involved in the autocorrelation existence was treated by the individual modelling of each series or the application of vector autoregression (VAR) models. In the former case, the analysis of the cross correlation structure between the variables is altered. In the latter one, if the cross correlation is not strong, the filtering process may modify the weakest relations. In order to improve these aspects, state-space models have been introduced into multivariate statistical process control. In the present paper, we consider a cutlery industry in order to develop a complete scheme for the efficient construction of control charts for innovations and the "inertial factor". This is the main difference from other proposals in the literature;that is, consideration of the inertial factor in the statistical process control.

关键词： multivariate statistical process control control charts Autocorrelation State-space models Inertial factor

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Identifying spatial variation patterns in multivariate manufacturing processes: A blind separation approach

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TECHNOMETRICS 2003年第3期45卷 220-234页

作者： Apley, DW Lee, HY Texas A&M Univ Dept Ind Engn College Stn TX 77843 USA

Large sets or multivariate measurement data are now routinely available through automated in-process measurement in many manufacturing industries. These data typically contain valuable information regarding the nature of each major source of process variability. In this article we assume that each variation source causes a distinct spatial variation pattern in the measurement data. The model that we use to represent the variation patterns is of identical structure to one widely used in the so-called "blind source separation" problem that arises in many sensor-array signal processing applications. We argue that methods developed for blind source separation can be used to identify spatial variation patterns in manufacturing data. We also discuss basic blind source separation concepts and their applicability to diagnosing manufacturing variation.

关键词： blind source separation factor rotation manufacturing variation reduction multivariate statistical process control principal components analysis

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The application of multivariate quality control in gas chromatography

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 1999年第1期47卷 107-125页

作者： Nijhuis, A de Jong, S Vandeginste, BGM Unilever Res Labs Vlaardingen NL-3130 AC Vlaardingen Netherlands Univ Ghent Dept Organ Chem B-9000 Ghent Belgium

Quality control is important in present laboratory activities. Nowadays, an analysis must satisfy high requirements, which can only be met under appropriate control. An example of a rather simple and often used tool for quality control is the Shewhart control chart. A disadvantage of the Shewhart chart is that it requires much effort with a risk for false alarms or mistakes, certainly when many control variables are involved. multivariate control charts are an alternative to univariate Shewhart charts. In this paper, the results are presented for both univariate Shewhart control charts and multivariate control charts applied to the capillary gas chromatographic analysis of the fatty acid composition in BCR162 (soya-maize oil). Quite often one may observe a shift in the data when a process is monitored for a long period. Although such a shift may result in statistical out-of-control situations, the analytical method may still be capable to perform within the specifications. In this paper, we introduce an extension of the T-2-chart for multivariate process control in order to handle statistically instable processes, with sufficient capability. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： quality control Shewhart control chart Hotelling's T-2 statistic multivariate statistical process control process capability (TC)(2)-chart

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Variable window adaptive Kernel Principal Component Analysis for nonlinear nonstationary process monitoring

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COMPUTERS & INDUSTRIAL ENGINEERING 2011年第3期61卷 437-446页

作者： Ben Khediri, Issam Limam, Mohamed Weihs, Claus Dortmund Univ Technol Dept Stat Dortmund Germany Univ Tunis Inst Super Gest Lab Operat Res Decis & Control Tunis Tunisia

On-line control of nonlinear nonstationary processes using multivariate statistical methods has recently prompt a lot of interest due to its industrial practical importance. Indeed basic process control methods do not allow monitoring of such processes. For this purpose this study proposes a variable window real-time monitoring system based on a fast block adaptive Kernel Principal Component Analysis scheme. While previous adaptive KPCA models allow only handling of one observation at a time, in this study we propose a way to fast update or downdate the KPCA model when a block of data is provided and not only one observation. Using a variable window size procedure to determine the model size and adaptive chart parameters, this model is applied to monitor two simulated benchmark processes. A comparison of performances of the adopted control strategy with various Principal Component Analysis (PCA) control models shows that the derived strategy is robust and yields better detection abilities of disturbances. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multivariate statistical process control Block adaptive Kernel Principal Component Analysis Variable window control chart

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