Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

A Multivariate Control Chart for Monitoring Several Exponential Quality Characteristics Using EWMA

In this paper, we propose a new multivariate control chart for monitoring several exponential distributed characteristics. We transform each exponential variable into the one following an approximately normal distribution. The control statistic of the proposed chart is constructed using the exponentially weighted moving average. The performance of the proposed control chart is studied using the average run length according to the process shift. Some tables are presented for bivariate and trivariate cases. The application of the proposed control chart is discussed with the help of simulated data.11Ysciescopu

Sensor Fusion and Process Monitoring for Ultrasonic Welding of Lithium-ion Batteries.

Ultrasonic metal welding is used for joining lithium-ion batteries of electric vehicles. The quality of the joints is essential to the performance of the entire battery pack. Hence, the ultrasonic welding process that creates the joints must be equipped with online sensing and real-time process monitoring systems. This would help ensure the process to be operated under the normal condition and quickly address quality-related issues. For this purpose, this dissertation develops methods in process monitoring and fault diagnosis using online sensing signals for ultrasonic metal welding. The first part of this dissertation develops a monitoring algorithm that targets near-zero misdetection by integrating univariate control charts and a multivariate control chart using the Mahalanobis distance. The proposed algorithm is capable of monitoring non-normal multivariate observations with adjustable control limits to achieve a near-zero misdetection rate while keeping a low false alarm rate. The proposed algorithm proves to be effective in achieving near-zero misdetection in process monitoring in ultrasonic welding processes. The second part of the dissertation develops a wavelet-based profile monitoring method that is capable of making decisions within a welding cycle and guiding real-time process adjustments. The proposed within-cycle monitoring technique integrates real-time monitoring and within-cycle control opportunity for defect prevention. The optimal decision point for achieving the most benefit in defect prevention is determined through the formulation of an optimization problem. The effectiveness of the proposed method is validated and demonstrated by simulations and case studies. The third part of this dissertation develops a method for effective monitoring and diagnosis of multi-sensor heterogeneous profile data based on multilinear discriminant analysis. The proposed method operates directly on the multi-stream profiles and then extracts uncorrelated discriminative features through tensor-to-vector projection, and thus preserving the interrelationship of different sensors. The extracted features are then fed into classifiers to detect faulty operations and recognize fault types. The research presented in this dissertation can be applied to general discrete cyclic manufacturing processes that have online sensing and control capabilities. The results of this dissertation are also applicable or expandable to mission-critical applications when improving product quality and preventing defects are of high interests.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113405/1/graceguo_1.pd

Comparison of change-points in multivariate statistical process control using the performance of Lapage-type (nonparametric)

The inability of the Shewhart‟s, the EWMA, and the CUSUM, Hotelling‟s T2 and many other control charts to indicate the time of shift poses great problems in production, Medicine, etc. To overcome the problems the need to identify the period of change (shift) in the process becomes inevitable. The study used Lapage-type Change-point (LCP) to detect the simultaneous shift in both mean and variance. In the study we compare the performance of generalized likelihood ratio change-point (GLRCP) a parametric-base with our proposed method (LCP) at different varying start-ups using real life data. We run the data on Normal, Laplace and Lognormal distributions and also Average Run Length (ARL0) to assess the performance of the methods. Evaluating in-control ARLs (IC-ARLs) for each of the methods at change-point 250 and ARL0 500 indicates the same performance irrespective of the start-up value; LCP and GLR methods have rather a similar performance IC-ARLs at change-point 50 and change-point 100 under the normality assumptions, but under non-normal distributions, LCP has substantially higher IC-ARLs compared to GLRCP at 20. The LCP outperformed the GLRCP when applied to children bronchial pneumonia status. We therefore recommend that new method be used in short-run situations and also when underlying distributions are usually unknown

An improved mixture of probabilistic PCA for nonlinear data-driven process monitoring

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal component analyzers is utilized to establish the model of the underlying nonlinear process with local PPCA models, where a novel composite monitoring statistic is proposed based on the integration of two monitoring statistics in modified PPCA-based fault detection approach. Besides, the weighted mean of the monitoring statistics aforementioned is utilized as a metrics to detect potential abnormalities. The virtues of the proposed algorithm are discussed in comparison with several unsupervised algorithms. Finally, Tennessee Eastman process and an autosuspension model are employed to demonstrate the effectiveness of the proposed scheme further

A nonparametric control chart based on the Mann-Whitney statistic

Nonparametric or distribution-free charts can be useful in statistical process control problems when there is limited or lack of knowledge about the underlying process distribution. In this paper, a phase II Shewhart-type chart is considered for location, based on reference data from phase I analysis and the well-known Mann-Whitney statistic. Control limits are computed using Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with Monte Carlo estimation. The derivations take account of estimation and the dependence from the use of a reference sample. An illustrative numerical example is presented. The in-control performance of the proposed chart is shown to be much superior to the classical Shewhart $\bar{X}$ chart. Further comparisons on the basis of some percentiles of the out-of-control conditional run length distribution and the unconditional out-of-control ARL show that the proposed chart is almost as good as the Shewhart $\bar{X}$ chart for the normal distribution, but is more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma. Interactive software, enabling a complete implementation of the chart, is made available on a website.Comment: Published in at http://dx.doi.org/10.1214/193940307000000112 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org