Disturbance detection and isolation by dynamic principal component analysis

Statistical Process Control of Multivariate Processes

Multiscale principal-component analysis (MSPCA) combines the ability of PCA to decorrelate the variables by extracting a linear relationship with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. MSPCA computes the PCA of wavelet coefficients at each scale and then combines the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for the modeling of data containing contributions from events whose behavior changes over time and frequency. Process monitoring by MSPCA involves combining only those scales where significant events are detected, and is equivalent to adaptively filtering the scores and residuals, and adjusting the detection limits for easiest detection of deterministic changes in the measurements. Approximate decorrelation of wavelet coefficients also makes MSPCA effective for monitoring autocorrelated measurements without matrix augmentation or time-series modeling. In addition to improving the ability to detect deterministic changes, monitoring by MSPCA also simultaneously extracts those features that represent abnormal operation. The superior performance of MSPCA for process monitoring is illustrated by several examples.

Multiscale PCA with application to multivariate statistical process monitoring

A review of the literature on control charts for multivariate quality control (MQC) is given, with a concentration on developments occurring since the mid-1980s. Multivariate cumulative sum (CUSUM) control procedures and a multivariate exponentially weighted moving average (EWMA) control chart are reviewed and recommendations are made regarding their use. Several recent articles that give methods for interpreting an out-of-control signal on a multivariate control chart are analyzed and discussed. Other topics such as the use of principal components and regression adjustment of variables in MQC, as well as frequently used approximations in MQC, are discussed.

A review of multivariate control charts

Data quality for data science, predictive analytics, and big data in supply chain management: An introduction to the problem and suggestions for research and applications

A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ2 and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ2 charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.

A multivariate exponentially weighted moving average control chart

The Shewhart R–and S–charts are often used to monitor the variability of a quality characteristic of interest. In order to improve the sensitivity of these charting procedures to detecting small shifts in the process standard deviation, runs rules have been suggested. We evaluate the properties of the run length distributions of these charting procedures using a Markov chain approach. We show that the rules commonly used in practice based on the Western Electric Handbook do not have the statistical performance one might expect. Alternative runs rules are provided that provide the same in-control ARL's as the usual X-chart with runs rules. Average run length comparisons are made among various charts for monitoring variability, including cumulative sum charts and exponentially weighted moving average charts. It is shown that detection of decreases in variability is problematic with all of these methods.

The Performance of Control Charts for Monitoring Process Variation

Ten nonparametric estimators of quantiles are compared in small samples by Monte Carlo simulation methods. The estimators are compared by using properties such as mean square error and mean absolute deviation. Nine distributions are used for the comparisons and include long-tailed distributions (e.g., Laplace), short-tailed distributions (e.g., uniform), and skewed distributions (e.g., exponential)

Cynthia A. Lowry

Papers

A multivariate exponentially weighted moving average control chart

A review of multivariate control charts

The Performance of Control Charts for Monitoring Process Variation

A comparison of quantile estimators

Adjusting the S-Chart for Detecting Both Increases and Decreases in the Standard Deviation