A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis

Process monitoring and fault diagnosis using profile data remains an important and challenging problem in statistical process control (SPC). Although the analysis of profile data has been extensively studied in the SPC literature, the challenges associated with monitoring and diagnosis of multichannel (multiple) nonlinear profiles are yet to be addressed. Motivated by an application in multioperation forging processes, we propose a new modeling, monitoring, and diagnosis framework for phase-I analysis of multichannel profiles. The proposed framework is developed under the assumption that different profile channels have similar structure so that we can gain strength by borrowing information from all channels. The multidimensional functional principal component analysis is incorporated into change-point models to construct monitoring statistics. Simulation results show that the proposed approach has good performance in identifying change-points in various situations compared with some existing methods. The codes for implementing the proposed procedure are available in the supplementary material.     

Phase I Distribution-Free Analysis of Multivariate Data

In this study, a new distribution-free Phase I control chart for retrospectively monitoring multivariate data is developed. The suggested approach, based on the multivariate signed ranks, can be applied to individual or subgrouped data for detection of location shifts with an arbitrary pattern (e.g., isolated, transitory, sustained, progressive, etc.). The procedure is complemented with a LASSO-based post-signal diagnostic method for identification of the shifted variables. A simulation study shows that the method compares favorably with parametric control charts when the process is normally distributed, and largely outperforms other multivariate nonparametric control charts when the process distribution is skewed or heavy-tailed. An R package can be found in the supplementary material.     

Pairwise Estimation of Multivariate Gaussian Process Models With Replicated Observations: Application to Multivariate Profile Monitoring

Profile monitoring is often conducted when the product quality is characterized by profiles. Although existing methods almost exclusively deal with univariate profiles, observations of multivariate profile data are increasingly encountered in practice. These data are seldom analyzed in the area of statistical process control due to lack of effective modeling tools. In this article, we propose to analyze them using the multivariate Gaussian process model, which offers a natural way to accommodate both within-profile and between-profile correlations. To mitigate the prohibitively high computation in building such models, a pairwise estimation strategy is adopted. Asymptotic normality of the parameter estimates from this approach has been established. Comprehensive simulation studies are conducted. In the case study, the method has been demonstrated using transmittance profiles from low-emittance glass. Supplementary materials for this article are available online.     

Phase II Monitoring of Nonlinear Profile Variance Using Wavelet

In some statistical process control applications, the quality of a process or a product can be characterized by a nonlinear relationship between a response variable and one or more explanatory variables. Monitoring nonlinear profiles using nonlinear regression has been proposed by several researchers as a potential area for research. To avoid disadvantages of parameter estimation in nonlinear regression, we used nonparametric regression with wavelets for monitoring nonlinear profiles. In nonparametric regression framework, traditional variance estimator is not proper; other estimators should be used instead. Parametric or nonparametric control charts in phase II are proposed to monitor error term variance when nonparametric regression with wavelet is used. Multivariate control chart based on regression coefficients (approximate wavelet coefficients) is added to variance control chart to check stability in the process mean. It is well known that the performance of control schemes in detecting shifts in multivariate control charts deteriorates as the dimension of regression coefficient increases. To improve the performance of control schemes, we considered decomposition level as a smoothing parameter, which determines the form of regression function (size of approximate wavelet coefficients vector) in nonparametric regression with wavelet. A method based on an analysis of variance is proposed to determine the optimal decomposition level. The statistical performances of the proposed methods are evaluated using average run length criterion using vertical density profile data. Numerical results indicate that the proposed methods perform satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.     

Phase I Monitoring of Spatial Surface Data from 3D Printing

In recent years, 3D printing gets more and more popular in manufacturing industries. Quality control of 3D printing products thus becomes an important research problem. However, this problem is challenging due to the facts that (i) the surface of a product from 3D printing can have arbitrary shape, even when the 3D printing process is in-control, (ii) surface observations of the product obtained from a laser scanner may not have regularly spaced locations, and (iii) the overall geometric positions of 3D printing products might be all different, making proper comparison among different products difficult. In this article, we propose a Phase I control chart for monitoring products from 3D printing that addresses all these challenges. Numerical studies show that it works well in practice.     

主成分分析法在纸或纸板质量综合评价中的应用

为了探索多元统计分析应用于纸或纸板质量综合评价的可行性和合理性,运用主成分分析法构造了纸或纸板的综合质量评价的模型,建立了一个度量纸或纸板质量好坏的综合指标值R,R值的大小较好地反映了纸或纸板的综合质量好坏.并将该方法应用于实例检验,结果表明主成分分析法评价纸和纸板的综合性质量适应性强,方法可行,结果合理.     

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.     

主成分分析-二阶导数在中红外光谱定量分析中的应用

介绍了运用最小二乘法建立傅立叶变换中红外光谱定量分析模型的原理和方法。以苯甲酸和邻苯二甲酸氢钾为实验材料获取红外吸收光谱,采用MATLAB工程语言编程,分别以吸收光谱和二阶导数光谱为校正集样本,采用主成分分析方法对样本进行优选压缩,以建立了中红外光谱定量分析模型。用此模型预测混合物的含量,预测值与实际值的相对误差小于5.0%。     

Principal alarms in multivariate statistical process control using independent component analysis

This article proposes a methodology that helps to predict the main mean shifts, denoted as principal alarms, in a non-normal multivariate process using the available in-control data. The analysis is based on the transformation of the observed correlated variables into independent factors using independent component analysis. These independent components allow us to simulate shifts preserving the covariance structure. The graphical representations of those simulated shifts are helpful in improving the design and control of the process. Two real manufacturing processes are presented showing the advantage of the proposed methodology.     

A Multivariate Process Capability Index Based on the First Principal Component Only

Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well‐known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non‐conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two‐dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further. Copyright © 2012 John Wiley & Sons, Ltd.     

Monitoring Correlated Profile and Multivariate Quality Characteristics

Monitoring multivariate quality characteristics is very common in production and service environment. Therefore, many control charts have been suggested by authors for monitoring multivariate processes. In another side, profile monitoring is a new approach in the area of statistical process control. In this approach, the quality of a product or a process is characterized by a relation between one response variable and one or more independent variables. In practice, sometimes the quality of a product or a process is represented by a correlated profile and multivariate quality characteristics. To the best of our knowledge, there is no method for monitoring this type of quality characteristics. Note that monitoring correlated profile and multivariate quality characteristics separately leads to misleading results. In this article, we specifically focus on correlated simple linear profile and multivariate normal quality characteristics and propose a method using multivariate exponentially weighted moving average control chart to monitor the correlated profile and multivariate quality characteristics simultaneously. The performance of the proposed control chart is evaluated by simulation studies in terms of average run length criterion. Finally, the proposed method is applied to a real case in the electronics industry. Copyright © 2013 John Wiley & Sons, Ltd.     

An Efficient Online Monitoring Method for High-Dimensional Data Streams

Monitoring high-dimensional data streams has become increasingly important for real-time detection of abnormal activities in many data-rich applications. We are interested in detecting an occurring event as soon as possible, but we do not know which subset of data streams is affected by the event. By connecting to the problem of detecting heterogenous mixtures, a new control chart is developed based on a powerful goodness-of-fit test of the local cumulative sum statistics from each data stream. Numerical results show that the proposed method is able to balance the detection of various fractions of affected streams, and generally outperforms existing methods. Supplementary materials for this article are available online.     

The Phase I Dispersion Charts for Bivariate Process Monitoring

Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase‐I study is generally used when population parameters are unknown. This article develops Phase‐I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP₀). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out‐of‐control situations. The analysis shows that the proposed Phase‐I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of Multiple Cause-Selecting Charts for Multistage Processes with Model Uncertainty

The cause-selecting chart (CSC) is an effective statistical process control tool for monitoring multistage processes. The multiple cause-selecting chart (MCSC) is the further development of the CSC, which deals with the case when the output measure is a function of multiple input measures. In practice, the model relating the input and output measures often needs to be estimated before the MCSC is implemented. However, the traditional design of MCSCs does not take parameter uncertainties into account when estimating the control limits. The actual false-alarm rate can substantially differ from what is expected. This article presents the design and implementation of MCSCs using prediction limits to account for parameter uncertainties. These limits are developed using two types of procedures: the least-squares estimation and principal component regression. The simulation results show that the prediction limits are quite effective in terms of maintaining a desired false-alarm rate.     

主成分分析法在气调包装果蔬质量评价中的应用

用主成分分析法构造了气调包装后果蔬质量的综合评价模型,并将该方法用于实例作效果检验.结果表明用主成分分析法评价气调包装后果蔬质量的方法可行,结果客观合理.     

A Semiparametric Mixed Model Approach to Phase I Profile Monitoring

Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric (P) modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. More recently, in the absence of an obvious P model, nonparametric (NP) methods have been employed in the profile monitoring context. For situations where a P model is adequate over part of the data but inadequate of other parts, we propose a semiparametric procedure that combines both P and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). These three methods (P, NP and MMRPM) can account for the autocorrelation within profiles and treat the collection of profiles as a random sample from a common population. For each approach, we propose a version of Hotelling's T² statistic for use in Phase I analysis to determine unusual profiles based on the estimated random effects and obtain the corresponding control limits. Simulation results show that our MMRPM method performs well in making decisions regarding outlying profiles when compared to methods based on a misspecified P model or based on NP regression. In addition, however, the MMRPM method is robust to model misspecification because it also performs well when compared to a correctly specified P model. The proposed chart is able to detect changes in Phase I data and has easily calculated control limits. We apply all three methods to the automobile engine data of Amiri et al.⁵ and find that the NP and the MMRPM methods indicate signals that did not occur in a P approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Statistical Validation of Reproducibility of HPLC Peptide Mapping for the Identity of an Investigational Drug Compound Based on Principal Component Analysis

Peptide mapping is a key analytical method for studying the primary structure of proteins. The sensitivity of the peptide map to even the smallest change in the covalent structure of the protein makes it a valuable “fingerprint” for identity testing and process monitoring. We recently conducted a full method validation study of an optimized reverse-phase high-performance liquid chromatography (RP-HPLC) tryptic map of a therapeutic anti-CD4 monoclonal antibody. We have used this method routinely for over a year to test production lots for clinical trials and to support bioprocess development. One of the difficulties in the validation of the peptide mapping method is the lack of proper quantitative measures of its reproducibility. A reproducibility study may include method and system precision study, ruggedness study, and robustness study. In this paper, we discuss the use of principal component analysis (PCA) to quantitate peptide maps properly using its projected scores on the reduced dimensions. This approach allowed us not only to summarize the reproducibility study properly, but also to use the method as a diagnostic tool to investigate any troubles in the reproducibility validation process.     

主成分分析在企业安全评价中的应用

主成分分析能将原有的指标重新组合成相互无关的综合指标,并由较少的综合指标反映85%以上原有指标信息。文章运用该法对某化工厂进行安全评价,以聚氯乙烯合成的生产过程中各个工段为样本,收集相关指标建立评价体系,求出综合表达式并对计算结果进行排序,从而反映出企业的安全生产状况,有助于采取有效防范措施。     

Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

In this paper, we propose four control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts include sum of squares exponential weighted moving average (SS‐EWMA) and sum of squares cumulative sum (SS‐CUSUM) for monitoring regression parameters and corresponding covariance matrix and SS‐EWMARe and SS‐CUSUMRe control charts for monitoring mean vector and covariance matrix of residual. Proposed methods are able to identify the out‐of‐control parameter responsible for shift. The performance of the proposed control charts is compared with existing method through Monte‐Carlo simulations. Moreover, the diagnostic performance of the proposed control charts is evaluated through simulation studies. The results show better performance of the proposed control charts rather than competing control chart. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry. Copyright © 2016 John Wiley & Sons, Ltd.