Comparing Confidence Intervals for Multivariate Process Capability Indices

Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index C_p. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way. Copyright © 2011 John Wiley & Sons, Ltd.     

Improving automotive dimensional quality by using principal component analysis

Dimensional quality is a measure of conformance of the actual geometry of products with the designed geometry. In the automotive body assembly process, maintaining good dimensional quality is very difficult and critical to the product. In this paper, a dimensional quality analysis and diagnostic tool is developed based on principal component analysis (PCA). In quality analysis, the quality loss due to dimensional variation can be partitioned into a mean deviation and piece-to-piece variation. By using PCA, the piece-to-piece variation can be further decomposed into a set of independent geometrical variation modes. The features of these major variation modes help in identifying the underlying causes of dimensional variation in order to reduce the variation. The variation mode chart developed in this paper provides the explicit and exact geometrical interpretation of variation modes, making PCA easily understood. A case study using an automotive body assembly dimensional quality analysis will illustrate the value and power of this methodology in solving actual engineering problems in a practical manner.     

主成分分析的入侵检测方法研究

直接将入侵检测算法应用在粗糙数据上,其入侵检测分析的效率非常低.为解决该问题,提出了一种基于主成分分析的入侵检测方法.该方法通过提取网络连接中的相关信息,对它进行解码,并将解码的网络连接记录与已知的网络连接记录数据进行比较,发现记录中的变化和连接记录分布的主成分,最后将机器学习方法和主成分分析方法结合实现入侵检测.实验结果表明该方法应用到各种不同KDD99入侵检测数据集中可以有效减少学习时间、降低各种数据集的表示空间,提高入侵检测效率.     

Multivariate process trajectories: capture, resolution and analysis

Modern process analytical chemistry and technology applications are reviewed from the point of view of acquisition, resolution and analysis of trajectories in a designed analytical space.     

基于模糊理论决策的双向二维PCA步态识别算法

针对步态识别中的平均步态能量图像系数矩阵维数过高和分类较困难的特点,提出一种基于模糊理论决策分类的双向二维主成分分析的步态识别算法.通过预处理技术得到平均步态能量图并将得到的图像分割为多个子图像,利用双向二维主成分分析来降低平均步态能量子图像的系数矩阵维数,加快识别速度.引入模糊理论决策的方法进行最近邻分类器的分类.最后在CASIA步态数据库上对所提出的算法进行实验,实验结果表明该算法具有较好的识别性能并有较强的鲁棒性.     

On properties of probability-based multivariate process capability indices

Multivariate process capability indices (MPCIs) have been proposed to measure multivariate process capability in real-world application over the past three decades. For the practitioner's point of view, the intention of this paper is to examine the performances and distributional properties of probability-based MPCIs. Considering issues of construction of capability indices in multivariate setup and computation with performance, we found that probability-based MPCIs are a proper generalization of univariate basic process capability indices (PCIs). In the beginning of this decade, computation of probability-based indices was a difficult and time-consuming task, but in the computer age statistics, computation of probability-based MPCIs is simple and quick. Recent work on the performance of MPCI NMC_pm and distributional properties of its estimator reasonably recommended this index, for use in practical situations. To study distributional properties of natural estimators of probability-based MPCIs and recommended index estimator, we conducted simulation study. Though natural estimators of probability-based indices are negatively biased, they are better with respect to mean, relative bias, mean square error. Probability-based MPCI MC_pm is better as compared with NMC_pm with respect to performance and as its estimator quality. Hence, in real-world practice, we recommend probability-based MPCIs as a multivariate analogue of basic PCIs.     

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.     

基于电容测量和PCA法的两相流相浓度检测方法

介绍利用电容层析成像系统阵列传感器结构和采样特点,引入主成分分析法(PCA)求取两相流相浓度的新方法.对大量测量值样本进行统计分析后,求出用测量值第一主成分求取相浓度的经验公式,仿真及静态实验表明:两者之间有着良好的对应关系,其测量结果不受两相流流型的影响,是一种有较好应用前景的测量方法.     

Multivariate process incapability vector

Process capability indices evaluate the capability of the processes in satisfying customer's requirements. This paper introduces a superstructure multivariate process incapability vector for multivariate normal processes and then, compares it with four recently proposed multivariate process capability indices to show its better performance. In addition, the effects of two modification factors are investigated. Also, bootstrap confidence intervals for the first component of the proposed vector are obtained. Furthermore, real manufacturing data sets are presented to demonstrate the applicability of the proposed vector.     

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.     

Statistical process monitoring with principal components

Most industrial processes are characterized by a system of several variables, all of which are subject to drifts, disturbances, and assignable causes of variation. In the chemical and process industries, there are often inertial forces arising from raw material streams, reactors and tanks that introduce serial correlation over time into these variables. This autocorrelation can have a profound impact on the effectiveness of the statistical monitoring methods used for such processes. This paper reviews some of the available methodology for multivariate process monitoring and shows the effectiveness of principal components in this context. An application of the principal components approach with correlated observation vectors is presented. The effectiveness of this procedure to indicate process upsets is discussed.     

Displacement field denoising for high-temperature digital image correlation using principal component analysis

Principal component analysis (PCA) was extended to minimize the noise effect in digital image correlation (DIC) measurement under a high-temperature atmosphere environment. First, the principle of PCA was introduced, and the singular vectors and singular values for each component of the displacement fields from DIC were obtained. Then, the simulated high-temperature speckle images were developed to investigate the influences of noise on the DIC method under a high-temperature environment. Finally, the displacement fields of several special conditions were extracted from the simulated speckle images and experimental images; the effects of noise on the PCA were also analyzed.     

On-line batch process monitoring using batch dynamic kernel principal component analysis

In this paper, a new dynamic and nonlinear batch process monitoring method, referred to as BDKPCA, is developed for on-line batch process monitoring, tactfully integrating kernel PCA and ARMAX time series model through estimating the Average Kernel Matrix (AKM) of all batch runs. AKM is an average of I, the batch number, Single-Batch Kernel Matrixes (SBKM). Each of the I SBKM is also an average of I kernel matrixes for each batch. The AKM contains the information of the stochastic variations and deviations among batches. This information will be very useful for the BDKPCA model to characterize the batch process in detail. The structure of BDKPCA model is very simple, and BDKPCA calculates the Hotelling's T² statistic and the Q-statistic for every time point, enhancing the method's sensitivity to the faults. Two cases are used to investigate the potential application of the proposed method, and its application to on-line batch process monitoring shows better performance than MKPCA.     

Identifying product shape relationships using principal component analysis

Product forms with multiple features, like automobiles, have traditionally accepted feature definitions and relationships between those features. These relationships drive how the product is created by focusing on expected, and accepted, feature development to push the form outside the traditional bounds. This paper uses principal component analysis to determine the fundamental characteristics within vehicle classes. The results of this analysis can then be considered by product designers to create new designs based upon the derived shape relationships. These new designs will be novel due to the non-traditional grouping of characteristics.     

基于互信息的主成分分析用于声场景分类

主成分分析是声场景分类中常用的特征选择方法。针对主成分分析的局限性,提出一种基于互信息的主成分分析方法。这一方法引入类别信息,用不同声场景条件下特征之间的互信息矩阵之和替代传统主成分分析中的协方差矩阵,计算其特征向量与特征值,特征向量表示由原始特征空间向新的主成分空间的转换系数,特征值则用于计算主成分的累计贡献率并判断主成分维数。声场景分类实验结果表明,该方法较之传统主成分分析方法降维效果更好,辅以神经网络分类器,计算得到的分类正确率更高。     

频域主分量模态分析法及在颤振试飞中的应用

为提高对颤振边界预测至关重要的模态阻尼的识别精度,基于频域多参考点法,采用主分量分析、奇异值分解和最小二乘技术,考虑频率响应函数负共轭部分和带外模态的影响,提出频域主分量分析模态参数识别方法,具有处理速度快、所需用户交互少的特点。通过飞机模型仿真算例验证在模态高度耦合情况下该方法的有效性,并在实际飞行颤振试验中进行应用。     

Fault diagnosis in chemical processes using Fisher discriminant analysis, discriminant partial least squares, and principal component analysis

Principal component analysis (PCA) is the most commonly used dimensionality reduction technique for detecting and diagnosing faults in chemical processes. Although PCA contains certain optimality properties in terms of fault detection, and has been widely applied for fault diagnosis, it is not best suited for fault diagnosis. Discriminant partial least squares (DPLS) has been shown to improve fault diagnosis for small-scale classification problems as compared with PCA. Fisher's discriminant analysis (FDA) has advantages from a theoretical point of view. In this paper, we develop an information criterion that automatically determines the order of the dimensionality reduction for FDA and DPLS, and show that FDA and DPLS are more proficient than PCA for diagnosing faults, both theoretically and by applying these techniques to simulated data collected from the Tennessee Eastman chemical plant simulator.     

基于主成分分析的护听器优选方法研究

为了探究不同护听器对抽水蓄能电站内不同工作场所的降噪效果及适用情况,以便于工作人员根据不同需要选择合适的护听器,根据112种护听器的插入损失测试结果,应用主成分分析(Principal Component Analysis, PCA)对数据进行分析。结合某抽水蓄能电站10个工作场所的现场测试结果,得出文中所测试的112种护听器大部分适用于该蓄水电站中1#发电机隔声罩内、1#水车室外、1#水车室内、2#尾水锥管室外、2#尾水锥管检修门、3#尾水锥管室外和3#尾水锥管检修门7个工作场所,其他场所需要有针对性地选择适合的护听器。该文同时可以为其他不同工作场所情况下护听器的选择提供借鉴。     

基于核主分量分析的经验模式分解及其工程应用

若信号的信噪比较小,经验模式分解不能正确分解出基本模式分量,分量中含有伪分量。根据此种情况,提出一种核主分量分析与经验模式分解相结合的方法。该方法首先建立信号相空间,利用核主分量分析方法提取相空间的核主分量,然后利用投影逆过程将得到的核主分量逆向投影回原相空间,从而重建信号相空间。最后对重建的相空间所对应的信号作经验模式分解。此方法可以有效消除噪声和冗余对经验模式分解的影响,提高经验模式分解的适应能力保证分解的有效性,确保其能够分解出正确的基本模式分量。通过工程实例进一步验证了该方法的可行性。     

Kernel principal component analysis and support vector machines for stock price prediction

Technical indicators are used with two heuristic models, kernel principal component analysis and factor analysis in order to identify the most influential inputs for a forecasting model. Multilayer perceptron (MLP) networks and support vector regression (SVR) are used with different inputs. We assume that the future value of a stock price/return depends on the financial indicators although there is no parametric model to explain this relationship, which comes from the technical analysis. Comparison studies show that SVR and MLP networks require different inputs. Furthermore, proposed heuristic models produce better results than the studied data mining methods. In addition to this, we can say that there is no difference between MLP networks and SVR techniques when we compare their mean square error values.