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 Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

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

The Quality Movement in Hospital Care

The purpose is to introduce the demand for the quality movement practice in hospital care. We show both the need and application of quality monitoring, especially the need monitoring activities having auto correlated data flows of which there are many in the hospital environment. The goal is to control the flow of quality care data in the dynamic behavior of these systems of acre in hospitals. These monitoring systems are designed to control and improve changes in the hospital care environment

Combining Multivariate Density Forecasts Using Predictive Criteria

This paper combines multivariate density forecasts of output growth, inflation and interest rates from a suite of models. An out-of-sample weighting scheme based on the predictive likelihood as proposed by Eklund and Karlsson (2007) and Andersson and Karlsson (2007) is used to combine the models. Three classes of models are considered: a Bayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR) and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australian data over the inflation-targeting period, we find that, at short forecast horizons, the Bayesian VAR model is assigned the most weight, while at intermediate and longer horizons the factor model is preferred. The DSGE model is assigned little weight at all horizons, a result that can be attributed to the DSGE model producing density forecasts that are very wide when compared with the actual distribution of observations. While a density forecast evaluation exercise reveals little formal evidence that the optimally combined densities are superior to those from the best-performing individual model, or a simple equal-weighting scheme, this may be a result of the short sample available.density forecasts; combining forecasts; predictive criteria

Combining multivariate density forecasts using predictive criteria

This paper combines multivariate density forecasts of output growth, inflation and interest rates from a suite of models. An out-of-sample weighting scheme based on the predictive likelihood as proposed by Eklund and Karlsson (2005) and Andersson and Karlsson (2007) is used to combine the models. Three classes of models are considered: a Bayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR) and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australian data, we find that, at short forecast horizons, the Bayesian VAR model is assigned the most weight, while at intermediate and longer horizons the factor model is preferred. The DSGE model is assigned little weight at all horizons, a result that can be attributed to the DSGE model producing density forecasts that are very wide when compared with the actual distribution of observations. While a density forecast evaluation exercise reveals little formal evidence that the optimally combined densities are superior to those from the best-performing individual model, or a simple equal-weighting scheme, this may be a result of the short sample available.Density forecasts, combining forecasts, predictive criteria

A Neural Network Approach to Synthetic Control Chart for the Process Mean

In this project, a multivariate synthetic control chart for monitoring the process mean vector of skewed populations using weighted standard deviations has been proposed. The proposed chart incorporates the weighted standard deviation (WSD) method of Chang and Bai (2004) into the standard multivariate synthetic chart of Ghute and Shirke (2008)

On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts

The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth based control charts. Data depth provides data reduction to large-variable problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviates normality assumption. For detecting slow or moderate shifts in the process target mean, the multivariate version of the EWMA is generally robust to non-normal data, so that nonparametric alternatives may be less often required

A Study Of Exponentially Weighted Moving Average (Ewma) Methodologies

Tesis ini adalah berkenaan dengan penggunaan carta PBBE, suatu alternatif kepada carta Shewhart dan Carta Hasil Tambah Longgokan (HTL), untuk mengesan perubahan yang berlaku di dalam suatu proses. Kami menulis tesis ini berdasarkan dua objektif: i) untuk meninjau metodologi carta kawalan PBBE, dan ii) untuk mencadangkan beberapa kaedah tambahan yang boleh meningkatkan lagi keupayaan carta PBBE·: This thesis concerns the use of the EHHA chart, an alternative to the Shewhart and Cumulative Sum (CUSUM) charts, for detecting a change in a process. We have written this thesis with two objectives in mind: i) to review the control charting methodologies of the EWMA control chart, and ii) to suggest some additional enhancements that can further enhance the EWMA chart